Emergence_Seminar_Em.Tech.2011-12 by Sushant Verma

Emergent Technologies and Design

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Emergence Seminar Documentation

ARCHITECTURAL ASSOCIATION SCHOOL OF ARCHITECTURE GRADUATE SCHOOL PROGRAMMES

COVERSHEET FOR SUBMISSION 2011-2012

PROGRAMME:

Emergent Technologies and Design

TERM:

STUDENT NAME(S)

Guy Austern, Lei Liu, Christopher Hill, Sushant Verma

SUBMISSION TITLE

Emergence Seminar Documentation

COURSE TUTOR

Michael Weinstock

COURSE TITLE

Emergence Seminar

SUBMISSION DATE

13th February 2012

DECLARATION: “I certify that this piece of work is entirely my/our own and that any quotation or paraphrase from the published or unpublished work of others is duly acknowledged.” Signature of Student(s):

Guy Austern

Lei Liu

Christopher Hill

Date:

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Sushant Verma

Contents Introduction Sequence 1 Genome to Individual Population 1 Fitness Criteria Population 2 Population 3 Population 4 Population 5 Population 5A Summaries Sequence 2 Additional Fitness Criteria Population 6 Population 6A Body Plan Population 7 Population 8 Summaries Sequence 3 Genome Structure Specialized Genes HomeoBox Strategies Population 9 Population 10 Population 11 Evaluation Data Structures Algorithms Gene Chart Conclusions Bibliography

1 3 5 7 9 12 16 20 24 28 31 32 36 40 42 46 50 55 56 57 58 61 65 69 74 75 77 79 80 81

Introduction This paper documents the process, analysis and results of a research project undertaken during the Emergence Seminar Course of the Emergent Technologies Programme at the Architectural Association in January and February 2012. Evolutionary principles of growth and breeding are developed through three sequences to formulate ideas for how design may be driven by evolutionary computation. The investigation first explores how a population of individuals may be created by applying a list of simple instructions, a genotype, to a primitive piece of geometry and render its results as a phenotype. New populations are generated through the assessment of individuals in the parent population against fitness criteria, ranked and selected for breeding by different strategies applied to the parent’s genomes. Progressing through the sequences, the process increasingly becomes more complex as ideas for a body plan, mutations to the genome structures at breeding and an environmental pressure are applied to new generations. Evolutionary Computation Evolutionary computation is a field of computer science which utilises iterative processes for seeking solutions which are problematic or intangible. The processes have been structured on abstracted logics of biological evolution and are deeply rooted in the work of John Holland in the 1960’s, which recognizes the fact that software already has a genotype and phenotype structure: the code and what it does (Steven Johnson,Emergence, p.59). Thus the process of natural selection can be performed on bits of code, using them as a genome, while evaluating their result in order to select genes to be transmitted to further generations. Since simulating such mechanisms requires generating large populations and then performing evaluation and breeding on them for hundreds of subsequent generations, these simulations are reliant on heavy computational power and were not widely implemented until the 1980’s, with models like Jefferson and Taylor’s “Tracker” which was implemented on a new and massively parallel “connection machine” (Steven Johnson ,Emergence, p.62). Our investigation tries to abstract this method of research, using grasshopper code whenever possible for describing the genome while implementing evaluation and breeding manually. This process has many shortcomings, the primary one being the inability to generate the sheer numbers of individuals and populations necessary to perform proper genetic calculations, but we feel it could be implemented using python scripting given sufficient time. Evo-Devo There has been a shift in the past twenty years from Darwin’s theories of evolution and natural selection in 1859, the work of William Bates (1894) suggesting order and logic to animal architecture, and D’Arcy Thompson ideas on growth and form 1917, to a united realm of ‘Evolutionary Developmental Biology’, ‘Evo-Devo’. The break through work of Stephen Jay Gould in 1977 argued the direct link between development of form by rate and time. This led to more recent embryological development studies by Berril and Godwin (1996), and Sean B. Carroll authoring ‘Endless Forms Most Beautiful’ (2005) to forefront the field of ‘Evo-Devo’ ‘Evolution’ accounts for the exchanges in genetic code over several generations; ‘development’ vindicates Embryology, the growth of an embryo to adult form. Whilst both studies occur over very different time scales, the biological field of ‘Evo-Devo’ unites the disciplines to study the intertwined hereditary links that may account for variations in form and growth. Employing the concept of ‘Evo-Devo’, this paper explores how ‘Evolutionary Algorithms’ may define a methodology for evolving Architectural forms which are context sensitive and functionally specific. (M. Weinstock, Emergent Technologies and Design, Towards a biological paradigm for architecture, p. 38) Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Introduction to Emergence Workshop

Sequence 1

3 transition functions applied to the primitive pyramid object in the order Rotate, Move, Scale (NonUnform). The sequence defines a Gene.

local xyz axis set to the centre of the pyramid base

Rotation x y 53 z -

Move x y 1.4 z

Scale (NonUniform) x 1.5 y z -

Gene A = (Ry53,My1.4,Sx1.5)

Defining the gene Sequence One commenced with the selection of â&#x20AC;&#x2DC;The Pyramidâ&#x20AC;&#x2122; as the primitive component for the creation of individuals and populations. To create a set of individuals with controlled yet impartial variations, a set of rule definitions is created. The rule definitions are imperative for creating a population of individuals which can be equally compared and not totally alien to each other. A local coordinate system is first positioned at the centre of the pyramids square base. For any future transformations the axis remains in the same position relative to the pyramid.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Genome to Individual

PAA

A PA Fully Grown Individual

PAB

B A

Gene A = (Rx19,Mz1.4,Sz1.8) Gene B = (Rz12,My1.4,Sy1.6)

PBA P+PA+PB+PAA+PAB+PBA+PBB

B PBB

Defining the genome and Individual A system is created to resemble embryological development. An individual phenotype (physical manifestation), is generated by applying the growth rules stored in the hereditary genotype. As the genome structure uses a branching system to record the order of the application of the different genes , the resulting individual is defined by a branching system which aggregates utilising the genetic data available and is a unique expression of the genome.

