Frei Otto

_ Frei Otto’s Extensive research and modelling

_ Multihalle, Mannheim

_ Olympiastadion Olympic Stadium, Munich _ Stuttgart Highspeed Railway Station – Stuttgart, Germany

Networks, cities and trees - Occupying and connecting Unit DS10 - Kayleigh Dickson

Frei Otto studied architecture in Berlin before he was drafted a fighter pilot in the final years of World War II. It was noted that he was interned in a French POW camp and, with his aviation engineering training, the urgency for housing and the lack of material it was here he began to experiment with tents to shelter the prisoners. After the end of the war he returned to studying briefly in the United States after which he visited people such as Erich Mendelsohn, Mies van der Rohe, Richard Neutra, and Frank Lloyd Wright. In 1952 Otto began a private practice in Germany, of which he received his first significant attention at his Bundesgartenschau saddle-shaped cable-net music pavilion in Kassel. Shortly followed after when in 1954 he earned a doctorate for tensioned constructions Otto challenged the advances in structural m athematics and civil engineering and is a phenomenal mind in the world of lightweight tensile and membrane structures, founding the famous Institute for Lightweight Structures at the University of Stuttgart in 1964, remaining as head till his retirement as university professor. Barry Patten is regarded to have influenced Frei Otto’s architectural and structural designs, his most famous design is the Myer Music Bowl, Melbourne in 1959. Otto’s project list includes: _The West German Pavilion,1967 Montreal Expo _ Tuwaiq Palace, Saudi Arabia, 1970 _ The roof for the 1972 Munich Olympic Arena, inspired by Vladimir Shukhov’s architecture. _ The Japanese Pavilion at Expo 2000, with a roof structure made entirely of paper in collaboration with Shigeru Ban. Awards: _ Thomas Jefferson Medal in Architecture, 1974 _ Wolf Prize in Architecture, 1996-1997 _ RIBA Royal Gold Medal, 2005 Networks, cities and trees - Occupying and connecting Natures natural systems construct organic and efficient forms, which we have chosen to overlook in place of ‘unnatural’ buildings for a number of decades. We now demand from architecture lighter, energy efficient and adaptable buildings that could grow or shrink with societies needs with out compromising safety, security or quality of life. Frei Otto argued that the human spontaneous networks of urbanity follow similar patterns to the structures within nature such as leaves, insect colonies or soap bubbles. Focusing on energy analysis the networks are not formally planned and therefore depict the evolutionary process to create an efficient minimal energy path. Frei Otto evolved his research through extensive models to define, research and test complex tensile forms. As the scale of his projects increased he researched how man-made landscape might be redefined, not only aesthetically but in its sustainability. Developing an alternative system of gridshell structures built on the principles of elegance and structural lightness.

Images: _ First Row _ Natures natural efficient structure _ Second Row _ _ Third Row _ The Geometry Of Bending, a 2D study

Buckminster Fuller

_ The Geodesic Dome and The Montreal Biosphère, 1967

_ Tensegrity Sphere

The lattice shell structures - geodesic domes, which have been used as parts of military radar stations, civic buildings, environmental protest camps and exhibition attractions, follows the same methodology as Bauersfeld’s design. The dome construction is based on the basic principles of building simple tensegrity structures which is lightweight and stable. The design of the geodesic dome was a result of Fuller’s exploration of nature’s constructing principles. In Fiction the Fuller Dome is referenced by John Brunner in his novel Stand on Zanzibar, in which a geodesic dome was said to cover the entire island of Manhattan, floatation on air due to the hot-air balloon effect of the large air-mass under the dome.

Buckminster Fuller pioneered terms such as “ephemeralization” meaning “more and more with less and less until eventually you can do everything with nothing” and synergetics which referenced the study of systems in transformation with emphasis on total system behavior. His studies lead to the exploration of energy and materiality principles in Architecture. As well as the theorization that “natural analytic geometry of the universe was based on arrays of tetrahedral”, explored through the close-packing of spheres and the number of compressive or tensile members required to stabilize an object in space.

Ephemeralization & Synergetics

Unit DS10 - Kayleigh Dickson

Buckminster Fuller, an American engineer, theorist, author, designer, inventor, futurist, as well as the second president of Mensa International. He published near to 30 books and developed numerous inventions; of which is the geodesic dome is his most noted. Carbon molecules known as fullerenes or ‘buckyballs’ were named due to their close resemblance to Buckminster Fuller’s geodesic spheres. Buckminster initially struggled with geometry, and the inability to understand the abstraction that ‘a chalk dot on the blackboard represented a mathematical point, or that an imperfectly drawn line with an arrow on the end was meant to stretch off to infinity’. He would design items from materials he brought home from the woods, and even making his own tools, experimenting with designing a new apparatus for human propulsion of small boats. Fuller’s education started at Milton Academy in Massachusetts, and lead to Harvard University, even though he expelled from Harvard twice as he saw himself as a non-conforming misfit in the fraternity environment. Later on he received a Sc.D. from Bates College in Lewiston, Maine. In an unconventional manner for an architect he worked in Canada as a mechanic in a textile mill, then as a laborer in the meat-packing industry, a shipboard radio operator during WW1, as an editor of a publication, and as a crash-boat commander. By 32, Buckmister Fuller was bankrupt, jobless, and living in low-income housing in Chicago, Illinois. In 1922 with the death of his daughter he apparently was said to have responsible for her death what caused him to drink frequently and to contemplate suicide. Somehow he chose to turn this experience to embark on “an experiment, to find what a single individual [could] contribute to changing the world and benefiting all humanity.” His recovery was greatly linked to his commitment to “the search for the principles governing the universe and help advance the evolution of humanity in accordance with them... finding ways of doing more with less to the end that all people everywhere can have more and more.” In 1928, Fuller accepted a job decorating the interior of the café in exchange for meals, lecturing several times a week, and later models of the Dymaxion house were exhibited at the café. In a collaboration with Isamu Noguchi, Fuller soon designed the Dymaxion car. One if not the most notable project of Buckminster Fullers was founded at the Black Mountain College in North Carolina, 1948 and 1949, where with the support of a group of professors and students, he began reinventing a project the geodesic dome. The concept of the geodesic dome had been created around 30 years earlier by Dr. Walther Bauersfeld, though due to Fuller’s popularizing this type of structure he was awarded United States patents. In 1949, he built his first geodesic dome building that could sustain its own weight and measured at 4.3 meters in diameter and constructed of aluminum aircraft tubing and a vinyl-plastic skin, in the form of an icosahedron. To prove his design, and to awe non-believers, seeming slightly eccentric Fuller suspended from the structure’s framework several students who had helped him build it. Within a few years there were thousands of these domes around the world. Fuller had a passion for bettering life through his designs and developed many ideas, designs and inventions, particularly regarding practical, inexpensive shelter and transportation. He documented his life, philosophy and ideas scrupulously by a daily diary which was to be called Dymaxion Chronofile, and consisted of twenty-eight publications documenting his life from 1915 to 1983, equating to approximately 270 feet (82 m) of papers. Fuller then designed one of the most efficient representation of landmass through an alternative projection map, called the Dymaxion map. This was designed to show Earth’s continents with minimum distortion when projected or printed on a flat surface. Philosophy and worldview Fuller strongly believed in thinking globally, and he explored principles of energy and material efficiency in the fields of architecture, engineering and design. And was deeply concerned with sustainability and about human survival under the existing socio-economic system, yet remained optimistic about humanity’s future. “Selfishness,” to Buckminster Fuller was deemed as, “unnecessary and hence-forth unrationalizable.... War is obsolete.” To him for Utopia to work, he thought that a utopia needed to include everyone. Buckmister Fuller was incredibly quirky and was noted to be a frequent flier, who when crossing time zones he wore three watches; one for the current zone, one for the zone he had departed, and one for the zone he was going to. Infact The “Omega Incabloc Oyster Accutron 72” Buckminster Fuller designed the case. Whilst flying he also inserted a sheet of newsprint over a shirt and under a suit jacket, to provide completely effective heat insulation during long flights. He experimented with polyphasic sleep, which he called Dymaxion sleep. In 1943, he told Time Magazine that he had slept only two hours a day for two years. He quit the schedule because it conflicted with his business associates’ sleep habits, but stated that Dymaxion sleep could help the United States win World War II.

_ Tensegrity Dome

Experimentation_01 Differential Growth, Edge Effects and Other Interactions

Material

Rule Theory

Unit DS10 - Kayleigh Dickson

_Cracked Mud Cracked Surface Rule

Through the study of two-dimensional networks in the hexagonal cell, in the study of biological systems it is important to study growth sequences, sequential solidification of forms and “edge effects” as this will greatly effect the outcome of the final form.

3-connected vertices will appear with some areas appearing to form at 90 degrees – with later cracks then appearing perpendicular to the original crack. Though the configuration may be formed with three lines meeting at a central point at 120 degrees, an isotropic force or growth. The isotropic force or isotropy will produce a simple net and a form of a three-rayedhexagonal pattern.

