Encoded Assemblies | AADRL

K

ADAPTIVE SELF-BALANCING SYSTEM WorkshopII - Encoded Assemblies

Taizhong Chen

Dingming Wang

Tyson Hosmer Qiquan Lu Suyang Li 2017.11.27

Abstract We will develop a bottom up encoded design system that is capable of self-assessment and self-improvement using an evolutionary algorithm. This form of probabilistic learning utilises the evolutionary process in nature to quantify the performance of a system and iteratively improve it. We will develop software that generates geometries using local rule systems, assesses each geometry’s connectivity and structural performance using a fitness function, and iteratively breeds potentially improved versions. Our geometric models will be subject to an efficient real time structural analysis, giving each geometry the ability to assess its own structural performance. A direct linkage is maintained between the simple geometric data and material fabrication strategies. This allows the digital assessment of multiple design performances through simple geometric assemblies which are then translated into more intricate architectural languages.

Contents Concept

1

Program

7

Cellular automaton mimic the laws of biology

The infinite Processing programme

Rule

13

Form

21

Application

47

Test 495 rules for growth rate

Research the influence of 'K' & 'seeds'

Application of the system

· CONCEPT ·

1

Cellular automaton

Stanisław Marcin Ulam Stanisław Marcin Ulam; 13 April 1909 – 13 May 1984) was a Polish-American scientist in the fields of mathematics and nuclear physics. He participated in Manhattan Project, originated the Teller–Ulam design of thermonuclear weapons, discovered the concept of cellular automaton, invented the Monte Carlo method of computation, and suggested nuclear pulse propulsion. In pure and applied mathematics, he proved some theorems and proposed several conjectures. https://en.wikipedia.org/wiki/Stanislaw_Ulam

Cellular Automaton A cellular automaton is a discrete model studied in computer science, mathematics, physics, complexity science, theoretical biology and microstructure modeling.

Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays https://en.wikipedia.org/wiki/Cellular_automaton

LONGLINESS

OVERPOPULATION

KEEP

REPRODUCTION

If the neighbours are too few, the cell will die in the next generation.

If the neighbours are too many, the cell will die in the next generation.

If the neighbours are suitable, the cell will keep the same in the next generation.

If the neighbours are in a certain range, the dead cell will be reproduced in the next generation.

2

Natrual law LOGISTIC GROWTH When resources are limited, populations exhibit logistic growth. In logistic growth, population expansion decreases as resources become scarce, leveling off when the carrying capacity of the environment is reached, resulting in an S-shaped curve.d Assemblies.

VALUE 'K' Here, t is time, N stands for the amount, N0 is the initial amount (at time 0), K is the maximum amount that can be sustained, and r is the rate of growth when N is very small compared to K.

SELF-BALANCING A school of clownfish is always built into a hierarchy with a female fish at the top. When she dies, the most dominant male changes sex and takes her place. This method is used to rapidly increase the population of the spieces when it is too few.

The phenomenon of lemmings' suiside is regarded as the balancing method of population, when the population is too big or resouses are not enough, lemmings will suiside to rapidly decrease the population.

3

Digital law

K

- -Rapidly decreasing

K

++Rapidly increasing

K

-Decreasing

K

+Increasing

To imitate the natural law of generation in the environment, we set four rules to control the trends of increasing and decreasing, when the population is within the range around 'K', increasing &decreasing rules will control it balancing around 'K'. If the population is out of the safe range, rapidly increasing& rapidly decreasing rule will be used to control it bake to the safe range.

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5

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· PROGRAM ·

7

PROCESS OF DESIGN During the whole process of design, we used Processing to imitate the generation of cellular automaton, and continue to use grasshopper, Rhino, Maya to make the model in detail. Because the purpose of the workshop is about 3D printing, we also use CURA to set models in Ultimakers.

8

Infinite Programme

The process of cellular automata can also be seen as reproductive system.

If the numbers of each level can be stabilized on an exact figure, the system can be able to run infinitely.

The infinite programme uses 4 rules to keep the status of the system in balance. When the number of a level is too high, the rule “++” or “+” will increase it and the rule”--” or “-” will do the same when it is too low. By this way, the system can not only run infinitely but also run diversely, since the changing rule can prevent the system from getting into a cycle.

Proportions of different statuses of livecell and dead cell.

The increasing rules results in more reproduction cell and the decreasing rules results in more overpopulation cell.

Use the transparency to show the density, higher opacity represents higher density.

The numbers of cell in levels are in a wavy status.

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The pro ent den

The age display mode Most of cell are not able to keep longer.

The density display mode The density is based on numbers of neighbours.

oportions of cell with differnsity and in different ages.

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Infinite Programme

The exact increment of cells

The exact numbers of cell in different ages

Numbers of cell in all levels are wavy, but it is the wavy status that keep the averge number of cell in all level stabilise at the K value

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The rule display mode The frequent change of rule leads to wavy numbers.