A A

A B

gene structure, p 79. library chart of all gene definitions used through population 1-11

In the example shown two genes are defined to first create two components, PA and PB. A gene comprises a sequence of three commands. Utilising the origin of the coordinate system the primitive is first rotated, and then moved before scaled non-uniformly (this order is held and not changed for the first sequence). Each transformation has the choice of transforming about the x, y or z axis. The same genes are then applied to the two newly created components to create a further four component (PAA, PAB, PBA, PBB). The six newly created components and original un-transformed primitive combine to form an individual. 4

Sequence 1

Name: POP1-1 Surface to BBVolume Ratio: 0.27

Name: POP1-2 Surface to BBVolume Ratio: 0.81

Name: POP1-3 Surface to BBVolume Ratio: 0.67

Name: POP1-4 Surface to BBVolume Ratio: 0.32

Name: POP1-5 Surface to BBVolume Ratio: 0.61

Name: POP1-6 Surface to BBVolume Ratio: 0.73

Name: POP1-7 Surface to BBVolume Ratio: 0.98

Name: POP1-8 Surface to BBVolume Ratio: 0.39

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 1

Name: POP1-9 Surface to BBVolume Ratio: 0.16

Name: POP1-13 Surface to BBVolume Ratio: 0.30

Name: POP1-10 Surface to BBVolume Ratio: 0.30

Name: POP1-14 Surface to BBVolume Ratio: 0.12

Name: POP1-11 Surface to BBVolume Ratio: 0.30

Name: POP1-12 Surface to BBVolume Ratio: 0.16

Name: POP1-15 Surface to BBVolume Ratio: 1.32

Population 1

Sequence 1

Surface Area + Volume

Bounding Box Volume

boolean union

Fitness Criteria Charles Darwin observed in ‘The Origin of Species’ that ‘Natural Selection’ plays a pivotal part in the reproduction of organisms through evolving generations and an efficient way for removing the ‘unfit’. In nature ‘selection’ operates by choosing the fittest individuals for the environment in which they compete and survive for resources. The following experiments apply a ‘Fitness Criteria’ to the individuals as a method for evaluating and selecting which are the fittest. For the first population two different fitness criteria are evaluated to comprehend the importance and outcome of selecting different criteria. The components within the individual are merged (Boolean) together analysis and measurement. The first criterion measures the ratio of surface area over volume for the individual. The second measures surface area over the volume of an individual’s bounding box. The measurements of the fitness criteria are ranked and Standard Deviation applied to measure the diversity of results. A low standard deviation indicates that the results are close to the average indicating a fitter population as a whole, whereas a high value indicates a population with a larger range and more variability. Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Fitness Criteria

Fitness Option I: Surface Area / Volume

Fitness Option II: 1.41 Surface Area / Bounding Box Volume

5.95 5.18

Average: 3.64 Standard Deviation: 0.77

1.10

Average: 0.48 Standard Deviation: 0.31

4.41

0.79

3.64

0.48

2.87

Individual 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Surface/ Volume 2.98 3.65 3.17 3.21 3.23 5.92 4.39 3.30 3.92 3.23 3.60 3.92 3.23 2.80 4.29

Rank 14 6 13 12 9 1 2 8 4 9 7 4 9 15 3

0.17

2.10

Individual

1.33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Distribution of Values

1.33

2.1

2.87

Normal Distribution Plot

3.64

4.41

5.18

5.95

Surface/ BBvolume 0.27 0.81 0.67 0.32 0.61 0.73 0.98 0.39 0.16 0.30 0.30 0.16 0.30 0.12 1.32

Rank 12 3 5 7 6 4 2 8 13 9 11 14 9 15 1

-0.14 -0.45

Distribution of Values

-0.45

-0.14 0.17 Normal Distribution Plot

0.48

0.79

1.1

1.41

Population 1 Initial Genome Branch Structure Fifteen individuals are created by randomly setting the values of the variables that define the two genes. The fifteen individuals display variation and differentiation whilst maintaining commonality in their definition. The genome of each individual is recorded and logged for tracking, as future populations evolve. Whilst feeling Surface Area over Volume would be rather limiting fitness criteria, the second criterion analysing â&#x20AC;&#x2DC;surface area over bounding box volumeâ&#x20AC;&#x2122; displayed values falling within a smaller range and thus standard deviation. This proved our assumptions that depending upon the fitness criteria to be analysed, individuals and populations can be created and breed for very different purposes.

Population 1

Sequence 1

Name: POP2-16 Surface to BBVolume Ratio: 0.31

Name: POP2-17 Surface to BBVolume Ratio: 0.13

Name: POP2-18 Surface to BBVolume Ratio: 0.19

Name: POP2-19 Surface to BBVolume Ratio: 1.12

Name: POP2-20 Surface to BBVolume Ratio: 0.58

Name: POP2-21 Surface to BBVolume Ratio: 0.67

Name: POP2-22 Surface to BBVolume Ratio: 0.51

Name: POP2-23 Surface to BBVolume Ratio: 0.53

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 2

Name: POP2-24 Surface to BBVolume Ratio: 0.35

Name: POP2-28 Surface to BBVolume Ratio: 0.43

Name: POP2-25 Surface to BBVolume Ratio: 0.02

Name: POP2-29 Surface to BBVolume Ratio: 0.05

Name: POP2-26 Surface to BBVolume Ratio: 0.38

Name: POP2-27 Surface to BBVolume Ratio: 0.07

Name: POP2-30 Surface to BBVolume Ratio: 0.15

Population 2

Sequence 1

Population 2: Wider Range

5.95 5.18

Average: 0.37 Standard Deviation: 0.29

4.41 3.64 2.87

Individual 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Surface/ BBVolume 0.31 0.13 0.19 1.12 0.58 0.67 0.51 0.53 0.35 0.02 0.38 0.07 0.43 0.15 0.05

Rank 9 12 10 1 3 2 5 4 8 15 7 12 6 11 14

Surface/BBVolume Ratio and Ranking

2.10 1.33

Distribution of Values

1.33 2.1 2.87 Normal Distribution Plot

3.64

4.41

5.18

5.95

Population 2 Results The average and standard deviation fell compared to the results of Population 1, suggesting a wider range of variability in the population. The increased range created more monsters with elongated components and larger bounding boxes relative to their surface area and no individuals which would rank better than those in Population 1.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 2

Individual 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Surface/ Volume 2.98 3.65 3.17 3.21 3.23 5.92 4.39 3.30 3.92 3.23 3.60 3.92 3.23 2.80 4.29

Rank

Individual

21 4 6 16 8 5 3 13 23 18 18 23 18 27 1

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Surface/ BBVolume 0.31 0.13 0.19 1.12 0.58 0.67 0.51 0.53 0.35 0.02 0.38 0.07 0.43 0.15 0.05

Rank 17 26 22 2 9 6 11 10 15 30 14 28 12 25 29

Individuals were randomly chosen for variation in Surface Area / Bounding Box Volume ratio

Population 3 Random Selection for Population Variation Population 1 and 2 are ranked together creating a list of thirty individuals, from which fifteen individuals are chosen at random. A random seed is applied to the selection in order to increase the variation of individuals in the population. 12

Population 3

Sequence 1

Name: POP3-2 Surface to BBVolume Ratio: 0.81

Name: POP3-5 Surface to BBVolume Ratio: 0.61

Name: POP3-15 Surface to BBVolume Ratio: 1.32

Name: POP3-18 Surface to BBVolume Ratio: 0.19

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Name: POP3-7 Surface to BBVolume Ratio: 0.98