Cracking or shrinkage occurs in accordance with strict rules. This will normally occur with an original fault line in the material. The tensile stress will act evenly in all directions is greater on the top., which will accelerate the linear growth of the ‘cracks’. Side Cracks will take form at right angles, starting from a weak point in the wall of a material. If this crack in the side of the wall was to connect with an existing crack, then they are orientated by the tensile stress in parallel to the wall surface at 90 degrees. If the material was to contract in uniform then a hexagonal shape will appear, and three lines will meet at 120 degrees 1 _ with cracked surfaces such as ceramic glaze, mud, etc., the ‘cracking’ effect will not form immediately yet it will appear over time 2 _ the surface of a heated aluminum sheet will show the formation at early stages of melting, is unlike the two-dimensional formation showing with soap bubbles.

_ Heated Aluminum Sheet Heated Aluminum Sheet Rules

4 _ the grain boundaries in Niobium forms through the appearance of etching and shows a lack of uniformity.

The formation not only follows the rule of three lines meeting at one singular point but you will commonly find that the point will be surrounded by angle of 120 degrees.

_ Soap Bubbles Soap Bubbles Rules The four vertices are meet at approximately 109 degrees. They must be in juxtaposition as to fill all the space and their interfaces must conform to the laws of surface tension.

_Grain Boudaries in Niobium Grain Boundaries in Niobium Rules Here you would see few exceptions to the three-rayed vertex rule in which the point is surrounded by an angle of 120 degrees. Each grain is a polyhedral crystal which will mesh close to another crystal in a closest packed array. The intrinsic forces will confront the extrinsic forces exerted from another neighbouring crystal

Material Net Formation

Detail

Visual Rule

Experimentation_02 Foam Fun! The Natural Formation of Bubbles and The Effects of Freezing Conditions Unit DS10 - Kayleigh Dickson

Sculpted Foam Fun! The soap bubble holds its form as a surface layer of a liquid has a certain surface tension, which causes the layer to act like an elastic sheet. The film of the soap bubble is extremely flexible and can produce waves based on the force exerted. However as I found out if a bubble made solely of pure liquid alone is not stable and soap is needed to stabilize a bubble. When I made the soap foam by ‘hand’ the foam contained levels of soap and water that were too heavy for the structure of the foam to support and it would collapse under its own weight. The second attempt at the experiment involved high-pressure water to create the foam, which effectively built a lighter structure and was able to support weight, cantilevering, etc. to be sculpted into a form. The foam has an adhesive quality that enabled it to take its form, though especially with the heavier solution as the foam broke its bonds in areas voids, spaces and environments appeared. From the analysis gained through this experiment I plan to push the theory further, which the intention to focus on the lighter foam and these spaces which are naturally formed through the materials strengths and weaknesses.

Natural Foam Fun! For the second experimentation attempt I mixed the foam solution in a bath which produced a lighter foam and therefore a greater strength foam, as I transferred the foam I noticed that it naturally demonstrated an organic structure of its own choosing. The photo documentation notes this unintentional form. The Third Experiment which is currently on-going involves placing the foam solution into a freezer to document the effect of the adverse conditions on the form. If soap bubbles are kept in an environment with a temperature −15 °C (5 °F) or below it will freeze, though if they were to be brought into a warmer environment it will cause the bubble to crumble under its own weight at a rapid weight. Photo documentation of this experiment is to follow.

Experimentation_2D The Geometry of Bending

_ Grasshopper and Kangaroo Definition

2D_Bending from a singluar point

Bending Lines Slender or two-dimensional objects change their form under the influence of applied force acting transverse to their axis. The result of buckling may occur to the structure due to a lack of stability in relation to the axial forces. The characteristic of bending lines can be mathematical formulated as long as the material laws were to be abided by. The deformation configuration can be derived from the type of load, with the stiffness and length influencing greatly the outcome of the bending movement. Parabola If a rod or elastic material which has a constant cross section and a linear force-elongation curve is loaded with a single force then the bending line is equal to a third-order parabola.

2D Line Experiments by Frei Otto

Unit DS10 - Kayleigh Dickson

Circular Arc Circular bending lines develop when fixed-end moments acting in opposite directions are active at the ends of an elastic rod. If the two ends are to be held to one another then the bending resistance remains constant and a circle is formed. Combined Forms

Physical Analysis of Grasshopper

Grasshopper Experiments

Typical bending lines can be produced by combining different types of load, in architecture these may result in numerous characteristic building forms. Since naturally grown rods are used for building which are seldom and prismatic, the building will adapt to the bending line of conical rods.

2D_Bending from two points

2D_Bending from two points

2D_Bending from one point with a fixed centre

Digital Confirmation_01 The Geometry of Bending

Unit DS10 - Kayleigh Dickson

Digital Confirmation_02 The Geometry of Bending

Unit DS10 - Kayleigh Dickson

Singular Anchor Point

Two Point Movement

Singular Anchor Point

_ Comparing physical 2D Bening compared to the Grasshopper model

Generative Rules Generative path systems based on nature’s angles Unit DS10 - Kayleigh Dickson

Through the study of two-dimensional networks in the hexagonal cell, in the study of biological systems it is important to study growth sequences, sequential solidification of forms and “edge effects” as this will greatly effect the outcome of the final form. Cracking or shrinkage occurs in accordance with strict rules. This will normally occur with an original fault line in the material. The tensile stress will act evenly in all directions is greater on the top., which will accelerate the linear growth of the ‘cracks’. Side Cracks will take form at right angles, starting from a weak point in the wall of a material. If this crack in the side of the wall was to connect with an existing crack, then they are orientated by the tensile stress in parallel to the wall surface at 90 degrees. If the material was to contract in uniform then a hexagonal shape will appear, and three lines will meet at 120 degrees 1 _ with cracked surfaces such as ceramic glaze, mud, etc., the ‘cracking’ effect will not form immediately yet it will appear over time 2 _ the surface of a heated aluminum sheet will show the formation at early stages of melting, is unlike the two-dimensional formation showing with soap bubbles. 4 _ the grain boundaries in Niobium forms through the appearance of etching and shows a lack of uniformity.

The rig aids in the manipulation of ply strips, through holding fixed the two points of bending control on the strip allowing for an angle of degree to be permanent, unless soaked in boiling water when it will return to its original form. 90 Degrees

Generative Paths In generative path systems, users, when close to paths connecting at a right angle of the second generation tend to take a short cut as soon at the ‘T-junction’ becomes visible. This is especially true when the way not only to the next occupier but also the occupier beyond is sought.

The theory of generative paths has similarities to my studies into the geometry of bending, where the curve in the bending of ply is not tight to point 0,0, but actually rounds on to the new angle prematurely of point 0,0. So when analyzing the strength in nature’s angles I can approach the experimentation with this theory and rigorously test multiple angles. To analyse if nature does produce the strongest geometry of bending or if does not is it the most efficient structure?

33 Degrees

Would a structure become stronger if in this experiment the material was set at a required angle, with multiple strips then placed up against each other tightly, before pouring hot water over the top, creating compression on the neighbouring strip?

Experimentational Experimentation_3D Process The Geometry of Bending

Unit DS10 - Kayleigh Dickson

Experimentation_3D Bending from two points in 2D

The Geometry of Bending

Theory

Multiple Influenced Bending

Influenced Bending Form

Natural Bend Form

Rig

Unit DS10 - Kayleigh Dickson Rig System

Process in 3D

Experimentation_3D The Geometry of Bending

Unit DS10 - Kayleigh Dickson

Digitalised Geometry Delaunay Triangulation & Voronoi Diagram Unit DS10 - Kayleigh Dickson

Delaunay triangulation The Delaunay Triangulation was invented by Boris Delaunay in 1934. The Delaunay Triangulation is used in mathematics and computational geometry for a set P of points in the plane is the triangulation DT (P) such that no point in P is inside the circumcircle of any triangle in DT(P). The point of the Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the triangulation; they tend to avoid skinny triangles. For a set of points on the same line there is no Delaunay triangulation (the notion of triangulation is degenerate for this case). For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the “Delaunay condition”, i.e., the requirement that the circumcircles of all triangles have empty interiors.

The DTFE consists of three main steps: Step 1 The starting point is a given discrete point distribution. In the upper left-hand frame of the figure a point distribution is plotted in which at the center of the frame an object is located whose density diminishes radially outwards. In the first step of the DTFE the Delaunay tessellation of the point distribution is constructed. This is a volume-covering division of space into triangles (tetrahedra in three dimensions), whose vertices are formed by the point distribution (see figure, upper right-hand frame). The Delaunay tessellation is defined such that inside the interior of the circumcircle of each Delaunay triangle no other points from the defining point distribution are present.