K value

K value

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· RULE ·

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Values

R0 R1 R2 R3 For the rules in cellular automaton, there are four velues defined to control the rules. R0 & R1 control the death, R2 & R3 control the reproduction. If the number of neighbors is less than R0, cells die of lonliness. If the number of neighbors is bigger than R1, cells die of overpopulation. If the number of neighbors is within the domain between R2 and R3, cells will be reproduced. Else, they will keep same as last genaration.

RULE TEST

G0 = ∑(Ci+1-Ci) / levelNumber

Another program was coded to test every rules, in order to find the average growthrate of rules. The seeds appeared randomly every time, and the growth rate will be calculated 10 times to get the average number.

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Screening principle

CRASHED There are two kinds of errors we called it crashed, one is every cell will be reproduced in the matrixe, the other is redusing speed is too fast to be calculated. We deleted 50 pieces rules crashed.

NO EXPANSION If R2 is bigger than 3, cells in this kinds of position will not be reproduced forever, so the main form will not expand even if the growth rate is very big.

There are 99 pieces.

15

NO LONELINESS & NO OVERPOPULATION If R0=0 or R2=8, there will be no condition of loneliness or overpopulation, this is conflict with other concept, we deleted 284 pieces.

CYCLED Some rules easily cause cycling, which have no advangates for our form test.

Screening outcome

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17

18

RAPIDLY INCREASING 2,3,2,2 19

RAPIDLY DECREASING 4,6,5,5

INCREASING 3,4,3,4

DECREASING 2,3,3,3 20

· FORM ·

21

Set up Basic Seeds

Basic Rule s ++

Rapidly increasing rule

( 2, 3, 2 ,2 )

+

Increasing rule

( 3, 4, 3, 4 )

-

Decreasing rule

( 2, 3, 3, 3 )

Rapidly decreasing rule

( 4, 6, 5, 5 )

--

Non-directional

Directional

Let's start with two simple based patterns. One is non-directional and the another one is directional. That is to say the directional one can be oriented by locating in front, back, letf and right to the non-directional one, and by rotating itself into different orientation. This could be an essentail figure to control the upper levels.

Growing Principle

k0 = 1 k1 = 1 k2 = 1 k3 = 1 k4 = 1

k0 = 1 k1 = 1 k2 = 4 k3 = 4 k4 = 4

k0 = 6 k1 = 2 k2 = 4 k3 = 2 k4 = 2

k0 = 1 k1 = 4 k2 = 4 k3 = 2 k4 = 6

level = 100

k4

level = 75

k3

level = 50

k2

level = 25

k1

level = 0

k0

The figure "k value" means the mutiples of the set up cell number. When changing the k value, the system would compare the population and the k value which causes the system to use increasing rules when the population is below the k value and decreasing rules when beyond. Relatively when not changing the k value, system would use the consistent k value which equals to the set up cell number. Thus k value can be seen as a threshold of controling the forms since a higher value causes a bigger shape and a lower value causes a smaller shape.

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Simulation Mirror Symmetry

Nonintervention

Intervention 1

Intervention 2

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Mirror Symmetry

Nonintervention

Intervention 1

Intervention 2

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Simulation Centrosymmetry

Nonintervention

Intervention 1

Intervention 2

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Centrosymmetry

Nonintervention

Intervention 1

Intervention 2

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Spiral Symmetry

Nonintervention

Intervention 1

Intervention 2

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Spiral Symmetry

Nonintervention

Intervention 1

Intervention 2

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Simulation

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Simulation

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Seed 1

Interaction

Seed 2

Interaction

Seed 3

Interaction

Seed 4

Interaction

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Seed 5

Interaction

Seed 6

Interaction

Seed 7

Interaction

Seed 8

Interaction

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37

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CONCEPT

39 1

CONCEPT

40 1

CONCEPT

41 1

CONCEPT

42 1

43

44

45

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· APPLICATION ·

47

Table

Forms created by the system can be applied to be architectural elements.

Four different base interact together at higher levels and become a plane together can be utilized to make tables. Unlike normal tables, the kind of tables can be generated more easily into various shape, and to some extent, the process have some randomness,which can bring unexpected beauty.

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Table

49

Building

Habitat 67

The stacking form of cellular automata have an oppotunity to be organized to a building. The process with K value can be a proper tool to control the shape of the building as well as numbers of units on each level.

Public Space Higher K

Lower K

HIGH DENSITY HOUSING SOLUTION

Higher K means more housing unit (private area) and lesser public space, which decides the standard of living will be lower but it will be more inexpensive.

Reproduction

Lower K can create organizations with more pulice space and the costly housing.

With K value adjustment, we can set different standard of houses on specific levels.

Stay the same

Overpopulation

RULES UTILIZATION

When the number of houses is too low, the rule “reproduction” will mantian the living quantity

When the number of houses is appropriate, the rule “stay the same” will stay in the trend.

When the density is to high, the rule “overpoupulation” can increase their public sapce.

50

The Vertical City

The whole system can create a complex organization of different kind of sapce. In this case, through the controlled K vaule and rules, a diverse vertical city can be imagined. Also, we can use the infinite programme to create vertical cities with any height.

Architectural Association School of Architecture Design Research Lab 2017 / Phase 1 / Workshop2