Name: POP3-19 Surface to BBVolume Ratio: 1.12

Name: POP3-13 Surface to BBVolume Ratio: 0.30

Name: POP3-21 Surface to BBVolume Ratio: 0.67

Population 3

Name: POP3-24 Surface to BBVolume Ratio: 0.35

Name: POP3-28 Surface to BBVolume Ratio: 0.43

Name: POP3-25 Surface to BBVolume Ratio: 0.02

Name: POP3-29 Surface to BBVolume Ratio: 0.05

Name: POP3-26 Surface to BBVolume Ratio: 0.38

Name: POP3-27 Surface to BBVolume Ratio: 0.07

Name: POP3-30 Surface to BBVolume Ratio: 0.15

Population 3

Sequence 1

Population 3: Random Choice for Pop. Variation

1.63 1.25

Average: 0.49 Standard Deviation: 0.38

0.87 0.49 0.11

Individual 13 15 18 19 2 21 7 5 24 25 26 27 28 29 30

Surface/ BBVolume 0.30 1.32 0.19 1.12 0.81 0.67 0.98 0.61 0.35 0.02 0.38 0.07 0.43 0.15 0.05

Rank

Surface/BBVolume Ratio and Ranking

10 1 11 2 4 5 3 6 9 15 8 13 7 12 14

-0.27 -0.65

Distribution of Values

-0.65 -0.27 0.11 Normal Distribution Plot

0.49

0.87

1.25

1.63

Population 3 Results The random selection approach led to an average and standard deviation higher than the previous two Populations suggesting that random selection is not a method for ensuring that the next population will be necessarily fitter.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 3

Individual 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Surface/ Volume 2.98 3.65 3.17 3.21 3.23 5.92 4.39 3.30 3.92 3.23 3.60 3.92 3.23 2.80 4.29

Rank

Individual

21 4 6 16 8 5 3 13 23 18 18 23 18 27 1

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Surface/ BBVolume 0.31 0.13 0.19 1.12 0.58 0.67 0.51 0.53 0.35 0.02 0.38 0.07 0.43 0.15 0.05

Rank 17 26 22 2 9 6 11 10 15 30 14 28 12 25 29

The fittest individuals were chosen by ranking the individuals Surface Area / Bounding Box Volume ratio

Population 4 Fittest Selection Population 1 and 2 are ranked together creating a list of thirty individuals, from which the top (fittest) fifteen individuals are chosen. By chance the ranking chart suggests that are seven individuals are taken from the first population and eight from the second, almost a fifty-fifty split. If the genes in population 1 and 2 were created again, a very different ranking list may be created. 16

Population 4

Sequence 1

Name: POP4-2 Surface to BBVolume Ratio: 0.81

Name: POP4-6 Surface to BBVolume Ratio: 0.73

Emergence

Name: POP4-3 Surface to BBVolume Ratio: 0.67

Name: POP4-7 Surface to BBVolume Ratio: 0.98

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Name: POP4-4 Surface to BBVolume Ratio: 0.32

Name: POP4-5 Surface to BBVolume Ratio: 0.61

Name: POP4-15 Surface to BBVolume Ratio: 1.32

Name: POP4-19 Surface to BBVolume Ratio: 1.12

Population 4

Name: POP4-20 Surface to BBVolume Ratio: 0.58

Name: POP4-21 Surface to BBVolume Ratio: 0.67

Name: POP4-22 Surface to BBVolume Ratio: 0.51

Name: POP4-24 Surface to BBVolume Ratio: 0.35

Name: POP4-26 Surface to BBVolume Ratio: 0.38

Name: POP4-28 Surface to BBVolume Ratio: 0.43

Name: POP4-23 Surface to BBVolume Ratio: 0.53

Population 4

Sequence 1

Population 4: Fittest Population

1.39 1.14

Average: 0.64 Standard Deviation: 0.25

0.89 0.64 0.39

Individual 2 3 4 19 20 21 22 23 24 5 26 6 28 7 15

Surface/ BBVolume 0.8149 0.6657 0.3166 1.1177 0.5763 0.6657 0.5139 0.5301 0.3535 0.6056 0.3808 0.7336 0.4350 0.9758 1.3158

Rank 4 6 15 2 9 6 11 10 14 8 13 5 12 3 1

0.14 -0.11 Distribution of Values

-0.11 Surface/BBVolume Ratio and Ranking

0.14

0.39

0.64

0.89

1.14

1.39

Normal Distribution Plot

Population 4 Results The normal distribution documents a population with a better distribution of Surface Area to Bounding Box ratio than the previous two populations. The curve is almost a bell shaped showing an equal distribution of individuals either side of the average. The low standard deviation figure suggests a population which are within a reasonably tight distribution and are fit about the average of the population.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 4

5-15-19A

C B

A A

5-15

A D

D C

C D

B C

15 19 7 2 6 3 21 5 20 23 22 28 26 24 4

1.32 1.12 0.98 0.81 0.73 0.67 0.67 0.61 0.58 0.53 0.51 0.43 0.38 0.35 0.32

4-15 4-19 4-07 4-02 4-06

5-15-19B 5-15-19C 5-15-19D

5-19 5-07 5-02 5-06 5-03

4-03 4-21

5-21 5-21-05A 5-21-05B

4-05

5-21-05C

Name

Surface/ BB Volume

(19-15)B 15 19 (19-15)C (19-15)A 07 (21-5)D 02 (21-5)B 06 21 03 (19-15)D 05 (21-5)C (21-5)A

2.04 1.32 1.12 1.02 1.02 0.98 0.85 0.81 0.79 0.73 0.67 0.67 0.65 0.61 0.57 0.44

5-21-05D

B B

Name

Surface/ BB Volume

5-05 and child. Four diffenent possible offspring Substitution of all occurances of a gene between parent between each two parents. Each offspring has exactly 50% of each of his parents.

Population 5 Cross Gene Breeding To create Population 5, two different breeding strategies were investigated. The first strategy ranks individuals from Population Four, choosing the first and second, and seventh and eighth for respective breeding and third, fourth, fifth and sixth to create a population of sixteen individuals. For two of the breeding individuals a gene is identified and substituted. Four different offspring are created, ensuring that the child has 50% of the parentâ&#x20AC;&#x2122;s genome.