By considering circumscribed spheres, the notion of Delaunay triangulation extends to three and higher dimensions. Generalizations are possible to metrics other than Euclidean. However in these cases a Delaunay triangulation is not guaranteed to exist or be unique.

d-dimensional Delaunay For a set P of points in the (d-dimensional) Euclidean space, a Delaunay triangulation is a triangulation DT(P) such that no point in P is inside the circum-hypersphere of any simplex in DT(P). It is known[2] that there exists a unique Delaunay triangulation for P, if P is a set of points in general position; that is, there exists no k-flat containing k + 2 points nor a k-sphere containing k + 3 points, for 1 ≤ k ≤ d − 1 (e.g., for a set of points in ℝ3; no three points are on a line, no four on a plane, no four are on a circle, and no five on a sphere). The problem of finding the Delaunay triangulation of a set of points in d-dimensional Euclidean space can be converted to the problem of finding the convex hull of a set of points in (d + 1)-dimensional space, by giving each point p an extra coordinate equal to |p|2, taking the bottom side of the convex hull, and mapping back to d-dimensional space by deleting the last coordinate. As the convex hull is unique, so is the triangulation, assuming all facets of the convex hull are simplices. Nonsimplicial facets only occur when d + 2 of the original points lay on the same d-hypersphere, i.e., the points are not in general position.

Step 2 The Delaunay tessellation forms the heart of the DTFE. In the figure it is clearly visible that the tessellation automatically adapts to both the local density and geometry of the point distribution: where the density is high, the triangles are small and vice versa. The size of the triangles is therefore a measure of the local density of the point distribution. This property of the Delaunay tessellation is exploited in step 2 of the DTFE, in which the local density is estimated at the locations of the sampling points. For this purpose the density is defined at the location of each sampling point as the inverse of the area of its surrounding Delaunay triangles (times a normalization constant, see figure, lower right-hand frame). Step 3 In step 3 these density estimates are interpolated to any other point, by assuming that inside each Delaunay triangle the density field varies linearly

_ Delaunay Triangulation

Ref: http://en.wikipedia.org/wiki/Delaunay_triangulation

Relationship with the Voronoi Diagram The Delaunay triangulation of point set P in general position corresponds to the dual graph of the Voronoi tessellation for P. Special cases include the existence of three points on a line and four points on circle. The Delaunay triangulation with all the circumcircles and their centers is een to the left. Connecting the centers of the circumcircles produces the Voronoi diagram is seen to the right.

Voronoi diagram In the simplest case, we are given a set of points S in the plane, which are the Voronoi sites. Each site s has a Voronoi cell, also called a Dirichlet cell, V(s) consisting of all points closer to s than to any other site. The segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi nodes are the points equidistant to three (or more) sites.

A graphical representation of the Voronoi diagram from two-dimension to three-dimension

In general, the set of all points closer to a point c of S than to any other point of S is the interior of a (in some cases unbounded) convex polytope called the Dirichlet domain or Voronoi cell for c. For each point x in S take the set of points closer to c than to x (as described above). Then take the intersection of all these sets to get the Vonoroi cell for c. The set of such polytopes tessellates the whole space, and is the Voronoi tessellation corresponding to the set S. If the dimension of the space is only 2, then it is easy to draw pictures of Voronoi tessellations, and in that case they are sometimes called Voronoi diagrams. Ref: http://en.wikipedia.org/wiki/Voronoi_diagram

_ Voronoi Diagram

Marc Fornes design was inspired by Voronoi Diagram theory

Approximate Voronoi diagram of a set of points. The blended colors represented the blurred boundary of the Voronoi cells.

Circle Packing Analysis_01

Unit DS10 - Kayleigh Dickson

Circle packing The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that all circles touch another. The associated “packing density”, η of an arrangement is the proportion of the surface covered by the circles. Generalisations can be made to higher dimensions – this is called sphere packing, which usually deals only with identical spheres. The branch of mathematics generally known as “circle packing”, however, is not overly concerned with dense packing of equal-sized circles (the densest packing is known) but with the geometry and combinatorics of packings of arbitrarily-sized circles: these give rise to discrete analogs of conformal mapping, Riemann surfaces and the like. While the circle has a relatively low maximum packing density, it does not have the lowest possible. The “worst” shape to pack onto a plane is not known, but the smoothed octagon has a packing density of about 0.902414, which is the lowest maximum packing density known of any centrally-symmetric convex shape.[1] Packing densities of concave shapes such as star polygons can be arbitrarily small.

Packings in the plane The centers of three circles in contact form an equilateral triangle, making this a hexagonal packing.

Identical circles in a hexagonal packing arrangement, the densest packing possible. In two dimensional Euclidean space, Joseph Louis Lagrange proved in 1773 that the lattice arrangement of circles with the highest density is the hexagonal packing arrangement,[2] in which the centres of the circles are arranged in a hexagonal lattice (staggered rows, like a honeycomb), and each circle is surrounded by 6 other circles. The density of this arrangement is Axel Thue provided the first proof that this was optimal in 1890, showing that the hexagonal lattice is the densest of all possible circle packings, both regular and irregular. However, his proof was considered by some to be incomplete. The first rigorous proof is attributed to László Fejes Tóth in 1940.[2] At the other extreme, very low density arrangements of rigidly packed circles have been identified.

Packings on the sphere

Packings in bounded areas

Unequal circles

A related problem is to determine the lowestenergy arrangement of identically interacting points that are constrained to lie within a given surface. The Thomson problem deals with the lowest energy distribution of identical electric charges on the surface of a sphere. The Tammes problem is a generalisation of this, dealing with maximising the minimum distance between circles on sphere. This is analogous to distributing non-point charges on a sphere.

Fifteen equal circles packed within the smallest possible square. Only four equilateral triangles are formed by adjacent circles.

A compact binary circle packing with the most similarly sized circles possible.

Packing circles in simple bounded shapes is a common type of problem in recreational mathematics. The influence of the container walls is important, and hexagonal packing is generally not optimal for small numbers of circles.

There are also a range of problems which permit the sizes of the circles to be non-uniform. One such extension is to find the maximum possible density of a system with two specific sizes of circle (a binary system). Only nine particular radius ratios permit compact packing, which is when every pair of circles in contact is in mutual contact with two other circles (when line segments are drawn from contacting circle-center to circle-center, they triangulate the surface).

Circle Packing Analysis_02

Unit DS10 - Kayleigh Dickson

Kepler conjecture

Kepler conjecture

Face-centered cubic packing

Face-centered cubic packing

The Kepler conjecture, named after the 17th-century German astronomer Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements. The density of these arrangements is slightly greater than 74%.

The Kepler conjecture, named after the 17th-century German astronomer Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic close packing (face-centered cubic) and hexagonal close packing arrangements. The density of these arrangements is slightly greater than 74%.

In 1998 Thomas Hales, following an approach suggested by Fejes Tóth (1953), announced that he had a proof of the Kepler conjecture. Hales’ proof is a proof by exhaustion involving the checking of many individual cases using complex computer calculations. Referees have said that they are “99% certain” of the correctness of Hales’ proof, so the Kepler conjecture is now very close to being accepted as a theorem.

In 1998 Thomas Hales, following an approach suggested by Fejes Tóth (1953), announced that he had a proof of the Kepler conjecture. Hales’ proof is a proof by exhaustion involving the checking of many individual cases using complex computer calculations. Referees have said that they are “99% certain” of the correctness of Hales’ proof, so the Kepler conjecture is now very close to being accepted as a theorem.

Imagine filling a large container with small equal-sized spheres. The density of the arrangement is the proportion of the volume of the container that is taken up by the spheres. In order to maximize the number of spheres in the container, you need to find an arrangement with the highest possible density, so that the spheres are packed together as closely as possible.

Imagine filling a large container with small equal-sized spheres. The density of the arrangement is the proportion of the volume of the container that is taken up by the spheres. In order to maximize the number of spheres in the container, you need to find an arrangement with the highest possible density, so that the spheres are packed together as closely as possible.

Experiment shows that dropping the spheres in randomly will achieve a density of around 65%. However, a higher density can be achieved by carefully arranging the spheres as follows. Start with a layer of spheres in a hexagonal lattice, then put the next layer of spheres in the lowest points you can find above the first layer, and so on – this is just the way you see oranges stacked in a shop. At each step there are two choices of where to put the next layer, so this natural method of stacking the spheres creates an uncountably infinite number of equally dense packings, the best known of which are called cubic close packing and hexagonal close packing. Each of these arrangements has an average density of

Experiment shows that dropping the spheres in randomly will achieve a density of around 65%. However, a higher density can be achieved by carefully arranging the spheres as follows. Start with a layer of spheres in a hexagonal lattice, then put the next layer of spheres in the lowest points you can find above the first layer, and so on – this is just the way you see oranges stacked in a shop. At each step there are two choices of where to put the next layer, so this natural method of stacking the spheres creates an uncountably infinite number of equally dense packings, the best known of which are called cubic close packing and hexagonal close packing. Each of these arrangements has an average density of

The Kepler conjecture says that this is the best that can be done—no other arrangement of spheres has a higher average density.

