Brief 01 + 02 | TEST + TEMPLATE Brief 01 | Test - Harmonics Analyse three generative natural, structural, geometrical, physical or mathematical systems. Using digital and physical modelling tools gain an understanding of the rules that govern the systems. Systems chosen - Harmonics Fungi Cephalopod
[Presented in Appendix A] [Presented in Appendix B]
Brief 02 | Template - Burning Man Festival Developing one or more of the systems analysed, design an installation to be built in Black Rock Desert, Nevada, USA, as part of Burning Man Festival 2013. Explore Burning Man Festival’s founding principles and ideas relating to temporary and modular construction techniques.
Brief 01 | Test - Appendices - Fungi & Cephalopod Systems chosen - Harmonics Fungi Cephalopod
[Presented in Appendix A] [Presented in Appendix B]
Brief 01 | Test - Harmonics Harmonics | Physical recording machines Harmonograph with two pendulums Simulated harmonograph - 2D Consonance and dissonance Simulated harmonograph - 3D Augmented reality - 3D harmonograph representation
Harmonics | Physical recording machines Open Phase
Closed Phase
Intervals
1:1 Unison
The harmonograph was invented in the late 1800s as an instrument for exploring harmonics, but because popular as a Victorian parlour toy. It uses two pendulums attached by levers to a single drawing instrument. It maps the relationship between the two pendulums as a drawn graph. The frequency of the pendulums can be changed by changing their lengths. This is done by moving the weights up and down the length of the pendulum shaft.
2:1 Octave
3:2 Fifth
4:3 Fourth
5:3 Major sixth
5:4 Major third
6:5 Minor third
8:5 Minor sixth 1
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9:8 Wholetone
3 1. A Victorian Two-Pendulum Harmonograph from the Science Museum 2. Pintograph with equally sized cams, powered by two separate variable speed motors 3. Output drawings form the pintograph. 4. Diagrams showing the relationship between wavelenght and harmony 5. Diagram explaining the way that Lissajous curves represent simple harmonic relationships
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The harmonic relationship between the two pendulums produces patterns that relate to the Lissajous curves [pictured left], that map the relationship between two perpendicular sine waves. The pintograph is another mechanical means of recording a harmonic relationship, this time between the circular motion of two gears using a simple set of levers. A simple pintograph powered by tow small electric motors is shown [left]. The main difference between the figures drawn by a pintograph and harmonograph is that the harmonograph has a decay element due to friction decreasing the amplitude of the pendulums over time, whereas the pintograph runs at a constant amplitude, and therefore produces drawings that are closer to the Lissajous curves.
Harmonics | Harmonograph with two pendulums Constructed using softwood dowel and with pivots and hinges made from 1mm piano wire, the physical Two Pendulum Harmonograph managed to produce some interesting results.
Ratio 2:3
The pendulums were made from 4.5kg cast iron weights attached to the softwood dowel by a screw fixing. The lengths of the pendulums were fully adjustable by moving the weights up and down the dowel. Experiments with different weights and length ratios indicated that larger weight meant that the decay rate was slower, and that ratios close to but not exactly on harmonic ratios gave the most interesting an clear patterns.
Ratio 3:4
Ratio 7:10 Platform and pen move against each other to draw the graph Unidirectional pivot allows pendulums to swing along opposing axes [X and Y] Ratio 8:10
Length of pendulum can be adjusted by moving weights vertically
Ratio 9:10
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1. Diagram showing the constructed harmonograph made from softwood 2. Drawings in red pen from the physically constructed harmonograph - categorized by harmonic relationship between the two pendulums. 3. Diagram showing the principles of a two pendulum harmonograph
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Harmonics | Simulated harmonograph - 2D The equation that describes a harmonograph is essentially the relationship between two decaying sine waves. The Lissajous Curves [far left] at the cross product of two sine waves, and the Grasshopper definition that created these simulated harmonograph drawings is simply an extension of this principle. The decay rate is set as an adjustable constant. The following equation is the basis for this Grasshopper definition, which simulates a two pendulum harmonograph producing a 2D output. X = sin(at)*(1-kt) Y = sin(b(t+d))*(1-kt) t = time [s] a = X frequency [Hz] b = Y frequency [Hz] d = Y phase displacement [s] k = decay [fraction/cycle]
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Adjustable sliders control frequency, phase and decay
1. Harmonograph produced where harmonic ratio is nearly 1:1 2. Lissajous Curves made from non decaying sine waves at different harmonies 3. Simulated two pendulum 2D harmonographs created using Grasshopper definition - images created using different harmonies 4. Grasshopper definition used to create the above harmonographs
Performs the required mathematical function on a series of numbers to be used as X, Y co-ordinates
Plots points according to X,Y functions, and interpolates these into a smooth curve
Harmonics | Consonance and dissonance As the ratio between the frequencies of the x and y axes are changed, the harmonograph output is changed, as the plots the relationship between the two frequencies. This corresponds to changing the ratio of pendulum lengths in a physical harmonograph. Interestingly, there are points at which the ratios are simple [1:1, 1:2, 2:3, 3:4, etc], and the harmonographs are correspondingly simple. These are also the ratios of frequencies at which musical notes sound harmonious. In the diagram opposite, the difference between the consonant and dissonant ratios is very clear to see. The consonant harmonographs appear to pop out from a huge sea of dissonant ones. All of the harmonographs to the left were digitally simulated using the equation below.