Population 5

Sequence 1

Name: POP5-4-19 Surface to BBVolume Ratio: 1.12 Intersection Length: 95.24

Name: POP5-(19X15)A Surface to BBVolume Ratio: 1.02 Intersection Length: 122.08

Name: POP5-(19X15)B Surface to BBVolume Ratio: 2.04 Intersection Length: 81.52

Name: POP5-(19X15)C Surface to BBVolume Ratio: 1.02 Intersection Length: 57.73

Name: POP5-(19X15)D Surface to BBVolume Ratio: 0.65 Intersection Length: 51.75

Name: POP5-4-15 Surface to BBVolume Ratio: 1.32 Intersection Length: 63.98

Name: POP5-5-7 Surface to BBVolume Ratio: 0.98 Intersection Length: 108.97

Name: POP5-5-2 Surface to BBVolume Ratio: 0.81 Intersection Length: 147.99

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 5

Name: POP5-5-6 Surface to BBVolume Ratio: 0.73 Intersection Length: 22.59

Name: POP5-5-3 Surface to BBVolume Ratio: 0.67 Intersection Length: 68.65

Name: POP5-4-21 Surface to BBVolume Ratio: 0.67 Intersection Length: 37.98

Name: POP5-(21X5)A Surface to BBVolume Ratio: 0.44 Intersection Length: 56.06

Name: POP5-(21X5)B Surface to BBVolume Ratio: 0.79 Intersection Length: 37.66

Name: POP5-(21X5)C Surface to BBVolume Ratio: 0.57 Intersection Length: 93.21

Name: POP5-(21X5)D Surface to BBVolume Ratio: 0.85 Intersection Length: 63.18

Name: POP5-4-05 Surface to BBVolume Ratio: 0.61 Intersection Length: 163.98

Population 5

Sequence 1

Population 5: Cross Gene Breeding

2.03

1.65

Average: 0.89 Standard Deviation: 0.39

1.27

0.89

Individual 5-19 5-(19X15)A 5-(19X15)B 5-(19X15)C 5-(19X15)D 5-15 5-07 5-02 5-06 5-03 5-21 5-(21X05)A 5-(21X05)B 5-(21X05)C 5-(21X05)D 5-05

Surface/ BBVolume 1.12 1.02 2.04 1.02 0.65 1.32 0.98 0.81 0.73 0.67 0.67 0.44 0.79 0.57 0.85 0.61

Rank 3 5 1 4 13 2 6 7 10 11 11 16 9 15 8 14

Intersection Length 95.24 122.08 81.52 57.73 51.75 63.98 108.97 147.99 22.59 68.65 37.98 56.06 37.66 93.21 63.18 163.98

Rank 11 13 9 6 4 8 12 14 1 9 3 5 2 10 7 15

0.51

0.13

Distribution of Values

-0.25

Surface/BBVolume Ratio and Ranking

0.13

0.51

Normal Distribution Plot

0.89

1.27

1.65

2.03

Genes from initial parents may be reunited after the second generation depending upon ranking criteria

Population 5 Results This method does not create widespread variation through the population. Furthermore the breeding process may evolve to create an individual identical to the parent after two generations. The analysis and evaluation does show however that an offspring can potentially be better, and also far worse than their parents as seen in the table.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 5

5A-15 A

C B

D C

A B

Name

Surface/ BB Volume

15 19 7 2 6 3 21 5 20 23 22 28 26 24 4

1.32 1.12 0.98 0.81 0.73 0.67 0.67 0.61 0.58 0.53 0.51 0.43 0.38 0.35 0.32

5A-15-19A

4-15 4-19

5A-15-19B 5A-15-19C 5A-15-19D 5A-15-19E 5A-15-19F

5A-19 5A-21 5A-21-05A 5A-21-05B

4-21

5A-21-05C 5A-21-05D

4-05

5A-21-05E 5A-21-05F

Surface/ BB Volume

15 (15-19)-E 19 (15-19)-B (15-19)-C (15-19)-D (15-19)-F (15-19)-A (21-5)-D 21 (21-5)-A (21-5)-E 05 (21-5)-C (21-5)-F (21-5)-B

1.32 1.16 1.12 1.07 1.05 0.99 0.85 0.77 0.67 0.67 0.63 0.61 0.61 0.59 0.57 0.48

5A-05

Name

Substitution of a branch in the growth structure with one of the other parents. Six different offspring for every two parents, each retaining a larger similiarity to one of the parents. Many more options arise if only one gene is replaced.

Population 5A Translocation Branch Breeding The second strategy ranks individuals from Population Four choosing the first and second, and seventh and eighth for respective breeding. The four parents and twelve children all proceed to create a population of sixteen individuals. The strategy for breeding in this case takes two individuals and substitutes a branch from the respective genome structures. This creates six possible offspring, each retaining a higher proportion of similarity to one of their parents.

Population 5A

Sequence 1

Name: POP5A-15 Surface to BBVolume Ratio: 1.32 Intersection Length: 63.98

Name: POP5A-19 Surface to BBVolume Ratio: 1.12 Intersection Length: 84.90

Name: POP5A-(15X19)-A Surface to BBVolume Ratio: 0.77 Intersection Length: 64.76

Name: POP5-(15X19)C Surface to BBVolume Ratio: 1.05 Intersection Length: 61.99

Name: POP5-(15X19)D Surface to BBVolume Ratio: 0.99 Intersection Length: 89.72

Name: POP5-(15X19)E Surface to BBVolume Ratio: 1.16 Intersection Length: 80.92

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Name: POP5-(15X19)B Surface to BBVolume Ratio: 1.07 Intersection Length: 96.68

Name: POP5-(15X19)F Surface to BBVolume Ratio: 0.85 Intersection Length: 67.58

Population 5A

Name: POP5A-21 Surface to BBVolume Ratio: 0.67 Intersection Length: 37.98

Name: POP5A-5 Surface to BBVolume Ratio: 0.61 Intersection Length: 163.98

Name: POP5A-(21X5)-A Surface to BBVolume Ratio: 0.63 Intersection Length: 45.26

Name: POP5A-(21X5)-B Surface to BBVolume Ratio: 0.48 Intersection Length: 39.42

Name: POP5A-(21X5)-C Surface to BBVolume Ratio: 0.59 Intersection Length: 66.20

Name: POP5A-(21X5)-D Surface to BBVolume Ratio: 0.67 Intersection Length: 40.02

Name: POP5A-(21X5)-E Surface to BBVolume Ratio: 0.61 Intersection Length: 73.18

Name: POP5A-(21X5)-F Surface to BBVolume Ratio: 0.57 Intersection Length: 107.68

Population 5A

Sequence 1

Population 5A: Translocation Branch Breeding

1.34

Average: 0.82 Standard Deviation: 0.26

1.08 0.82 0.56

Individual 5A-15 5A-19 5A-(15-19)-A 5A-(15-19)-B 5A-(15-19)-C 5A-(15-19)-D 5A-(15-19)-E 5A-(15-19)-F 5A-21 5A-05 5A-(21-05)-A 5A-(21-05)-B 5A-(21-05)-C 5A-(21-05)-D 5A-(21-05)-E 5A-(21-05)-F

Surface/ BBVolume 1.32 1.12 0.77 1.07 1.05 0.99 1.16 0.85 0.67 0.61 0.63 0.48 0.59 0.67 0.61 0.57

Rank 1 3 8 4 5 6 2 7 9 12 11 16 14 9 12 15

Intersection Rank 0.30 Length 63.98 6 0.04 84.9 12 64.76 Distribution 7 of Values 96.68 14 61.99 5 89.72 13 80.92 11 67.58 9 37.98 1 163.98 16 45.26 4 39.42 2 66.2 8 40.02 3 73.18 10 107.68 15 0.11

Surface/BBVolume Ratio and Ranking

0.14

0.39

Normal Distribution Plot

5B 7A 7B

19B 20A

8A 6A

19A

20B

21A

15A

21B

15B

23A 22A 22B 22A 22B

23B 24A 24B

15A 15B

19A 19B

26A

05A

26B

05B

21A 21B

28A 28B

0.64

0.89

1.14

1.39

Breeding method reduces gene pool determining more similar individuals and less variation as future generations evolve