The Kepler conjecture says that this is the best that can be done—no other arrangement of spheres has a higher average density.

The conjecture was first stated by Johannes Kepler (1611) in his paper ‘On the six-cornered snowflake’. He had started to study arrangements of spheres as a result of his correspondence with the English mathematician and astronomer Thomas Harriot in 1606. Harriot was a friend and assistant of Sir Walter Raleigh, who had set Harriot the problem of determining how best to stack cannon balls on the decks of his ships. Harriot published a study of various stacking patterns in 1591, and went on to develop an early version of atomic theory.

The conjecture was first stated by Johannes Kepler (1611) in his paper ‘On the six-cornered snowflake’. He had started to study arrangements of spheres as a result of his correspondence with the English mathematician and astronomer Thomas Harriot in 1606. Harriot was a friend and assistant of Sir Walter Raleigh, who had set Harriot the problem of determining how best to stack cannon balls on the decks of his ships. Harriot published a study of various stacking patterns in 1591, and went on to develop an early version of atomic theory.

Nineteenth century Kepler did not have a proof of the conjecture, and the next step was taken by Carl Friedrich Gauss (1831), who proved that the Kepler conjecture is true if the spheres have to be arranged in a regular lattice. This meant that any packing arrangement that disproved the Kepler conjecture would have to be an irregular one. But eliminating all possible irregular arrangements is very difficult, and this is what made the Kepler conjecture so hard to prove. In fact, there are irregular arrangements that are denser than the cubic close packing arrangement over a small enough volume, but any attempt to extend these arrangements to fill a larger volume always reduces their density. After Gauss, no further progress was made towards proving the Kepler conjecture in the nineteenth century. In 1900 David Hilbert included it in his list of twenty three unsolved problems of mathematics—it forms part of Hilbert’s eighteenth problem.

Six circles theorem Some examples of theorem configuration changing the radius of the first circle. In the last configuration the circles are pairwise coincident. In geometry, the six circles theorem relates to a chain of six circles together with a triangle, such that each circle is tangent to two sides of the triangle and also to the preceding circle in the chain. The chain closes, in the sense that the sixth circle is always tangent to the first circle. The name may also refer to Miquel’s six circles theorem, the result that if five circles have four triple points of intersection then the remaining four points of intersection lie on a sixth circle.

Nineteenth century Kepler did not have a proof of the conjecture, and the next step was taken by Carl Friedrich Gauss (1831), who proved that the Kepler conjecture is true if the spheres have to be arranged in a regular lattice. This meant that any packing arrangement that disproved the Kepler conjecture would have to be an irregular one. But eliminating all possible irregular arrangements is very difficult, and this is what made the Kepler conjecture so hard to prove. In fact, there are irregular arrangements that are denser than the cubic close packing arrangement over a small enough volume, but any attempt to extend these arrangements to fill a larger volume always reduces their density. After Gauss, no further progress was made towards proving the Kepler conjecture in the nineteenth century. In 1900 David Hilbert included it in his list of twenty three unsolved problems of mathematics—it forms part of Hilbert’s eighteenth problem.

Twentieth century

Twentieth century

The next step toward a solution was taken by Hungarian mathematician László Fejes Tóth. Fejes Tóth (1953) showed that the problem of determining the maximum density of all arrangements (regular and irregular) could be reduced

The next step toward a solution was taken by Hungarian mathematician László Fejes Tóth. Fejes Tóth (1953) showed that the problem of determining the maximum density of all arrangements (regular and irregular) could be reduced

Circle Packing Analysis_02

Unit DS10 - Kayleigh Dickson

Malfatti circles Apollonian gasket

In geometry, the Malfatti circles are three circles inside a given triangle such that each circle is tangent to the other two and to two sides of the triangle. They are named after Gian Francesco Malfatti, who made early studies of the problem of constructing these circles in the mistaken belief that they would have the largest possible total area of any three disjoint circles within the triangle. Malfatti’s problem has been used to refer both to the problem of constructing the Malfatti circles and to the problem of finding three area-maximizing circles within a triangle.

In mathematics, an Apollonian gasket or Apollonian net is a fractal generated from triples of circles, where each circle is tangent to the other two. It is named after Greek mathematician Apollonius of Perga. An Apollonian gasket can be constructed as follows. Start with three circles C1, C2 and C3, each one of which is tangent to the other two (in the general construction, these three circles can be any size, as long as they have common tangents). Apollonius discovered that there are two other non-intersecting circles, C4 and C5, which have the property that they are tangent to all three of the original circles – these are called Apollonian circles (see Descartes’ theorem). Adding the two Apollonian circles to the original three, we now have five circles.

Malfatti’s problem Comparison of the Malfatti circles and the three area-maximizing circles within an equilateral triangle In 1803 Gian Francesco Malfatti posed the problem of cutting three cylindrical columns out of a rectangular wedge of marble, maximizing the total volume of the columns. He assumed, as did many others after him, that the solution to this problem was given by three tangent circles within the triangular cross-section of the wedge. That is, more abstractly, he conjectured that the three Malfatti circles have the maximum total area of any three disjoint circles within a given triangle.

Malfatti circles

In a similar way we can construct another new circle C7 that is tangent to C4, C2 and C3, and another circle C8 from C1, C3 and C1. This gives us 3 new circles. We can construct another three new circles from C5, giving six new circles altogether. Together with the circles C1 to C5, this gives a total of 11 circles.

Malfatti published in Italian and his work may not have been read by many in the original. It was popularised for a wider readership in French by Joseph Diaz Gergonne in the first volume of his ``Annales” (1810/11), with further discussion in the second and tenth. However, this advertisement most likely acted as a filter, as Gergonne only stated the circle-tangency problem, not the area-maximizing one.

Continuing the construction stage by stage in this way, we can add 2·3n new circles at stage n, giving a total of 3n+1 + 2 circles after n stages. In the limit, this set of circles is an Apollonian gasket. The Apollonian gasket has a Hausdorff dimension of about 1.3057.

The conjecture is wrong; Lob and Richmond (1930), who went back to the original Italian text, observed that for some triangles a larger area can be achieved by a greedy algorithm that inscribes a single circle of maximal radius within the triangle, inscribes a second circle within the largest of the three remaining corners of the triangle, and inscribes a third circle within the largest of the five remaining pieces. The difference in area for an equilateral triangle is small, just over 1%, but as Howard Eves pointed out in 1946, for an isosceles triangle with a very sharp apex, the optimal circles (stacked one atop each other above the base of the triangle) have nearly twice the area of the Malfatti circles. Goldberg (1967) showed that, for every triangle, the Lob–Richmond procedure produces three circles with larger area than the Malfatti circles, so the Malfatti circles are never optimal. Zalgaller and Los’ (1994) classified all of the different ways that a set of maximal circles can be packed within a triangle; using their classification, they proved that the greedy algorithm always finds three area-maximizing circles, and they provided a formula for determining which packing is optimal for a given triangle. In his 1997 Ph.D. thesis, Melissen conjectured more generally that, for any integer n, the greedy algorithm finds the areamaximizing set of n circles within a given triangle; the conjecture is known to be true for n ≤ 3.

Curvature The curvature of a circle (bend) is defined to be the inverse of its radius.

First Ajima–Malfatti point

Apollonian sphere packing An Apollonian gasket can also be constructed by replacing one of the generating circles by a straight line, which can be regarded as a circle passing through the point at infinity.

The regular hexagonal packing is the densest sphere packing in the plane. (1890)

Alternatively, two of the generating circles may be replaced by parallel straight lines, which can be regarded as being tangent to one another at infinity. In this construction, the circles that are tangent to one of the two straight lines form a family of Ford circles.

The 2-dimensional analog of the Kepler conjecture; the proof is elementary. Henk and Ziegler attribute this result to Lagrange, in 1773 (see references, pag. 770). The hexagonal honeycomb conjecture

The three-dimensional equivalent of the Apollonian gasket is the Apollonian sphere packing.

The most efficient partition of the plane into equal areas is the regular hexagonal tiling. Hales’ proof (1999).

Symmetries

The dodecahedron conjecture

A related problem, whose proof uses similar techniques to Hales’ proof of the Kepler conjecture. Conjecture by L. Fejes Tóth

▪ Negative curvature indicates that all other circles are internally tangent to that circle. This is bounding circle ▪ Zero curvature gives a line (circle with infinite radius). ▪ Positive curvature indicates that all other circles are externally tangent to that circle. This circle is in the interior of circle with negative curvature. Variations

Thue’s theorem

The volume of the Voronoi polyhedron of a sphere in a packing of equal spheres is at least the volume of a regular dodecahedron with inradius 1. McLaughlin’s proof, for which he received the 1999 Morgan Prize.

Take one of the two Apollonian circles – say C4. It is tangent to C1 and C2, so the triplet of circles C4, C1 and C2 has its own two Apollonian circles. We already know one of these – it is C3 – but the other is a new circle C6.