X = sin(at)*(1-kt) Y = sin(b(t+d))*(1-kt) t = time [s] a = X frequency [Hz] b = Y frequency [Hz] d = Y phase displacement [s] k = decay [fraction/cycle]
1 1. A series of 2D harmonographs showing the difference between the consonance and dissonance displayed by different ratios of frequencies. Starting top left and progressing in horizontal lines, the ratio of X Freq [Hz] to Y Freq [Hz] increases in the following series: 10:0 , 10:1, 10:2, 10:3 , 10:4, 10:5, etc... 2. Close up views of a harmonious ratio [10:15 or 2:3] and a dissonant ratio [10:77]
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Harmonics | Simulated harmonograph - 3D The equation that describes the physically modelled two pendulum 2D harmonograph can easily be extended into three dimensions simply by adding a another sine wave in the Z axis. This is fficult to represent graphically on paper, as the 3D form is inevitably compressed into two dimensions in exporting an image. However it is possible to see in the series of view of the same form [left] that the form is defined by the harmonic relationship between these three waves, with the harmonic relationship between any two being seen at one time. The equations used to create the Grasshopper definition are as follows: X = sin(at)*(1-kt) Y = sin(b(t+d))*(1-kt) Z = sin(c(t+e)*(1-kt) t = time [s] a = X frequency [Hz] b = Y frequency [Hz] c = Z frequency [Hz] d = Y phase displacement [s] e = Z phase displacement [s] k = decay [fraction/cycle]
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Plots points according to X,Y,Z functions, and interpolates these into a smooth curve
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Adjustable sliders control frequency, phase and decay
1. A 3D harmonograph created using Grasshopper 2. Simulated three pendulum 3D harmonographs created using Grasshopper definition - images created differently rotated views of the same harmony 3. Grasshopper definition used to create the above harmonograph
Performs the required mathematical function on a series of numbers to be used as X, Y, Z co-ordinates
Harmonics | Augmented reality - 3D harmonograph representation The output of a 3D harmonograph simulated in Grassshopper is a 3D model composed of a single interwoven spiralling curve. Because the curve never intersects itself it its not suitable for 3D printing without modification. It is a very challenging thing to make in the physical world, and its therefor more suited to digital presentation. The challenge is to be able to pass on an understanding of the form as a three dimensional object without it appearing like a projection of a three dimensional form onto a two dimensional surface [the screen]. In order to achieve this it helps to either have the model rotating in space or to be able to manipulate the model in space yourself. For this reason augmented reality programs have been explored here as a way to present work. Two programs were tested; Autodesk Showcase AR Plugin and LinceoVR. The outcome of the tests is the ability to use LinceoVR to present virtual 3D models that can be manipulated by a viewer with their hands, by the process of moving a ‘marker’ that is tagged into the digital model. The viewer and marker are filmed, and the digital model is mapped into the video feed in real time, so that it appears to the viewer that they are manipulating the model.
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1. Multiple digital models can be tagged wtih physical ‘markers’. when these markers are moved into the view of the live video feed, ther software grafts the models into the feed 2-3. Screen shots of the augmented reality software being used to present a digital model.
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Harmonics | Simulated harmonograph - 3D
Brief 02 | Template - Burning Man Festival Burning Man | Physical context Social context Sacred & harmonic geometry Near Unison | Tracing with light Leaving a trace Decay and friction Concept & prototype - Interactive harmonograph 3D Harmonograph generation Construction process 1:10 Prototype Shadows and Moire patterns Visualisation - Day Visualisation - Night Harmonographic sand traces [physical model page]
Burning Man | Physical context The Black Rock Playa is the location for Black Rock City, the annual temporary home of Burning Man festival. The temporary city of 50,000 people is set up over a period of 3 weeks, inhabited for 10 days, and dismantled and removed at the end. Burning Man’s extreme location underpins the need the ‘radical self-reliance’ set out in the guiding principles for Burning Man. The temperature in September, when the festival happens, is around 30°C in the day and 6°C at night. The air is generally very dry, and dust storms with winds of up to 50mph are very common. The dust is also quite alkaline, and can irritate eyes and skin. The Black Rock Playa, elevation 1191m, is the second largest flat region in the Northern Hemisphere. Shaped like a “Y”, the Black Rock can be divided into 3 parts: the playa, west arm, and east arm. The longest stretch of playa is 27 miles along the west arm. South of the intersecting arms, the widest spot is 12 miles.
Black Rock City
USA
Nevada
Black Rock Desert
A very immediate relationship with the environment that comes from camping under such harsh conditions. This relationship has been used to guide Rod Garrett’s city plan as it has evolved over the last 15 years. “Large artworks were placed in a zone outside the precincts of our city. This was meant to lure participants away from our settlement and into the great silence and open space. Similarly, the open side to the circular scheme of the city takes on spiritual and psychological importance. Instead of completely circling the wagons, we invite the natural world to intrude. We will never further close that arc. It is humbling to have the vast desert and sky intrude into our self-styled small world.“ Rod Gerrett [Black Rock City master-planner]
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Sand and dust surface of the Black Rock Desert
Participants caught out in a dust storm on the Black Rock Playa [Detail]
Burning Man | Social context Immediacy
De-commodification
‘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.’