Population 5A Results The method instigates complications within the genome structure, whilst producing the positive result of a wide and varied set of offspring. There is less chance that further breeding will cause a return to the parent generation yet breeding six offspring from a single pair causes a great reduction of the gene pool, as the same genes appears in a large proportion of the population.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 5A

Population 1

Initial Genome Branch Structure

Population 2

Wider Range

Population 3

Random Selection

Population 4

Fittest Selection

Population 5

Cross Gene Breeding

Population 5A

Translocation Branch Breeding fittest individual

Populations 1-5

Sequence 1

Population 5 5(15-19)A

15 04

5(15-19)B

5(15-19)C

5(15-19)D

5-15

11 12

5-07

5-02

5-06

13 14

15 16 17

24 05

18 19

28 26

22 23

06 27

24 25 26

5-(21-05)A

5-(21-05)B

5-(21-05)C 07

5-(21-05)D 15

29 30

5-21

27 28

5-03

Emergence

5-19

Primitive

Breeding Strategy Introduced

Population 4

Population 3

Population 2

Population 1

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

5-05

Family Tree Populations 1-5 29

Sequence 2

Additional Fitness Criteria For the iteration of population 6 the second breeding strategy translocation or branch substitution is used. At this stage a critical analysis of the gene pool is undertaken for individuals of population 1 to 5 (Sequence 1) and to induce variation in the following populations. The variations are in form of mutating the genome before it grows. At this instance, the body plan starts to be defined and new fitness criteria are added for evaluation of the populations. I. II.

Average Z value for ‘four end parts’ of the individual Intersection Length

I. Average Z value (Higher value indicates better performance) The current hierarchy of individuals, in terms of body structure, consists of 3 levels of body parts which are added during the growth of an individual, as illustrated previously in the genome definition. The third level of hierarchy (added in the last part of growth) defines the body plan of the individual in the most dominant way as compared to the first two levels of hierarchy. Hence, the Z values of the base centroid of these body parts (which are derived from the primitive form-pyramid, after a set of genetic operations) are calculated and an average is taken for evaluation. A high value of Average Z indicates better performance, owing to verticality of the body plan.

Surface Area/ Bounding Box Volume

II. Intersection Length (Lower value indicates better performance) D’Arcy Thompson in ‘On Growth and Form’ (1917) built on Darwin’s theories to note the effects environmental pressures have on physical forms. In ‘Architecture of Emergence’ by Michael Weinstock this is summarised as “physical forces act on living forms and determine the scales, bounding limits and informing geometries of the development of all adult forms”. (P102, The Architecture of Emergence) The overlap of body parts of an individual creates intersections, thereby leading to waste ‘material’. This is introduced as an environmental pressure for the population. The area of material exposed as a surface becomes a constraint for the population. A low total intersection length within the parts of an individual indicates a better performance as it reduces the wastage of material. A high value of intersection length indicates the overlap of more surfaces, thereby increasing the amount of surface material used by the geometry of the individual and leading to an ‘unfit’ individual.

Average Z value for 4 end parts

A combination of three fitness criteria: High Surface Area / Bounding Box Volume (SA/BBvol.), High Average Z value and Low Intersection Length are weighed together for an overall ranking and evaluation of individuals for subsequent populations. The SA/BBvol. ratio is weighted with two times importance since desirable individuals are required to be more densely packed with more surface area, whilst holding preferable attributes of the other two criteria. Intersection Length Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Fitness Criteria

6-15-19B 6-15-19B 6A-01 5-15-19B

Name

Surface/ BBvolume

Intersection Name Length

4-19. 5-(19X15)A 5-(19X15)B 5-(19X15)C 5-(19X15)D 4-15. 5-07. 5-02. 5-06. 5-03. 4-21. 5-(21X5)A 5-(21X5)B 5-(21X5)C 5-(21X5)D 4-05.

1.12 1.02 2.04 1.02 0.65 1.32 0.98 0.81 1.05 0.67 0.67 0.44 0.79 0.57 0.85 0.61

4-19. 95.24 122.08 5-(19X15)A 81.52 5-(19X15)B 57.73 5-(19X15)C 51.75 5-(19X15)D 63.98 4-15. 108.97 5-07. 147.99 5-02. 62.59 5-06. 68.65 5-03. 37.98 56.06 4-21. 37.66 5-(21X5)A 93.21 5-(21X5)B 63.18 5-(21X5)C 163.98 5-(21X5)D 4-05.

Surface/

Intersection

Offspring? BBvolumeTotal Rank Length 1001.12 0 1.02 0 2.04 0 1.02 0 0.65 100 1.32 0 0.98 0 0 0.81 0 1.05 1000.67 0 0.67 0 0.44 0 0.79 0 0.57 100

0.85 0.61

95.24 100 3 122.08 1 81.52 9 57.73 10 51.75 100 63.98 4 108.97 5 147.99 2 62.59 8 68.65 100 11 37.98 7 56.06 12 37.66 6 93.21 100 63.18 163.98

5-06

Offspring?

6A-03

Total Rank

100 0 0 0 0 5-19-15A 100 0 5-07 0 5-02 0 0 5-21-5D 100 0 0 0 5-21-5B 0 100 5-03

6A-02

100 3 1 9 10 100 4 5 2 8 100 11 7 12 6 100

6A-01 5-15-19B

6A-02 6A-03

5-06

6A-04

6A-04 6A-05

6A-05

6A-06

6-06

6-19-15A-M 6-07-M 6-02-M 6-21-5D-M 6-21-5B

5-19-15A

6-19-15A-M

5-07

6-07-M

5-02

6-02-M

5-21-5D

6-21-5D-M 6-21-5B

6B-01

6B-02 6B-03 6B-04

5-21-5B

6B-02 6B-03

5-03

6B-05

Population 6 Translocation / Branch Substitution + Mutations (Leaves)

6B-04

6B-06

6B-05

6-03

6B-06

The first two populations in sequence two were created to evolve genes for defining parts of an abstracted tree body plan (the trunk and leaves). For the simulation of population 6, a translocation or branch substitution strategy is used for breeding. This creates a six offspring and the breeding individuals are also carried forward to this generation. Individuals which already bred in the previous generation are killed and discarded. Eight fittest individuals are taken from the preceding generation and two sets of parents are used for breeding, creating sixteen individuals. Random selection is used for the selection of the breeding individuals and the other four individuals are mutated to form twenty new individuals for population 6.