Comparison of the Malfatti circles and the three areamaximizing circles within an equilateral triangle

If two of the original generating circles have the same radius and the third circle has a radius that is two-thirds of this, then the Apollonian gasket has two lines of reflective symmetry; one line is the line joining the centres of the equal circles; the other is their mutual tangent, which passes through the centre of the third circle. These lines are perpendicular to one another, so the Apollonian gasket also has rotational symmetry of degree 2; the symmetry group of this gasket is D2.

Bubble Occupation Study Bubble Formation

Unit DS10 - Kayleigh Dickson

Bubbles and mountain passes Scientists had thought bubbles form when jostling liquid molecules create pockets of low density in the liquid containing relatively fewer molecules than surrounding regions. Most of the time, other molecules will just rush in to fill in these air pockets. However, an exodus of molecules can also occur, causing the pockets, or bubbles, to grow. David Corti, a chemical engineer at Purdue University in Indiana, compares the process to scaling a mountain. A pocket of air begins at the bottom of one side of the mountain (the liquid phase) and must climb the mountain and reach a destination on the other side (the vapor phase) to become a bubble. “A small bubble needs to climb up one side of the mountain, cross through a reasonably well-defined mountain pass before it rolls down the other side of the mountain towards forming very large bubbles,” Corti explained. According to the conventional view, once the bubble makes it over the pass, it tumbles down the other side of the mountain like a snowball, picking up more molecules and growing bigger. The new computer simulation suggests there “is no other side of the mountain,” Corti told LiveScience. “Once it gets over the pass, we have found that the mountain just disappears, in a sense.” Rather than having to descend another slope, the bubble just plummets directly into the vapor phase. As a result, bubble formation might occur more rapidly than previously thought, Corti said. Broader pathways

Surface Tension and Bubbles The surface tension of water provides the necessary wall tension for the formation of bubbles with water. The tendency to minimize that wall tension pulls the bubbles into spherical shapes (LaPlace’s law).

The new research also suggests the metaphorical mountain pass is actually more broad and flat than previously thought, allowing for several possible pathways from the liquid to the vapor phase.

The pressure difference between the inside and outside of a bubble depends upon the surface tension and the radius of the bubble. The relationship can be obtained by visualizing the bubble as two hemispheres and noting that the internal pressure which tends to push the hemispheres apart is counteracted by the surface tension acting around the circumference of the circle.

“In the traditional view … there are only a few pathways that go through the pass,” Corti said. “From our work, we have shown that it is in fact quite broad, so that there are a large number of pathways that will lead over the mountain top.”

For a bubble with two surfaces providing tension, the pressure relationship is:

The findings could have implications for how scientists predict the rate of bubble formation, and could help improve safety for industries that rely on bubbles, the researchers say. “We are still working out the full implications of this ourselves,” Corti said Experiments with Bubbles When many small bubbles are randomly distributed on a surface of water they will join together to form an expanse, until a singular raft if formed. If the small bubbles are the same size, they take on a structure, which is hexagonal when seen from above. The minimal territories are therefore formally identical with those of distancing occupation. The territory centres arrange themselves spontaneously into a grid of equilateral triangles. Even if the small bubbles, i.e. the narrowest occupations are of unequal size the pattern remains similar. Hexagonal >>meshes<< in triangular (non-equilateral) structures predominately. Pattern formation in attractive occupation is therefore identical to that of distancing occupation, with only one difference: with attractive occupation, the greatest density is reached.

Bubble Pressure The net upward force on the top hemisphere of the bubble is just the pressure difference times the area of the equatorial circle:

The surface tension force downward around circle is twice the surface tension times the circumference, since two surfaces contribute to the force:

This gives

This latter case also applies to the case of a bubble surrounded by a liquid, such as the case of the alveoli of the lungs.

Bending Analysis_01 _ Physical Bending Experiment 01

_ Physical Bending Experiment 02

_ Physical Bending Experiment 03

EXPERIMENTATION 01

EXPERIMENTATION 02

EXPERIMENTATION 03

Unit DS10 - Kayleigh Dickson

Bending Analysis_02 _ Physical Bending Experiment 04

_ Physical Bending Experiment 05

_ Physical Bending Experiment 06

Unit DS10 - Kayleigh Dickson

EXPERIMENTATION 04

EXPERIMENTATION 05

EXPERIMENTATION 06

Experimentation_3D The Geometry of Bending Pushing, Flexing and Testing Unit DS10 - Kayleigh Dickson

_ STRENGTH MANIPULATION EXPERIMENT 01

_ STRENGTH MANIPULATION EXPERIMENT 02

Natural Rule Analysis_01

Unit DS10 - Kayleigh Dickson

Patterns and Grids The advantage of the hexagonal grid resulting from the triangular grid has a broad spectrum of application. Any expansion and subdivision is possible. Natural Patterns _ Grasshopper Definition

When layers of mud shrink due to drying, the non-cracked expanses can be considered as >>territories<<. The majority of these >>territories<< are hexagonal. The key points of the surfaces form a clear triangular grid. Often, many generations can be seen, with an increasing number of pentagonal surfaces.

Natural and Technological Occupations Occupations belonging in the areas of non-living nature, living nature and technology can be distinguished. Geodesy or the division of the Earthâ€™s surface can be considered a planned, i.e. less natural occupation mechanism. The division of the Earthâ€™s surface in to meridians and circles of latitude, for instance, is both artificial and at the same time useful.

_ Cracked Mud Experimentation 01 In a series of experimentation of the behhaviour of mud I choose to digitalise the first experimemntatoi

_ The Voronoi output in grasshopper of the cracked mud which tests if the 120 degree rule applies

_ The cracked mud out line that was imput in to grashopper for testing and analysis

_ Theout put from grasshopper which shows that the cracked mud very closely applies natures rules of deformation

Almost all natural occupations are subject to self-constituting principles of varying strength. This is especially clear in the <<occupation>> of an even surface by shrinkage cracks (in clay or glazes), which predominately enclose hexagonal surfaces whose key points, in an ideal situation, form a triangular pattern.

The grasshopper definition which formed the Voronoi bubble formation below.

The grasshopper definition which formed the Voronoi bubble formation below.

The grasshopper definition which formed the Voronoi bubble formation below.

The grasshopper definition which formed the Voronoi bubble formation below.

The progress from the block voronoi form built in grasshopper, into the extracted face edges which leaves a simpler form, before being piped in to a 3D form

Burnt Mud Experimentation_01

Unit DS10 - Kayleigh Dickson

Mudcracks (also known as desiccation cracks or mud cracks) are sedimentary structures formed as muddy sediment dries and contracts. Naturally forming mudcracks start as wet, muddy sediment desiccates, causing contraction via a decrease in tensile strength. Individual cracks join up forming a polygonal, interconnected network. These cracks may later be filled with sediment and form casts on the base of the overlying bed. Syneresis cracks are broadly similar features that form from subaqueous shrinkage of muddy sediment caused by differences in salinity or chemical conditions, rather than subaerial exposure and desiccation. Syneresis cracks can be distinguished from mudcracks because they tend to be discontinuous, sinuous, and trilete or spindle-shaped

CRACKING EXPERIMENT _ 02

CRACKING EXPERIMENT _ 03

CRACKING EXPERIMENT _ 04

Regular

Crack Filling Simple

Complete Complete

Compound

Orientated

Irregular

Incomplete Incomplete

Random

Crack Shape

Unbridged

Complete

Incomplete

Bridged

Non-Orthogonal

CRACKING EXPERIMENT _ 01

Orthogonal

Naturally forming mudcracks start as wet, muddy sediment desiccates, causing contraction via a decrease in tensile strength[citation needed]. Individual cracks join up forming a polygonal, interconnected network. These cracks may later be filled with sediment and form casts on the base of the overlying bed.[citation needed] Syneresis cracks are broadly similar features that form from subaqueous shrinkage of muddy sediment caused by differences in salinity or chemical conditions,[1] rather than subaerial exposure and desiccation. Syneresis cracks can be distinguished from mudcracks because they tend to be discontinuous, sinuous, and trilete or spindle-shaped

Burnt Mud Experimentation_02 NON-ORTHOGONAL

CRACK FILLING

ORTHOGONAL

ORTHOGONAL

Unit DS10 - Kayleigh Dickson

Environments and substrates Naturally occurring mud cracks form in sediment that was once saturated with water. Abandoned river channels, floodplain muds, and dried ponds are localities that form mudcracks.[5] Mud cracks can also be indicative of a predominately sunny or shady environment of formation. Rapid drying, which occurs in sunny environments, results in widely spaced, irregular mud cracks, while closer spaced more regular mud cracks indicates a shady formation environment.[6] Polygonal crack networks similar to mudcracks can form in man-made materials such as ceramic glazes, paint film, and poorly made concrete. Similar features also occur in frozen ground, lava flows (as columnar basalt), and igneous dykes and sills.