Gifting
Leaving No Trace
‘Practicing a Leave No Trace Ethic is very simple: leave the place you visit the same or better than you found it; leave no trace of your having been there, so that others – both human and animal – can enjoy the land the rest of the year.’
Radical Self-reliance
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.’
Radical Self-expression
Radical Inclusion
Participation
Civic Responsibility
‘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.’
The 10 principles of Burning Man illustrated through photographs from Burning Man 2011 Photographs accessed via www.burningman.com
Burning Man sets out 10 principle to guide participants while they are in Black Rock City for the duration of the festival. Communal effort, participation and immediacy are the three principles that underpin the main aim of Burning Man, which is to allow free individuals to come together as communities to produce, enjoy, share experiences and spectacles that couldn’t or wouldn’t be achieved without participation from everyone. There are elements of all of these principles that the organisers believe are missing in the every-day lives of twenty-first century American citizens, and Burning Man sets out to be an outlet for these feelings, and a prototypical society building on them. The ethic of ‘Leave No Trace’ pervades Burning Man, with everything needed for the festival brought on-site beforehand and taken away afterwards. The idea is that the Playa should be left in exactly the same state that it was found in. This is taken very seriously, with everyone expected to clear up their own rubbish, right the way down to down to cleaning the Playa surface with magnets to pick up loose screws.
Burning Man | Sacred & harmonic geometry Burning Man Festival was founded as a beach party with its roots in pagan ritual. Its circular shape with an opening out along the valley of Black Rock Desert recalls the idea of wagons round a fire while also using simple geometric tools. It also recalls ideas relating to ancient temple layouts that have the suns path as their focus. There is a great deal of interest at Burning Man Festival in all things relating to sacred geometry and harmony, Johannes Keplar’s ‘Music of the Spheres’ attempted to relate harmonic geometry to the movements of the planets.
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1. Johannes Keplar’s ‘Music of the Spheres’ demonstrated his ideas about the harmonic relationships between the orbits of the planets 2. Diagram showing the relative positions of Earth and Venus a durations of 8 orbits - Demonstrating the harmonic ratio between the two. 3. Black Rock City’s circular plan with radial elements relating to times on the clock face 4. Harmonographs as a mathematical representation of a harmonic ratio 5. Sun worship at Burning Man Festival 6. Dancers at tBurning Man Festival using Fire Poi to leave traces of movements
Near Unison | Tracing with light Burning Man festival is alive at night, with light and fire playing an important role in the success of artworks and events. Acts and dances involving the use of fire and light include the Fire Poi - a flaming ball on the end of a string, that is used to create swirling races of movement during dances. A similar effect can be achieved ussing LED lights and long exposure photography. The idea of tracing movement using light works well with Harmonogrphs, and can be used to great effect to trace the movement of a pendulum without a physical mark being made. The face that there is much less friction that when using a pen means that the pendulums swing for much longer and produce very fine results. The idea of a physical space defined by the trace of a set of movements from the past is then explored in a sketch model using strands of Electroluminescent Wire.
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2 1. Fire Poi being used at Burning Man 2011 - leaving traces of the user’s movement hanging in the air 2. Initial experimentation using an LED and long exposure photograph to capture movement 3. An LED attached to a 2m long pendulum can creates beautiful harmonographs when photographed using long exposures; in this case 20 seconds; 2 minutes, 5 minutes, and 20 minutes 4. Initial experiments with electroluminescent wire to create glowing structures along the lines of traced movement
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Near Unison | Tracing Nearwith Unison light|
Concept | Near Unison - Leaving a trace Burning Man festival’s policy of ‘Leaving No Trace’ is interesting, because, although the organisers and participants are very careful to remove all physical objects from the Playa, there are still tracks in the sand that remain long after Black Rock City has been dismantled. These traces are only levelled over time by the wind and the rain that turns the Playa into a lake bed in the Winter. A series of experiments with pendulums explores the possibility of scratching a memory of a movement into a sand or dust overed surface. This could act as a way of leaving a trace of the participants activities while still keeping within the ‘Leave No Trace’ ethic. 00 seconds
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120 seconds
240 seconds The weight of the pendulum is of key iportance when marking into sand sue to the increase friction making the decay rate more rapid. The pendulum pictured was 2m long, with 5kg of weight, and produced a trace approximatedly 700mm in diameter. To produces larger traces a full harmonograph apparatus would need to be used, with a proportionate increase in weight and pendulum length. Jim Denevan’s nine mile wide land art piece in Black Rock Desert sets a precedent for marking movement into the sand to leave a trace of an event that lasts until the wind or rain wipes it away.