6-03

Population 6

Sequence 2

Name: Surface to BB Volume Ratio: Intersection Length:

Emergence

POP06 - 6-02-M 0.87 72.85

Name: POP06 - 6-03-M Surface to BB Volume Ratio: 0.60 Intersection Length: 149.37

POP06 - 6A-3 Name: 1.00 Surface to BB Volume Ratio: 38.87 Intersection Length:

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

POP06 - 6A-4 1.01 54.94

Name: POP06 - 6-06-M Surface to BB Volume Ratio: 0.72 Intersection Length: 45.64

Name: Surface to BB Volume Ratio: Intersection Length:

POP06 - 6-07-M Name: POP06 - 5-(15-19)A 0.65 Surface to BB Volume Ratio: 1.02 100.00 Intersection Length: 122.08

Name: POP06 - 6A-5 Surface to BB Volume Ratio: 0.77 Intersection Length: 26.03

Name: POP06 - 6A-6 Name: POP06 - 6B-1 Surface to BB Volume Ratio: Surface to BB Volume Ratio: 0.94 0.74 Intersection Length: 37.99 Intersection Length: 155.30

Population 6

Name: POP06 - 5-(15-19)B Name: POP06 - 5-(21-05)B Name: POP06 - 5-(21-05)D Surface to BB Volume Ratio: Volume Ratio: Volume Ratio: 2.04 Surface to BB 0.79 Surface to BB 0.85 Intersection Length: 81.52 Intersection Length: 37.66 Intersection Length: 63.18

Name: POP06- 6A-1 Name: Surface to BB Volume Ratio: Surface to BB Volume Ratio: 1.36 Intersection Length: 55.00 Intersection Length:

Name: Surface to BB Volume Ratio: Intersection Length:

Name: POP06 - 6B-5 Name: POP06 - 6B-6 Surface to BB Volume Ratio: Surface to BB Volume Ratio: 0.54 0.42 Intersection Length: 186.61 Intersection Length: 172.27

POP06 - 6B-2 Name: 0.66 Surface to BB Volume Ratio: 152.75 Intersection Length:

POP06 - 6B-3 Name: POP06 - 6B-4 Volume Ratio: 0.48 Surface to BB 0.62 153.23 Intersection Length: 159.70

Population 6

POP06 - 6A-2 1.37 100.49

Sequence 2

Population 6: Translocation and Mutation (Leaves)

Surface/BBVolume

Surface/BBVolume Average: 0.84 Standard Deviation: 0.42 Individual 6-02-M 6-03-M 6-06-M 6-07-M 6-(15-19)-A 6-(15-19)-B 6-(21-05)-B 6-(21-05)-D 6A-01 6A-02 6A-03 6A-04 6A-05 6A-06 6B-01 6B-02 6B-3 6B-4 6B-5 6B-6

2.10 1.68

Surface/ BBVolume

Rank

Intersection Length

Rank

0.87 0.60 0.72 0.00 1.02 2.04 0.79 0.85 1.36 1.37 1.00 1.01 0.77 0.94 0.74 0.66 0.48 0.62 0.54 0.42

8 16 13 20 4 1 10 9 3 2 6 5 11 7 12 14 18 15 17 19

72.85 149.366 45.64 0 122.08 81.52 37.66 63.18 55 100.49 38.87 54.94 26.03 37.99 155.3 152.75 153.23 159.7 186.61 172.27

9 13 5 20 12 10 3 8 7 11 4 6 1 2 16 14 15 17 19 18

1.26 0.84 0.42 0.00 Distribution of Values

-0.42 Surface/BBVolume and Intersection Ratio and Ranking

0.42

0.84

1.26

1.68

2.1

Normal Distribution Plot

Population 6 Results Twenty individuals emerge with a considerable amount of variation, facilitated by mutations and random selection. Some of parts in the individual 6-07-M failed to join thus dying and creating a void result. The individuals are analysed using the Surface/BBVolume and Intersection length criteria. These two criteria aim to describe the function leaves need to perform. A high Surface/BBVolume ratio would suggest a good surface area of the leaves compared to the bounding volume they occupy. Intersection Length was also measured for use in the seventh population as this criterion describes how the leaves spread. A low intersection length suggests a low level of overlap between the individuals, maximising the surface area exposed.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 6

Individual 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Estimated Individual Height 0.95 1.12 1.05 7.00 0.94 0.62 6.30 0.60 0.20 0.47 0.42 0.20 0.47 0.22 1.62 1.57 0.64 0.94 5.59 2.88 3.33 2.57 2.65 5.75 0.10 1.90 0.33 2.17 6.80 0.25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Estimated Height 0.95 1.12 1.05 7.00 0.94 0.62 6.30 0.60 0.20 0.47 0.42 0.20 0.47 0.22 1.62 1.57 0.64 0.94 5.59 2.88 3.33 2.57 2.65 5.75 0.10 1.90 0.33 2.17 6.80 0.25

6A-04-M

6A-07-M

6A-04-M

6A-07-M

6A-(04M-24M)-A

6A-(04M-24M)-B

6A-(04M-24M)-C

6A-(04M-24M)-D

6A-(04M-24M)-E

6A-(04M-24M)-F

6A-(07M-29M)-A 6A-24-M

6A-24-M

6A-(07M-29M)-B

6A-(04M-24M)-F

6A-(07M-29M)-A 6A-(07M-29M)-B

6A-(07M-29M)-C

6A-(07M-29M)-C 6A-(07M-29M)-D 6A-(07M-29M)-E 6A-(07M-29M)-F

6A-(07M-29M)-D 6A-(07M-29M)-E 6A-(07M-29M)-F

6A-29-M

Population 6A Translocation / Branch Substitution + Mutations (Trunk) A set of sixteen individuals are bred from the four fittest individuals from population 5A. The four parent individuals are mutated and cross bred using the translocation strategy.

Population 6A

Sequence 2

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-04-M 0.55 99.66 1.88

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-07-M 0.22 53.06 4.46

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-24-M 0.25 249.86 0.76

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-29-M 0.34 249.11 0.00

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A -6A-(29M-07M)E 0.29 100.63 3.05

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-(29M-07M)F 0.27 55.17 3.41

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A -6A-(04M-24M)A 0.17 198.51 1.00

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-(04M-24M)B 0.46 71.84 1.00

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 6A

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-(29M-07M)A 0.15 208.66 1.06

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-(29M-07M)B 0.16 184.38 1.06

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-(29M-07M)C 0.32 113.58 1.99

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-(29M-07M)D 0.21 161.78 2.11

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-(04M-24M)C 0.33 111.82 1.37

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-(04M-24M)D 0.30 167.5 1.36

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-(04M-24M)E 0.57 38.74 1.62

Name: Surface to BB Volume Ratio: Intersection Length: Average leaf Z:

POP6A - 6A-(04M-24M)F 0.23 96.88 1.57

Population 6A

Sequence 2

Population 6A: Mutation (Tree Trunk)

Leaf Z

5.06

Leaf Z Average: 1.73 Standard Deviation: 1.11

3.95 2.84 1.73

Individual 6A-04-M 6A-07-M 6A-24-M 6A-29-M 6A-(29M-07M)A 6A-(29M-07M)B 6A-(29M-07M)C 6A-(29M-07M)D 6A-(29M-07M)E 6A-(29M-07M)F 6A-(04M-24M)A 6A-(04M-24M)B 6A-(04M-24M)C 6A-(04M-24M)D 6A-(04M-24M)E 6A-(04M-24M)F