The term fold is used in geology when one or a stack of originally flat and planar surfaces, such as sedimentary strata, are bent or curved as a result of permanent deformation. Synsedimentary folds are those due to slumping of sedimentary material before it is lithified. Folds in rocks vary in size from microscopic crinkles to mountain-sized folds. They occur singly as isolated folds and in extensive fold trains of different sizes, on a variety of scales. Folds form under varied conditions of stress, hydrostatic pressure, pore pressure, and temperature - hydrothermal gradient, as evidenced by their presence in soft sediments, the full spectrum of metamorphic rocks, and even as primary flow structures in some igneous rocks.

Plan View

As the wind effect the sand particles the cracks will become filled with a compound, in this case the ‘simple’ image shows a single compound.

A set of folds distributed on a regional scale constitutes a fold belt, a common feature of orogenic zones. Folds are commonly formed by shortening of existing layers, but may also be formed as a result of displacement on a non-planar fault (fault bend fold), at the tip of a propagating fault (fault propagation fold), by differential compaction or due to the effects of a high-level igneous intrusion e.g. above a laccolith.

Compound

Section View

Plan View Section View

Plan View Section View

Mud cracks can be preserved as v-shaped cracks on the top of a bed of muddy sediment or as casts on the base of the overlying bed. When they are preserved on the top of a bed, the cracks look as they were at the time of formation. When they are preserved on the bottom of the bedrock the cracks are filled in with younger, overlying sediment. In most bottom-of-bed examples the cracks are the part that sticks out most. Bottom-of-bed preservation occurs when mud cracks that have already formed and are completely dried are covered with fresh wet sediment and buried. Through burial and pressure the new wet sediment is further pushed into the cracks where it dries and hardens. The mud cracked rock is then later exposed to erosional factors.[2] In these cases, the original mud cracks will erode faster than the newer material filling in the spaces. These types of mud cracks are useful for geologists to determine the vertical orientation of rock samples that have been altered through folding or faulting.

Simple

Preservation

The axial surface is the surface defined by connecting all the hinge lines of stacked folding surfaces. If the axial surface is a planar surface then it is called the axial plane and can be described by the strike and dip of the plane. An axial trace is the line of intersection of the axial surface with any other surface. Finally, folds can have, but don’t necessarily have a fold axis. A fold axis, “is the closest approximation to a straight line that when moved parallel to itself, generates the form of the fold.” . A fold that can be generated by a fold axis is called a cylindrical fold. This term has been broadened to include near-cylindrical folds. Often, the fold axis is the same as the hinge line

In the desert these is normally a mixture of different compounds that make up the ground composition. There you can see the range of particle sizes that show a tiering system.

BURN:

BURNING MAN _ BURNING MAN

_ BURNING MAN’ ANALYSIS

Unit DS10 - Kayleigh Dickson

What is Burning Man? What is Burning Man? As have so many others who’ve struggled to answer that difficult question, this section offers a comprehensive overview of the event and its history.

MOON PHASE (burn night) YEAR

Average Weekly Weather Forcast

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Ten Principles or The 10 core guiding concepts of the Burning Man project: Radical Inclusion Anyone may be a part of Burning Man. We welcome and respect the stranger. No prerequisites exist for participation in our community.

86 Degrees 41 Degrees HIGH

WIND SPEED

PARTICIPANTS

Gifting Burning Man is devoted to acts of gift giving. The value of a gift is unconditional. Gifting does not contemplate a return or an exchange for something of equal value. Decommodification In order to preserve the spirit of gifting, our community seeks to create social environments that are unmediated by commercial sponsorships, transactions, or advertising. We stand ready to protect our culture from such exploitation. We resist the substitution of consumption for participatory experience. Radical Self-reliance Burning Man encourages the individual to discover, exercise and rely on his or her inner resources. Radical Self-expression Radical self-expression arises from the unique gifts of the individual. No one other than the individual or a collaborating group can determine its content. It is offered as a gift to others. In this spirit, the giver should respect the rights and liberties of the recipient. Communal Effort Our community values creative cooperation and collaboration. We strive to produce, promote and protect social networks, public spaces, works of art, and methods of communication that support such interaction. Civic Responsibility We value civil society. Community members who organize events should assume responsibility for public welfare and endeavor to communicate civic responsibilities to participants. They must also assume responsibility for conducting events in accordance with local, state and federal laws. Leaving No Trace Our community respects the environment. We are committed to leaving no physical trace of our activities wherever we gather. We clean up after ourselves and endeavor, whenever possible, to leave such places in a better state than when we found them. Participation Our community is committed to a radically participatory ethic. We believe that transformative change, whether in the individual or in society, can occur only through the medium of deeply personal participation. We achieve being through doing. Everyone is invited to work. Everyone is invited to play. We make the world real through actions that open the heart. Immediacy Immediate experience is, in many ways, the most important touchstone of value in our culture. We seek to overcome barriers that stand between us and a recognition of our inner selves, the reality of those around us, participation in society, and contact with a natural world exceeding human powers. No idea can substitute for this experience

LOW

7 MPH

20

80

200

300

500 /120

250

600

1,000

2,000

4,000

$35

TICKET PRICE

8,000

$35

THEME CAMPS FIRE CONCLAVE GROUPS ARTS PROJECTS BLM CITATIONS

10,000

$65

15,000

$80 - 90

23,000 25,400 25,679 28,979

30,586 35,664 35,567 38,989 47,366 49,599 43,435

$65 - 130

$200

$200

$135 - 200

$145 - 225

$145 - 250

$145 - 250

$185 - 280

$195 - 280

$210 - 295

$210 - 360

466

445

477

503

485

508

681

746

618

15

30

29

29

32

32

29

29

32

150

120

261

204

275

240

300

240

215

100

135

177

218

218

155

331

129

194

$210 - 300

RECYCLED ALUMINUM CANS 70,000 80,000 100,000 90,000 100,000 120,000 120,000 126,000 125,000

COSTS (Total Expenditures)

$5,255,200 $5,624,200 $7,287,335 $8,557,308 $8,397,178 $10,278,000 $13,497,000 $14,091,000 $12,317,000

466

EVENT/FESTIVAL ATTENDANCE

Rainbow Gathering

466

466

466

466

_ 30,000

466

466

466

466

BLACK ROCK DESERT 1000 sq. mi.

Playa 200 sq. mi.

Hualapai Flat 1997

Burning Man Arts Festival _ 43,435 Super Bowl _ 70,774

City Populations of Nevada

Bonnaroo Music Festival _ 75,000 Glastonbury Festival

_ 137,500

Coachella Valley Music and Arts Festival

_ 225,000

Woodstock Festival

_ 137,500

BLACK ROCK CITY 5 sq. mi.

BLACK ROCK DESERT 1990 - 1996 1998 - PRESENT

Hajj

Las Vegas 1,228,883

_ 1,613,000

SEX

Baker Beach 1986 - 1990

Reno 246,826

PARTICIPANT DEMOGRAPHICS

Male 54%

AGE

GRADUATED COLLEGE

61+ 51 - 60 2% 9% Under 21 41 - 50 4% 18% No 31% 21 - 30 31%

Female 54%

No response 6%

31 - 40 36%

Black Rock City 42,425

Carson City 52,457

INCOME $500k + 2% $100-500k 13%

Yes 69%

$50-10k 1%

$80-100k 10%

$50-80k 18%

$10-80k 44%

EVAPORATION PONDS Natural and Burning Man’s Evaporation Ponds

_ NATURE’S EVAPORATION PONDS

_ BURNING MAN’S EVAPORATION PONDS

Unit DS10 - Kayleigh Dickson

Evaporation ponds are artificial ponds with very large surface areas that are designed to efficiently evaporate water by sunlight and exposure to the ambient temperatures. Evaporation ponds have several uses. Salt evaporation ponds produce salt from seawater. They are also used to dispose of brine from desalination plants. Mines use ponds to separate ore from water. Evaporation ponds at contaminated sites remove the water from hazardous waste, which greatly reduces its weight and volume and allows the waste to be more easily transported, treated and stored. It is important to understand that evaporation is not the same as condensation although evaporation in an enclosed environment can subsequently lead to the condition of condensation as evaporated moisture is “condensed” out of the air and is reverted back to a liquid stage. Evaporation ponds can also be used to evaporate the precipitation that falls on a contaminated site. The contaminants that the water picks up on the ground are left behind after it evaporates. This prevents the contamination from spreading further down the watershed. Evaporation ponds are used to prevent pesticides, fertilizers and salts from agricultural wastewater from contaminating the water bodies they would flow into. In California, selenium in agricultural wastewater has been especially problematic, causing birth defects in waterfowl. Calculating evaporation pond rates W = [A + (B)(V)](Pw - Pa)/Hv where: W = water evaporation rate, (lb/hr) per sq.ft. of pond surface area A = a constant = 95 (**see note below) B = a constant = 37.4 (**see note below) V = air velocity over the pond surface, miles/hr Pw = vapor pressure of water at the pond water temperature, inches of Hg Pa = vapor pressure of water at the air dewpoint temperature, inches of Hg Hv = heat of vaporization of water at the pond water temperature

WATER EVAPORATION RATE OF BURNING MAN = 1270 mm per year

How do I build an evaporative pond? The following design is borrowed from Astral Headwash, who has won the valuable ‘Earth Guardian Camp of the Day’ award for several years. This pond will dispose of up to 15 gallons a day, and is easily expandable for some camps.