2 1. Sequence of photos showing the act of a harmonograph being traced into a bed of sand 2. Detail photos showing the traced harmonographic pattern traced into the sand 3. Jim Denevan - Land art in the Black Rock Desert - Large scale marks in the sand made using tire tracks create a geometric trace of movement
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Near Unison | Decay and friction The depth to which the pendulum penetrates the sand is another factor in the pattern created. Friction between the pendulum and the sand increases proportionally to the amount of contact between the two. With more friction, the pendulums oscillation decays more rapidly, meaning that it can perform fewer cycles before it stops completely. The effect of friction can be minimised by increasing the weight of the pendulum. The photos below show four different depths, and therefore four different patterns,. However they are all created by the same 5Kg, 2m long pendulum, swung from the same starting point.
1 1. Sand penetrated to different depths - 15mm depth - 1 cycle; 10mm depth - 2 cycles; 5mm depth - 4 cycles; 2mm depth - 5 cycles
Near Unison | Concept & Prototype - Interactive harmonograph The trace left by a single pendulum is dependent only on its own characteristics and its starting vector. The trace let by two connected pendulums as in the harmonograph show [far left] can be much more complex and refined, and will show the relationship between the two pendulums. By shifting the weight up and down the shaft of one of the pendulums, the centre of gravity, and therefore the effective length of the pendulum is changed. At a larger scale, this weight could be a person, who could shift their weight to change the effective length of the pendulum they were riding. If two of these ‘sit on’ pendulums were connected together they could create an interactive harmonograph, where the interaction between two participants would be drawn. A prototype has shown this to work in principle: refinement is necessary in order that the two pendulums do not twist on their own axes.
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1. Harmonograph with three pendulums: showing the principle of connecting two pendulums together to achieve a trace of their interaction 2. Concept of a large sit-on harmonograph 3. Photograph of the first test of the 1:1 prototype interactive harmonograph 4. Construction diagram for the 1:1 prototype 5. Photos of the construction of the 1:1 prototype
Near Unison | 3D Harmonograph generation The 3D Harmonograph that is used for the permanent structure of the pavilion uses the concept of working in ‘Unison’ and ‘Near Unison’. The frequencies used for the three axes are almost the same, [x=2.040Hz, y=2.020Hz, and z=2.024Hz]; which equates to a physical harmonograph that uses pendulums with lengths that are almost exactly the same, but not quite.
Ratio 2:3
Ratio 3:4
Ratio 7:10
Ratio 8:10
Ratio 9:10
Near Unison - 99:100
The 3D Harmonograph generated from this set of frequencies is sectioned with the ground plane to create a set of related harmonograph curves, which are then sectioned in the vertical plane in order to create a cross braced structure from curves that otherwise do not intersect. This then becomes an inhabitable, climbable, harmonographic space.
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t = time [s] a = X frequency [Hz] b = Y frequency [Hz] c = Z frequency [Hz] d = Y phase displacement [s] e = Z phase displacement [s] k = decay [fraction/cycle] 2 1. Drawings in red pen from the physically constructed harmonograph - categorized by harmonic relationship between the two pendulums. 2. Diagrams showing the process of turning a 3D Harmonograph into a buildable structure using the principle of intersection with planes; demonstrated using a ‘Near Unison’ 3 axis harmonograph with the relevant frequencies listed below the diagram.
Using a set of frequencies in the ‘Near Unison’ range means that the tiny differences between the three axes have huge implications on the dynamic of the harmonograph output. this is appropriate for Burning Man festival as it is analogous to the collective yet radical spirit of the fesival: many different characters coming together to celebrate their shared humanity.
= 2.040 Hz = 2.020 Hz = 2.024 Hz = 4.915 seconds = 7.372 seconds = 23.236 cycles
X = sin(at)*(1-kt) Y = sin(b(t+d))*(1-kt) Z = sin(c(t+e)*(1-kt)
Near Unison | Construction process The principle behind the construction is that a straight pipe bent in its elastic zone will want to return to a straight line. This springiness is exploited to add a flexible yet strong layer that weaves into a series of laminated plywood section. The photographs below show the CNC milling of a 1:10 prototype plywood sections. The full scale plywood sections would need to be cut in several parts with staggered joints and laminated together afterwards. The base plates are made in the same way as the plywood sections, with holes drilled to allow the pipes to pass through but fit tightly. These holes are to be cut using a 4 axis robot so that the correct angles can be specified. These are then held in place with wedges. The different radii of the curves of all of the different pipes fight against each other and help to stiffen the structure.