Surface/ BBVolume

Rank

Intersection Length

Rank

Average leaf z

Rank

0.55 0.22 0.25 0.34 0.15 0.16 0.32 0.21 0.29 0.27 0.17 0.46 0.33 0.30 0.57 0.23

2 12 10 4 16 15 6 13 8 9 14 3 5 7 1 11

99.66 53.06 249.86 249.11 208.66 184.38 113.58 161.78 100.63 55.17 198.51 71.84 111.82 167.5 38.74 96.88

5 2 16 15 14 12 9 10 7 3 13 6 8 11 1 4

1.88 4.46 0.76 0.00 1.06 1.06 1.99 2.11 3.05 3.41 1.00 1.00 1.37 1.36 1.62 1.57

6 1 15 16 11 11 5 4 3 2 13 13 9 10 7 8

Surface/BBVolume,Intersection and Average Leaf Z value Ratio and Ranking

0.62 -0.49 -1.60 Distribution of Values

-1.6 -0.49 0.62 Normal Distribution Plot

1.73

2.84

3.95

5.06

Population 6A Results The population when analysed using the leaf fitness criteria suggests that the mutation created a good variety of individuals all displaying upwards growth. This suggests the strategy applied was successful and some of these are fit to be bred as trunks of a tree when read in combination with the other fitness criteria.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 6A

Body Plan A body plan starts to emerge after the populations of Sequence One, which exhibit properties such as verticality, branching and closed packing. A conscious effort is made at this stage to enhance these properties in subsequent populations by controlling the fitness criteria and abstracting the body plan as a tree-like structure. The tree-like structure is abstracted in just two levels of hierarchy, consisting of a Trunk and Leaves. The next few populations in Sequence 2 are simulated consisting of individuals exhibiting properties of a trunk (verticality) and leaves (branching and closed packing). These properties are enhanced with the effect of â&#x20AC;&#x2DC;controlled mutationsâ&#x20AC;&#x2122; of the genome. At this point there is no division between trunk and leaf genes, except the change of scale between the phenotypes of trunk and leaf parts, and the genome structure (a whole tree is placed on a branch of the genome as a leaf).

Body Plan

Sequence 2

A A

D A

C A

D B

B D B

C B B

C B

“Trunk” - composed of individuals form population 6A

Hierarchal Body Plan Organisation for Population 7

“Leaves” - composed of individuals form population 6

Population 7 Genome Extension (Trunk + Leaves) For simulation of population 7, individuals from both population 6 and 6A are used for cross breeding. However, another layer of hierarchy is added here to the individual form. The trunk genes and leaf genes are combined with the introduction of a hierarchical rule where the leaf individuals go through a 50% uniform scaling and are attached to the trunk at four points. This is operated at the genome level employing a homeobox within the DNA sequence of genes for regulating the pattern change in the development of individuals. At this point, an evolution in the population can be observed with increases in complexity of the body plan and a defined hierarchy of the gene set. Four fittest individuals from population 6A (Trunks) and five fittest individuals from population 6 (Leaves) are cross bred with certain defined combination techniques to produce twenty new individuals of population 7.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 7

Name

Surface/ BBvolume

Intersection Length

Time in simulation

6-02-M 6-03-M 6-06-M 6-07-M 6-(15-19)-A 6-(15-19)-B 6-(21-05)-B 6-(21-05)-D 6-A-1 6-A-2 6-A-3 6-A-4 6-A-5 6-A-6 6-B-1 6-B-2 6-B-3 6-B-4 6-B-5 6-B-6

0.87 0.60 0.72 0.00 1.02 2.04 0.79 0.85 1.36 1.37 1.00 1.01 0.77 0.94 0.74 0.66 0.48 0.62 0.54 0.42

72.85 149.37 45.64 100.00 122.08 81.52 37.66 63.18 55.00 100.49 38.87 54.94 26.03 37.99 155.30 152.75 153.23 159.70 186.61 172.27

1 1 1 1 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1

2 3

6A-04-M 6A-07-M 6A-24-M 6A-29-M 6A-(29M-07M)A 6A-(29M-07M)B 6A-(29M-07M)C 6A-(29M-07M)D 6A-(29M-07M)E 6A-(29M-07M)F 6A-(04M-24M)A 6A-(04M-24M)B 6A-(04M-24M)C 6A-(04M-24M)D 6A-(04M-24M)E 6A-(04M-24M)F

Surface Area/ Average BB volume leaf Z 0.35 0.22 0.25 0.34 0.15 0.16 0.52 0.21 0.29 0.47 0.17 0.46 0.33 0.30 0.57 0.43

1.88 1.46 0.76 0.00 1.06 1.06 1.99 2.11 3.05 3.41 1.00 1.00 1.37 1.36 1.62 1.57

3 D

4 5

2 3

“Leaves” - Individuals form population 6

Name

3 4

4 5

3 4 5

Population 7 Breeding Diagram

4 A B

5 1

4 B

5 1

4 D

5 1

A D

1 2 3

1 2

1 2 3

“Trunk” - Individuals form population 6A 42

Population 7

Sequence 2

A-2345

4AM 4BM 4A-M

4B-M 24AM 24BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

19A 15A

6A 6B

5B 25B

A-1234

6A 6B 19A 15A 6A 6B 6A 6B 19A 15A 6A 6B 3A 3B 5B 25B

POP07 - A-2345 0.34 512.37 2.30

4AM 4BM 4A-M

4B-M 24AM 24BM

29AM 29BM 7A-M

7B-M 7AM 7BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

Emergence

19A 15A

6A 6B

5B 25B

19A 15A

6A 6B

Name: POP07 - A-1234 Surface to Volume Ratio: 0.34 Intersection Length: 348.53 Average Leaf Z: 2.51

C-2345

19A 15A

2AM 2BM

A-5123

2AM 2BM 2AM 2BM 6A 6B 19A 15A 6A 6B 6A 6B 19A 15A 6A 6B

4AM 4BM 4A-M

4B-M 24AM 24BM

POP07 - C-2345 0.19 437.02 4.04

29AM 29BM 7A-M

7B-M 7AM 7BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

2AM 2BM

19A 15A

6A 6B

2AM 2BM

19A 15A

Name: POP07 - A-5123 Surface to Volume Ratio: 0.23 Intersection Length: 453.99 Average Leaf Z: 2.32

C-1234

6A 6B 19A 15A 6A 6B 6A 6B 19A 15A 6A 6B 3A 3B 5B 25B

5B 25B

A-4512

3A 3B 5B 25B 2AM 2BM 2AM 2BM 6A 6B 19A 15A 6A 6B 6A 6B

4AM 4BM 4A-M

4B-M 24AM 24BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP07 - C-1234 0.34 379.59 4.27