Materials and Construction for a 15 gallon evaporation pond • • • • • • • •

four 2x4’s 8 feet long, black plastic sheet, 6 mil thickness, 10 ft by 10 ft, 3” screws a screw gun (cordless drill), or nails and a hammer, a staple gun, a pump and a grey water container and gloves.

Construction & Operation: Pick a spot in your camp that’s secluded but sunny. Lay the 2×4’s on edge to form a square frame, and screw or nail the corners together. Lay a 10×10 ft piece of 6mil black plastic over the 2×4 frame loosely, so it lies on the ground. Staple it to the outside faces of the frame, and tuck the edges under. The plastic is probably already too hot to touch — that’s why you need gloves. Now you’re ready to dispose of your filtered grey water by simply pouring it in, by funneling shower runoff to it, or by running PVC pipe from your kitchen to the evaporation pond. To prevent punctures, anchor the pipe end to a 2×4 — a pipe end resting on the pond floor will tear it. To increase capacity, use more 2×4’s to build a larger-area pond. Remember to keep the water shallow. If the water gets to deep, pump water out for holding until the water level is less than one inch. Then slowly start evaporating again and check it every couple of hours. Figure about one quart evaporation per square foot per day. Improvements Since ponds do not work once the water level is too deep, many camps have experimented with using absorbant material (e.g., pieces of fabric dipping into the pond) to wick moisture out and so increase evaporation. Other camps have tried using fountains to increase evaporation. Lastly, in the spirit of reuse, other camps have taken their grey water home home and watered house plants with it. If you try out something along this line, please pass your results on to the Earth Guardians. Final Disposal and Clean-up: Save and re-use the 2×4’s. A 15-gallon pond uses about $3 of plastic sheet, which is pretty scuzzy by the end of the week, so you’ll want to pack it out as trash. Some camps report being able to roll it up and drive away without letting any of grey water hit the playa. Be sure to handle the sheets carefully so that no dried up soap or other showering residue on the plastic hits the playa or you!

GREY WATER DISPOSAL Water, Water Everywhere

_ BURNING MAN SHOWERS

_ PROPOSED PLAN FOR THE SHOWERS AT BURNING MAN

Shower Potential Problems: Your pond needs protection from leaks, from dust, and from renegade slipand-slide buckaroos. A leak could dump grey water onto the playa. Duct tape, applied to dry clean plastic, may handle a tiny leak. A heavy object resting on a scrap of plastic sheet, resting on a leak, makes a temporary stopgap. Dust WILL BLOW into your pond. Enough dust, and the sun won’t reach the black plastic and the water will not evaporate. Windbreaks haven’t proven to keep dust out. Once the pond stops working, you’ll need to pump out the water and clean or reline the pond. If you come up with a good technique to keep dust out, please let us know at Earth Guardians camp. Astral Headwash’s ponds were situated on their street frontage. It took fencing and shouted warnings to ward off slip-and-sliders, whose running jumps would have torn up the ponds. Be forewarned, and if possible choose a secluded site. You’ll want to avoid aromatic soaps and shampoos. The fragrances will linger, getting less fresh and less appealing with each new day. Dr. Bronner’s is recommended.

At Burning Man the showers are a luxury and to protet the Playa there has to be a strict set of rules. In the plan above the fours showers it on top of an evaporative pond, though this is not the most effective method for evaporative ponds due to the shaddows cast by the showers. Also another issue is how easily dust and dirt can get in to the evaporative pond which should be prevented.

Unit DS10 - Kayleigh Dickson

Most camps need to dispose of grey water during Burning Man. Grey water is produced from cooking, dish washing, and hair and body washing. Our permit from BLM does NOT allow us to dump grey water directly onto the playa. Therefore all grey water must be collected. Camps can then remove that water directly off the playa (by themselves or using Johnny on the Spot). Some camps may choose to use evaporation ponds to reduce the amount of water they need to haul off the playa, but these ponds can easily get clogged with dust. Some camps have even developed technologies to reuse their water. The appropriate methodology for you depends on the size of your camp, your background and experience, and the level of energy you want to spend dealing with grey water. What’s Simple? Small and mid-sized camps can collect your grey water and take it to several RV dump stations along highway 80 and in Reno after the event. A few are listed below. Please check with the dumping station before the event for disposal charges and determine if they can handle the amount of water you are planning to dump! Larger camps should consider setting up a contract with Johnny on the Spot to collect grey water. With 30 days notice, they will provide a collection tank for you at the event that they will collect at the end of the event for disposal. How can I reduce my grey water? First - remember Conservation, Conservation, Conservation! In your kitchen area, set up a low-volume water spray over a basin, for dishwashing and hand cleaning. A personal spray bottle, like the Cool Blast, is a good starting point. You’ll need remarkably little water to wash up with. Assign a water cop in your camp to remind campmates that you’re in the desert, not at home. Use a biodegradable detergent instead of soap. Camp Suds, available at REI, works well for dishes, hands, and showers. Rub your hands with a few drops of a waterless disinfectant lotion, available at drugstores, before you handle food. This saves water and is also good camp hygiene. Evaporation ponds are a technique that has been shown to reduce the volume of grey water. It is, however, important to construct a pond that is big enough for your camp. Too big - it will still work great. Too small - it stops working when the water gets too deep! Also limit showers the last few days of the event before you’ll need to pack up the evaporative pond for disposal.

All four showers have seperate entrances and are fixed down by guides and stakes.

CLOSED LOOP SYSTEM Water, Water Everywhere _ THE PROCESS OF THE CLOSED LOOP SYSTEM FOR A BURNING MAN ENVIRONMENT Unit DS10 - Kayleigh Dickson

EVAPORATION PONDS

PINNING THE PLAYA Based on the experimentions on mud cracks there will be a predertermined layout of pins that will optimised grey water evaporation. These pins will be placed in the Playa a year before hand so in the following year the cracks will start to form from predetermined points.

The evaporation ponds are a specific surface area to maximise grey water evaporation by sunlight and exposure to ambient temperatures. Leaving only the residue from the grey water to be removed and taken away at the end of the Burning Man Arts Festival.

SHOWERING Water which has been stored on the roof of the shower is warmed by the suns heat to be used whilst showering.

WATER FILTRATION PIPES Water will be filtrated away from the from the showers by pipes that run in between the mud cracks. This will efficiently remove the water from the showers for it to be recycled and filtrated ready for another shower use.

Glass Pipe

CAPILLARY ACTION Capillary action allows water to flow against gravity where liquid spontanously rise in a narrow space such as a thin tube. If the diameter of the tube is sufficiently small, then the combination of surface tension (which is caused by cohesion within the liquid) and force of adhesion between the liquid and container act to lift the liquid. In the closed loop system the water will be pulled up the wall of the structure to the top, which when the hot, dry, dusty passes through the wall the air temperature will cool and therefore cool the interior space on the other side of the wall.

SLOW SAND FILTRATION Slow sand filtration will remove the smallest particles from the water, even smaller than the gap between the fine sand. A slow and constant flow of water will filter through, with the top layer of sand trapping micro-organisms (i.e bacteria and viruses).

Water

Container

Frame

Water

Sand Gravel Perforated Pipe

_ CAPILLARY ACTION

_ SLOW SAND SYSTEM

OPTIMAL GREY WATER EVAPORATION

Unit DS10 - Kayleigh Dickson

_ PROCESS FOR CALCULATING THE OPTIMUM AREA FOR GREY WATER EVAPORATION

_ INITIAL SQUARE FORMATION

_ TRANSITION OF FORM BY THE USE OF A CIRCLE

_ FORM FOUND THROUGH THE RULES OF MUD CRACKS

HereI have overlaid the process from the standard square form of a grey water evaporation pond to the hexagonal form which would follow the rules I found in the study of mud cracking.

The ideal standard form used for grey water evaporation ponds is a square as this is a suitable shape for easy construction as well as being cost efficient,

In the transition I used the circle which is larger than the required evaporation geometry, though this would not be a suitable shape for use at burning man.

The theory of mud cracking is that angles will form at 120 degrees when 3 lines meet at one point, or 90 degrees when two lines meet at one point. Bearing these findings in mind I realised the optimum shape for the form and structure would be the hexagon as it will comply with these rules.

Area: 5.76 m2

Area: 9.07 m2

Area: 6 m2

_ EXPERIMENTATION - PREDETERMINED CRACKING

I composed an ordered pattern to guide the cracking formation that would allow myself the ability to control the directionality that the cracks will form in whilst abiding by the 120 degrees and 90 degrees rules.