Approximatedly 1000m of 32mm diameter plastic pipe is used to create the curves of the 3D harmonograph,
Standard sheets of 19mm structural plywood are CNC cut and laminated together into thicker sections to be assembled onsite. 1
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1. Materials palette showing that the structure is primarily made from plywood and plastic water-pipe - cheap and readily available materials 2. Construction elements diagram - Base plate, Plywood sections, with pendulum swings attached, and plastic pipe harmonograph curves 3. CNC cutting drawings from a 1:10 prototype; at full scale these would need to be divided into smaller sections, spread over several laminations to achieve the required thickness and stiffness. A 4 axis CNC router would need to be used in order to drill the holes for the pipes at the correct angles; on the 1:10 prototype this was done by hand and was very labour intensive. 4. Photograph of the 3 axis CNC router cutting the 1:10 prototype
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Near Unison | 1:10 Prototype
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1. Screen capture from the CNC interface during cutting process for the 1:10 prototype 2. CNC cut 6.5mm plywood sheet to make 1:10 prototype 3. Photograph of construction of the 1:10 prototype 4. Detail photographs of the 1:10 prototype showing the way that the harmonograph lines appear to cross over each other in space, creating moire patterns
Near Unison | Shadows and Moire patterns As the structure of the installation is a 3D harmonograph, when the sunlight shines through it, the shadow it casts on the ground is that of a 2D harmonograph. As the sun’s position in the sky moves throughout the day, the shadow changes. This change is very closely related to the ‘phase’ of the 2D harmonograph. This is the amount by which the sine wave on each axis is offset relative to the other. The diagrams below show the same harmonic relationship with only the phase changed. The shadow harmonograph appears as an extension to the 3D harmonograph, and when one is viewed through the other, interesting moire patterns emerge.
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1. Render of Near Unison showing 3D harmonograph structure and the 2D harmongraphic shadow cast at midday during September 2. Sun-path diagram for Black Rock City during September 3. A series of harmonographs all created using the harmonic ratio 2:3, showing the effect of changing the phase of one sine wave against another; a similar affect to projecting sun rays through a 3D harmonograph 4. Shadow diagrams showing the harmonographic shadows cast at different points during the day. Note the moire patterns caused when viewing the shadow through the structure
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Near Unison | Visualisation - Day
Near Unison | Visualisation - Night
Near Near Unison Unison | Visualisation | Visualisation - Night - Day
Brief 01 | Appendix A - Fungi Fungi | Life-cycle and macro structure Mycelium macro structure Simulated mycelium growth - 2D Simulated mycelium growth on a surface Prototype - Myceliated harmonographic surface Simulated mycelium growth - 3D Sporocarp growth through inflation Sporocarp growth experiment Simulated pileus inflation Simulated stipe growth Simulated lamellae arrangement Sporocarp parametric simulation
Fungi | Life-cycle and macro structure Fungi has a lifecycle that includes phases of both sexual and asexual reproduction. When a spore lands on a food source, it begins to form into a hyphae. This hyphae then grows at its tip, and if it finds sufficient food, it will split and clone itself. This process of asexual reproduction contnues unti the fungi has completely engulfed its food source. Thie network of hyphae that forms is called mycellium. As it spawned from only on spore, it is haploid. When a the mycelium meets another patch of myceilum from another spore it fuses and becomes diploid. The hyphae then have two independent nuclei. It is then able to spores by sexual reproduction occurring within the hypae. Once a patch of diploid mycellium has established itself and comes under environmental stress ti will form pin like balls of tightly packed hyphae called primordium. These primordium develop the structure of the sporocarp [fruiting body] at a small scale. During the next period of increased moisture [usually from rain], the mycelium routes water into the primordium causing it to swell and mature into a fully fledged sporocarp. The sporophore [spore carrying] layer of this sporocarp is found on the hymenophore, which can take the form of teeth, threads or lamellae [gills]. Once the spores are ready, they are released into the air by a process called ballistospore discharge, and may form new colonies where ever they land.
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1. Diagram showing the process of growing edible fungi at home serops
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Fungi | Mycelium macro structure Hyphae grow by apical extension; that is they grow from their tips. The fungus proliferates by branching, each tip elongates. Lateral cell division seen in tissues of plants and animals is not found in the fungi. Yet a variety of complex hyphal structures are observed. Lift a layer of moist leaf litter in the forest and a series of strands or cords are evident. These strands have a definite, aggregated structure and appear to link wefts of hyphae ramifying through the degrading litter. Some of the strands resemble shoe-laces indicating complex structure. The coarser strands are called rhizomorphs. They have a definite tubular structure. In transverse section, the outer layer of cells is thick-walled, empty of cytoplasm, and often melanised. The outer layer often contains hydrophobins at the surface of the wall. LINK The inner tissue is comparatively thin walled, and the cytoplasm is active. Often the core of the rhizomorph lacks cells, allowing movement of air, water and solutes to pass along the tube. The strand also has hyphal connections to the surrounding environment. Where the soil contains nutrient rich materials, the hyphae form a weft through the materials, and a major strand or rhizomorph may develop, establishing a branched structure. Over time, the degree of branching and pattern of rhizomorph distribution through the litter will change, reflecting the changing patterns of distribution of nutrients, and competition with other fungi. 1
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1-6. Mycelium growing out from a sporocarp that has been stored in a damp paper bag. The mycelium is composed of the same hypae that make up the rest of the sporocarp. 7. Diagram showing the branching structure of expolring hypae spreading out in the search for food. When the food supply is exhausted the fungi will either fruit in order to spread to another locationn or die off in patches.
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Fungi | Simulated mycelium growth - 2D In a situation where a spore settles somewhere with a sufficient food source and water content, it will begin to grow asexually into a hypae. Assuming that it finds another source of energy, it will continue to extend from its apex and clone itself. Hypae often branch out to explore their environment for potential energy sources. This simulation of mycelium growth by hypae branching and extension works by using points as to simulate potential food sources. A hypae will successfully survive if it reaches another food source that is within its maximum growth reach. This simple rule of branching and growth towards the nearest food nevertheless creates complex patterns that mimic the growth of mycelium cultures being grown in controlled 2D environments, for example a petri dish.
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Septum Growth from the tip of the Hypae 3 Hypae Creates a field of randomly placed points to act as ‘food’ for the mycelieum
Sets spore location and maxiumum reach to get food
Uses ‘Hoopsnake’ to repeat an iterative ‘food search’ branching process
1. Fungi mycelium growth from in 2D from a single spore generated using Hoopsnake for Grasshopper to loop an iterative process of growth 2. The same Grasshopper definition applied to three spores in the same food source 3. Grasshopper definition with explanation 4-6. Mycelium growing in almost 2D environments - agar jelly in a petri dish.
An expansion of the ‘food search’ process moves towards athe two or three closest food sources as long as they are within reaching distance; plots a line of this search, then culls the ‘eaten’ food from the food availabe for the next iteration.
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Fungi | Simulated mycelium growth - 2D
Fungi | Simulated mycelium growth on a surface As the simulateed mycelium growth pattern works by serching for the nearest avaiable food source [points], it can be made to ‘eat’ any specified collection of points. If a mesh is exploded in Grasshopper, a point at each vertex can be collected. This collection of points spead over the surface of the mesh can then be ‘fed’ to the mycelium growht definition. This effectively simulates the growth of a layer of mycelium over the surface of the mesh.
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Iteration 12
Iteration 19
Iteration 26
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1. Diagram showing the growth of mycelium over the surface of a predefined mesh; simulated using Grashsshopper 2-3. Renders showing a branched structure created by simulated growing mycelium over a mesh
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As the density of points depends on the density of the mesh, the mycellium can be directed towards areas of ‘high energy food’ and to void areas of ‘low energy food’ by altering the desity of the mesh in those locations. A too such as Weaverbird can by used to do this in Grasshopper. This gives a certain amount of control over the branching strucutre, while still leaving it up to the definition to work out the end path.
Fungi | Prototype - Myceliated harmonographic surface
Fungi | Simulated mycelium growth - 3D The same Grasshopper definition as created the simple 2D idealised mycelium growth pattersn can also be utilised to grow a 3D version of the fungi. This time the input ‘food’ for the mycellium definition is a field of randomly placed points within a 3D box. The hyphae strands move in three dimensions towards their nearest food source within reach. The way that the mycelium seeks out areas of high food density is more apparent in the way that this definition grows in 3D.
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Iteration 5
Iteration 8
Iteration 13
Iteration 16
Iteration 19
Iteration 22
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Iteration 25 2 1. Grasshopper definition simulating mycelium growth in 3D - diagram showing growth over 22 iterations 2. Growth pattern after 25 iterations of the mycelium growth definition 3. Photos of mycelium grwoth showing the branching system
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Fungi | Sporocarp growth through inflation A mushroom is the fleshy, spore-bearing fruiting body of a fungus, typically produced above ground on soil or on its food source. The word “mushroom” is most often applied to those fungi that have a stem (stipe), a cap (pileus), and gills (lamellae, sing. lamella) or pores on the underside of the cap. Forms deviating from the standard morphology usually have more specific names, such as “puffball”, “stinkhorn”, and “morel”, and gilled mushrooms themselves are often called “agarics”. By extension, the term “mushroom” can also designate the entire fungus when in culture; the thallus (called a mycelium) of species forming the fruiting bodies called mushrooms; or the species itself.
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Pileus
Hymenium [Lamellae] Annulus
Stipe
Base
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1-2. Photos of a the lamellae of a mushroom 3. Fungus growing parasitically on the side of a tree 4. Photo showing the development of a mushroom above ground 5-6. Photos detailing two large mushrooms at different stages of development 7. Diagram showing the different sections of a generic mushroom
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Fungi | Sporocarp growth experiment The rapid expansion of a crop of mushrooms from the edible Elm Fungi was grown on a bed of damp straw. The inflation of the sprorocarps occurred over a period of two days, and was aided by spraying several times a day with a light mist of water. This was rapidly absorbed into the hypal tissue of the sporocarps, and used to further inflate them. At the end of the experiment they were cooked and eaten as a delicious meal.
1 1. Series of photos showing the expansion of sporocarp over a two day period
Fungi | Sporocarp growth experiment The sporocarps of Elm Fungi grow in clusters. The pin mushrooms begin very close to each other, and compete with one another for available water and space to grow as they grow against gravity. This results in many variations of the ideal sporocarp form as the individuals push each other out of the way and sometimes merge into each other.
1 1. Detail photos of Elm Fungi sporocarps showing the lamellae on the underside, and the difference in form cause by competition for space and water.
Fungi | Simulated pileus inflation The pileus is the ‘cap’ of the sporocarp [fruiting body] of a fungus, that supports the spore holding hymenophore layer beneath it. Pileus can come in many shapes and sizes depending on environmental factors as well as species; as demonstrated in Diagram 1.