BURNING MAN ORIENTATION AND WEATHER CONDITIONS PROCESS FOR BUILDING THE BURNING MAN

_ STAGE ONE

_ STAGE TWO

_ STAGE THREE

_ STAGE FOUR

Unit DS10 - Kayleigh Dickson

_ OUTDOOR TEMPERATURE

Buring Man Period

_ WIND SPEED

High - 75%

High - 100 Degrees F

High - 15 MPH

Low - 10%

Low - 40 Degrees F

Low - 2% MPH

Average - 35%

Average - 75 Degrees F

Average - 7% MPH Wind Speed [Unit MPH]

Outdoor Temperature [Unit F]

Humidity [Unit %]

_ HUMIDITY

Buring Man Period

Outdoor Temperature

Wind Velocity

Dewpoint

Gust Velocity Buring Man Period

GROUND COMPOSITION _ BURNING MAN GROUND CONDITION

_ PEELING THE CRACKED SURFACE OF THE PLAYA BACK

_ THE PROCESS OF THE PEELING

Unit DS10 - Kayleigh Dickson

_1

_ SOIL COMPOSITION

_2

_3

5% SAND

30% SILT

65% CLAY _4

During the summer months the playa becomes incredibly dry resulting in extensive crack formation across the bed. The crtacking results from the finer grains of sand settling first, as they will filter down in between the silt and clay. Cracks will form when the deserts heat dries the surface from the top and therefore the surface will start to shrink from the top with the result being a ‘V’ formation. The high clay composition will produce a suface which is firm and suitable to be used as a mould whilst still producing a power which will settle in the cracks of the playa surface. _5

PROPOSED BURNING MAN LOCATION _ BURNING MAN ORIENTATION Unit DS10 - Kayleigh Dickson

_ INITIAL PROPOSED LOCATION AT BURNING MAN

_ PROPOSED LOCATION

MOOP_ing Burning Man Black Rock City Moop Map Metropoliis 2006-2010 Unit DS10 - Kayleigh Dickson

MOOP _ [Noun[

_ 2006

_ 2007

_ 2008

_ 2009

STEP 1 _ LINE UP!

Matter Out Of Place; especially as it applies to Black Rock City and itâ€™s citizens. _ Can Be Anything: cigarette butts, bottle caps, glowsticks, fireworks, but is often disguised as DEBRIS [i.e. broken bits of Wood, Plastic, Metal Glass, and Plants]

_ Can Also Be A Condition: Burn Scars, Grey Water, Dunes ...

MOOP _ [Verb] To pick up Matter Out Of Place.

STEP 2 _ SPREAD OUT!

LINE SWEEP _ [Noun] A forward moving line of moopers side by side and arms width apart; a quick and efficent community effort for scanning and piocking up Matter Out Of Place over a given areaof playa surface such as your camp, city block, art installation, village, etc ...

6 Foot

6 Foot

6 Foot

6 Foot

6 Foot

The Rule Of Thumb for Line Sweeps: Width of Camp [divided by] Arms Width Apart [approx 6ft] = OPTIMAL NUMBER OF MOOPERS

STEP 3 _ MOOP OUT! RED _ High Impact Trace

EXAMPLE _ A camp that is 60 ft wide should have atleast 10 Mooperson The Line

Also known as Hot Spots, the impact trace conditions embedded into the playain your vicinity were heavily problematic and spread out over a vast area. Set your boundaries, do your Line Sweep, Identify the issues, restore ... GO GREEN!

YELLOW _ Moderate Impact Trace While neither the best or the worst, your impact trace is the Ever-Changing Average. On the bright side, with a good strategy your camp has a strong potential to go green,. However slack and your camp can up in the Red!

RED _ Low Impact Trace Green as in GO! GO! GO! You Leave No Trace.

REPRESENTATION OF THE PLAYA Water, Water Everywhere

_ PROCESS

_ CRACK FORMATION FROM A HIGHLY MOISTURED SURFACE

_ CRACK FORMATION

SCALE _ 1:75

Unit DS10 - Kayleigh Dickson

Most camps need to dispose of grey water during Burning Man. Grey water is produced from cooking, dish washing, and hair and body washing. Our permit from BLM does NOT allow us to dump grey water directly onto the playa. Therefore all grey water must be collected. Camps can then remove that water directly off the playa (by themselves or using Johnny on the Spot). Some camps may choose to use evaporation ponds to reduce the amount of water they need to haul off the playa, but these ponds can easily get clogged with dust. Some camps have even developed technologies to reuse their water. The appropriate methodology for you depends on the size of your camp, your background and experience, and the level of energy you want to spend dealing with grey water. What’s Simple? Small and mid-sized camps can collect your grey water and take it to several RV dump stations along highway 80 and in Reno after the event. A few are listed below. Please check with the dumping station before the event for disposal charges and determine if they can handle the amount of water you are planning to dump! Larger camps should consider setting up a contract with Johnny on the Spot to collect grey water. With 30 days notice, they will provide a collection tank for you at the event that they will collect at the end of the event for disposal. How can I reduce my grey water? First - remember Conservation, Conservation, Conservation! In your kitchen area, set up a low-volume water spray over a basin, for dishwashing and hand cleaning. A personal spray bottle, like the Cool Blast, is a good starting point. You’ll need remarkably little water to wash up with. Assign a water cop in your camp to remind campmates that you’re in the desert, not at home. Use a biodegradable detergent instead of soap. Camp Suds, available at REI, works well for dishes, hands, and showers. Rub your hands with a few drops of a waterless disinfectant lotion, available at drugstores, before you handle food. This saves water and is also good camp hygiene. Evaporation ponds are a technique that has been shown to reduce the volume of grey water. It is, however, important to construct a pond that is big enough for your camp. Too big - it will still work great. Too small - it stops working when the water gets too deep! Also limit showers the last few days of the event before you’ll need to pack up the evaporative pond for disposal. The cracks have formed in a natural formation without any intervention by myself or any other influencing factors. Not all of the cracks are complete though all the rules still main the natural rule of angles, this is starting to display a set of natural territories that occur in the clay. These ‘territories’ that start to appear could start to define the boundaries of a program.

TESTING: MATERIAL EXPERIMENTATION Latex and Expanding Foam

Unit DS10 - Kayleigh Dickson

_ LATEX PROCESS

_ CRACK FORMATION IMPRINTED IN THE SURFACE OF THE LATEX

_ EXPANDING FOAM PROCESS

_ CRACK FORMATION IMPRINTED IN THE SURFACE OF THE EXPANDING FOAM

EXPERIMENTATION - ANALYSIS - SITE Predetermined Cracking Through Specific Points Unit DS10 - Kayleigh Dickson

_ CRACKING AND ANALYSIS PROCESS

_ PINNING PROCESS

GREY WATER RECYCLING AND CAPILLARY ACTION STRUCTURE Environmental studies

_ FLOOR EVAPORATION AND RECYCLING POND PLAN

_ COOL WALL FILTRATION ELEVATION

Unit DS10 - Kayleigh Dickson

The design incorporates five systems in order to achieve a closed loop system, of which grey water and capillary structure are two. The grey water evaporative system provides a sustainable system that results in less water having to be removed from Burning Man’s site and also Burning Man’s policy that no grey water may be dumped on the Playa. Here is demonstrated how the water can be circulated through two of these systems. This will be highly dependant of positioning, the suns path and the needs of the system.

_ Grey Water Recycling Ponds

_ Grey Water Evaporation Ponds

_ Water is filtrated through the capiliary pipes to the base of the wick wall. The water will collect at the bottom of the pool being absorbed up the fabric to cool the internal space. The water will then be filtrated to be used as drinking water.

_ GREY WATER EVAPORATION PONDS

_ SHOWERS

_ WATER FILTRATION PIPE SYSTEM

_ CAPILLARY EVAPORATION WALL

_ SLOW SAND FILTRATION

_ RECYCLED WATER RESERVOIR

PEELING BACK THE BURNING MAN PLAYA

Unit DS10 - Kayleigh Dickson

PEELING BACK THE BURNING MAN PLAYA PLAN

Unit DS10 - Kayleigh Dickson

SLOW SAND FILTRATION

CLOSED LOOP SYSTEM:

PINNING THE PLAYA

SHOWERING the filtration of water for recycling

WATER FILTRATION PIPESleads the water away from the showers to the evaporative wall

EVAPORATION WALL -

absorbs the water up the wall through capillary action

SLOW SAND FILTRATION -

will remove the smallest particles from the water

WATER RESERVOIR -

will remove the smallest particles from the water

GREY WATER EVAPORATION PONDS -

evaporation of grey water such as shower, hygiene and dish water.

EVAPORATIVE COOLING

WATER RESERVOIRS

SOLAR HEATED WATER PONDS

GREY WATER EVAPORATION PONDS