Cap Morphology - Irregularity Altering the curve that acts as the outer edge of the cap
Conical
A sporocarp develops from a pin [nodule] around a millimetre in diameter, called a primordium, which is typically found on or near the surface of the growing medium. It is formed within the mycelium, the mass of threadlike hyphae that make up the fungus. The primordium enlarges into a roundish structure of interwoven hyphae roughly resembling an egg, called a “button”.
Ovate
Once such the primordium is formed, the mushroom can rapidly pull in water from its mycelium and expand, mainly by inflating preformed cells that took several days to form in the primordia.
Cap Morphology - Inflation Adjusting the amount that the cap is inflated
The Grasshopper definition below models the pileus as an inflated surface connected at its outer edge. It uses ‘Kangaroo’ physics simulation to apply a uniform force over the inside of the upper surface of the pileus, in the direction of the growth of the sporocarp
Campanulate
The definition allows a pileus to be formed from any edge curve shape, and with a degree of control over the amount of inflation that allows it to range from a depressed cap to an ovate cap sporocarp.
Convex
The tests pictured show variations in irregularity, inflation, and tilt of the pileus.
Cap Morphology - Tilt Adjusting the angle of the cap compared to the growing medium
A commercially grown mushroom grows from 1 to 34 mm in height (i.e. a vertical linear change of 34x), the circumference of the stipe increases 9x, the outer circumference of the pileus increases 15x, but the volume increases more than 3000x.
Flat Sliders control inflation through force and stiffness
Depressed
Umbillicate
Infundibuliform
Input outer edge curve and stipe base point
VB Script creates a patch for the base of the pileus
Vector from stipe base to pileus centre determines inflation direction
Uniform force in the direction of mushroom growth
Kangaroo physics simulation used to inflate the pileus
Fungi | Simulated stipe growth Most, but not all, mushrooms have stipes [stalks] that connect the fruiting body back to the mycelium. They are also the structural connection from the pileus and hymenophore to the growing medium, as well as carrying water and nutrients.
Stipe Morphology - Slant Moving the base connection point in comparison to the mushroom body
The stipe can be central and support the cap in the middle, or it may be off-centre as in species of Pleurotus and Panus. In other mushrooms, a stipe may be absent, as in the polypores that form shelf-like brackets The Grasshopper definition below models the stipe of a mushroom by scaling an extrusion of the pileus shape as it goes down towards the base connection point of the mushroom. The shape of the stipe is determined by a function of the cube of the distance from the base. This means that the stipe generally thickens out rapidly as it reaches the underside of the pileus. This enables the definition to model mushrooms with stipes varying from a stumpy button mushroom to an elegant oyster mushroom.
Stipe Morphology - Thickness Adjusting the relationship between the cube of the distance to the base and a uniform thickness
The stipe is formed from hypae that bind together in parallel lines. They differentiate and while the outer ones remain narrow and act as a barrier, the inner ones loose the septae dividing the hypae, so that they become hollow tubes, through which water and other nutrients can flow. It is these larger tubes that route the water needed for the rapid inflation of the pilius.
Widened hyphae with septae dissolved away allow for vertical transport of fluid to aid rapid cap inflation
Densely woven hypae towards the edge of the stipe maintain a barrier to the external environment
Slilders control the power of the cubed distance against the uniform thickness
Input outer edge curve and stipe base point
Vector from stipe base to pileus centre determines inflation direction
Creates a series of copies of the base of the pileus, growing towards the base
Scales the stem sections according to slider preferences
Lofts the stem section curves into a single surface
Fungi | Simulated lamellae arrangement A lamella, or gill, is a papery hymenophore rib under the cap of some mushroom species. They are used by the mushrooms as a means of spore dispersal, and are important for species identification.
Lamellae Morphology - Quantity Altering the number of lamellae that divide the circumference of the pileus.
The attachment of the gills to the stem is classified based on the shape of the gills when viewed from the side, while colour, crowding and the shape of individual gills can also be important features.
Adnate
The apparent reason that various mushrooms have evolved gills is that it is an effective means of increasing the ratio of surface area to mass, which increases the potential for spore production and dispersal.
Lamellae Morphology - Flutter Adjusting the amount by which the lower edge of the gill is randomly displaced from its centreline
Adnexed
Decurrent
Lamellae Morphology - Curvature Adjusting the second power law that governs the shape of the lamellae
Cross-sections through primordium showing fractures that allow lamellae to separate
Emarginate Lamellae Morphology - Depth Adjusting the depth of the lamellae as a ratio of the circumference of the pileus
Free
Sliders control lamellae characteristics Cross-sections through the lamellae as they grow with the sporocarp
Seceding
Subdecurrent
Input outer edge curve and stipe base point
Divides the circumference of the pileus
Randomly moves points on the lower edge of the lamellae to create ribbon edge
Adjusts the curve of the lower edge of the lamellae
Adjusts the depth of the lower edge of the lamellae
Grows the lamellae towards the base connection point
Creates the lamellae surfaces
Fungi | Sporocarp parametric simulation By combining the Grasshopper definitions for the pileus, lamellae and stipe, a single base connection point and an outer edge curve can be made to take the form of a mushroom. By applying this definition to multiple curves and points, a collection of similar by subtly different mushrooms can be created.. Additional work is required to enable the definition to handle more than one mushroom at a time, as currently they interfere with each other and produce distorted results if all added at once. This Grasshopper definition was then baked into Rhino, and rendered out using VRay for Rhino. A small amount of post processing in Photoshop added texture to the stem, something that could potentially be altered in the definition.
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1 1-2. Renders of a collection of mushrooms built using the complete Grasshopper definition 3. Diagram of the Grasshopper definition showing the relationship the constituent parts of the complete mushroom.
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Brief 01 | Appendix B - Cephalopod Cephalopod | Life-cycle and macro structure 3D scan of ammonite Logarithmic growth analysis Simulated logarithmic shell growth
Cephalopod | Life-cycle and macro structure Cepholopods are a member of the mollusc class. They include Ammonites [extinct], Nautilus, octopus and squid. Although not all appear to have shells, they all decended from common ancestors with spiral shells. The squid can be seen to have the remains of a shell embedded into its body,a nd octopi have an egg case that is the vestige of the shell. The shells are all divided into multiple interconnceted cavities, disinguishing them from Gstropods that only have a single cavity.
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1. Photograph of a fossilised Ammonite shell 2-4. Photos of sectioned Nautilus shells cut in the plane of bilateral symmetry [Cephalopods coil in a single plane] 5. 19th Century etching of a Nautilus shell and a fossilised ammonite 6. Diagrams showing the internal structure of a squid’s cuttlefish ’bone’ and its eveolutionary link to the spiral shells of the other Cephlopods
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Cephalopod | 3D Scan of ammonite In order to evaluate the spiral growth in Cephalopods it is neccesary to have an accurate digital model of one to compare the parametrically generated spirals to. This is possible thanks to a piece of software made by Autodesk called 123D Catch. IT allows the user to take a seriese of between 20 and 40 still photos of an object or scene, aiming to capture it from as many vantage points as possible. It then analyses the photos and creates a point cloud from the matched points in the photos. It then uses this point cloud to output a mesh that approximates the objects photographed. This mesh can then be taken into 3D modelling programs such as Rhino, allowing futher analysis and modification.
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1. Ammonite fossiles as photographed using the camera on an iPhone. 2. Screen grab form 123D Catch showing the camera path as mapped by the phone’s geo location sensors [tilt/compas] 3. Output mesh representation of the scanned objects 4. Screen grab from augmented reality test comparing the digital output mesh to the origianl scanned object
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Cephalopod - Logarithmic growth analysis The growth of the shells of cephalpods can be described by the shape of a logarithmic spiral. The Nautilus shell is interesting for the fact that its spiral can be seen to approximate the golden spiral, which is a special case of the more general logarithmic spiral. However it appears that this appearance of the golden spiral occurs only by chance, as there are many other member so the Cephalopod family that have shells that also follow the logarithmic spiral, but no the golden spiral.
a = 15 b = 0.003
a = 12 b = 0.01
a=9 b = 0.05
a=6 b = 0.09
a=4 b = 0.12
a=2 b = 0.2
a = 0.9 b = 0.25
a = 0.3 b = 0.33
The golden spiral is often seen in flower growth as it relates to the Fibonacci series, but this is not the generative sequence in this case.
a = 0.06 b = 0.4
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a = phi b = 2 / pi 2
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a = 6.6 b = 0.094 t series = start -25 end 77 4 step 0.5
x(t) = aebt sin(t) y(t) = aebt cos(t) 5
Parametric equation positions points along a logarithmic spiral defined by a series of numbers [t] and two variables controling the scale [a] and tightness [b] of the spiral
1. Logarithmic spirals generated in Grasshopper; the value for a controls the scale, while b controls the rate of expansion 2. Nautilus shell with golden section rectangles laid over the top 3. Golden spiral derived from the logarithmic Grasshopper definition 4. 3D scan of an ammonite with overlaid logarithmic spiral 5. Grasshopper definition that generates a logarithmic spiral
Preforms translations on the spiral to move it to a position over the mesh of the scanned ammonite
Creates a pipe and ball structure to allow visualisation of the logarithmic spiral
Cephalopod - Simulated logarithmic shell growth Different shaped logarithmic spirals can be used as a base for generating cephalodpod shell forms. The Grasshopper script below takes a logatithmic spiral and divides it into congruent triangular segments, before raising each tringle into an arched surface to for the shell. Its input is the logarithmic spiral definition explained prviously.
a=6 b = 0.09
a=2 b = 0.2
a = 0.3 b = 0.33
a = 0.06 b = 0.4
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Input points on a logarithmic spiral
Input origin point
Divides curve into congruent triangluar segments 2 1. Selection of shell surfaces generated using a logarithmic grasshopper definition 2. Diagram showing the relationship between the shell surface and the trianglular array generated from the logarithmic spiral 3. Grasshopper definition that takes a logarithmic spiral and generates a shell surface.
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Creates a field of points within each traingle
Raises each point according to its distance from the centre of its bounding triangle segment, createing an arched surface over thetop of each triangular segment