29AM 29BM 7A-M

7B-M 7AM 7BM

5B 25B

2AM 2BM

19A 15A

5B 25B

2AM 2BM

19A 15A

POP07 - A-4512 0.29 615.16 2.27

C-5123

2AM 2BM 2AM 2BM 6A 6B 19A 15A 6A 6B 6A 6B 19A 15A 6A 6B

6A 6B

A-3451

19A 15A 6A 6B 3A 3B 5B 25B 2AM 2BM 2AM 2BM 6A 6B 19A 15A

4AM 4BM 4A-M

4B-M 24AM 24BM

Name: POP07 - C-5123 Surface to Volume Ratio: 0.26 Intersection Length: 514.02 Average Leaf Z: 4.03

29AM 29BM 7A-M

7B-M 7AM 7BM

6A 6B

5B 25B

2AM 2BM

19A 15A

6A 6B

5B 25B

2AM 2BM

6A 6B 6A 6B 19A 15A 6A 6B 3A 3B 5B 25B 2AM 2BM 2AM 2BM

Name: POP07 - A-3451 Surface to Volume Ratio: 0.22 Intersection Length: 566.82 Average Leaf Z: 2.40

C-4512

3A 3B 5B 25B 2AM 2BM 2AM 2BM 6A 6B 19A 15A 6A 6B 6A 6B

19A 15A

C-3451

19A 15A 6A 6B 3A 3B 5B 25B 2AM 2BM 2AM 2BM 6A 6B 19A 15A

Name: POP07 - C-4512 Surface to Volume Ratio: 0.32 Intersection Length: 501.64 Average Leaf Z: 3.80

29AM 29BM 7A-M

7B-M 7AM 7BM

19A 15A

6A 6B

5B 25B

2AM 2BM

6A 6B 6A 6B 19A 15A 6A 6B 3A 3B 5B 25B 2AM 2BM 2AM 2BM

Name: POP07 - C-3451 Surface to Volume Ratio: 0.24 Intersection Length: 405.64 Average Leaf Z: 4.05

Population 7

B-2345

29AM 29BM 7A-M

7B-M 29AM 29BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

19A 15A

6A 6B

5B 25B

B-1234

6A 6B 19A 15A 6A 6B 6A 6B 19A 15A 6A 6B 3A 3B 5B 25B

POP07 - B-2345 0.26 679.78 2.88

29AM 29BM 7A-M

7B-M 29AM 29BM

24AM 24BM 4A-M

4B-M 24AM 24BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

19A 15A

6A 6B

5B 25B

19A 15A

6A 6B

Name: POP07 - B-1234 Surface to Volume Ratio: 0.36 Intersection Length: 424.94 Average Leaf Z: 2.81

D-2345

19A 15A

2AM 2BM

B-5123

2AM 2BM 2AM 2BM 6A 6B 19A 15A 6A 6B 6A 6B 19A 15A 6A 6B

29AM 29BM 7A-M

7B-M 29AM 29BM

POP07 - D-2345 0.21 599.44 2.33

24AM 24BM 4A-M

4B-M 24AM 24BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

2AM 2BM

19A 15A

6A 6B

2AM 2BM

19A 15A

Name: POP07 - B-5123 Surface to Volume Ratio: 0.25 Intersection Length: 542.90 Average Leaf Z: 2.70

D-1234

6A 6B 19A 15A 6A 6B 6A 6B 19A 15A 6A 6B 3A 3B 5B 25B

5B 25B

B-4512

3A 3B 5B 25B 2AM 2BM 2AM 2BM 6A 6B 19A 15A 6A 6B 6A 6B

29AM 29BM 7A-M

7B-M 29AM 29BM

POP07 - D-1234 0.27 441.51 2.53

24AM 24BM 4A-M

4B-M 24AM 24BM

5B 25B

2AM 2BM

19A 15A

5B 25B

2AM 2BM

19A 15A

Name: POP07 - B-4512 Surface to Volume Ratio: 0.33 Intersection Length: 861.78 Average Leaf Z: 2.47

D-5123

2AM 2BM 2AM 2BM 6A 6B 19A 15A 6A 6B 6A 6B 19A 15A 6A 6B

6A 6B

B-3451

19A 15A 6A 6B 3A 3B 5B 25B 2AM 2BM 2AM 2BM 6A 6B 19A 15A

29AM 29BM 7A-M

7B-M 29AM 29BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

Name: POP07 - D-5123 Surface to Volume Ratio: 0.09 Intersection Length: 603.09 Average Leaf Z: 2.46

24AM 24BM 4A-M

4B-M 24AM 24BM

6A 6B

5B 25B

2AM 2BM

19A 15A

6A 6B

5B 25B

2AM 2BM

6A 6B 6A 6B 19A 15A 6A 6B 3A 3B 5B 25B 2AM 2BM 2AM 2BM

POP07 - B-3451 0.20 814.33 2.42

D-4512

3A 3B 5B 25B 2AM 2BM 2AM 2BM 6A 6B 19A 15A 6A 6B 6A 6B

19A 15A

D-3451

19A 15A 6A 6B 3A 3B 5B 25B 2AM 2BM 2AM 2BM 6A 6B 19A 15A

Name: POP07 - D-4512 Surface to Volume Ratio: 0.19 Intersection Length: 465.26 Average Leaf Z: 2.51

24AM 24BM 4A-M

4B-M 24AM 24BM

19A 15A

6A 6B

5B 25B

2AM 2BM

6A 6B 6A 6B 19A 15A 6A 6B 3A 3B 5B 25B 2AM 2BM 2AM 2BM

Name: POP07 - D-3451 Surface to Volume Ratio: 0.19 Intersection Length: 636.84 Average Leaf Z: 2.27

Population 7

Sequence 2

Population 7: Aggregated Growth (Tree Trunk and Leaves)

Surface/BBVolume

0.40

Surface/BBVolume Ratio Average: 0.26 Standard Deviation: 0.07 Individual A-2345 A-1234 A-5123 A-4512 A-3451 B-2345 B-1234 B-5123 B-4512 B-3451 C-2345 C-1234 C-5123 C-4512 C-3451 D-2345 D-1234 D-5123 D-4512 D-3451

0.33

Surface/ BBVolume

Rank

Intersection Length

Rank

Average leaf z

Rank

0.34 0.34 0.23 0.29 0.22 0.26 0.36 0.25 0.33 0.20 0.19 0.34 0.26 0.32 0.24 0.21 0.27 0.09 0.19 0.19

2 4 13 7 14 9 1 11 5 16 17 3 10 6 12 15 8 20 18 19

512.37 348.53 453.99 615.16 566.82 679.78 424.94 542.90 861.78 814.33 437.02 379.59 514.02 501.64 405.64 599.44 441.51 603.09 465.26 636.84

11 20 14 5 8 3 17 9 1 2 16 19 10 12 18 7 15 6 13 4

2.30 2.51 2.32 2.27 2.40 2.88 2.81 2.70 2.47 2.42 4.04 4.27 4.03 3.80 4.05 2.33 2.53 2.46 2.51 2.27

18 10 17 19 15 6 7 8 12 14 3 1 4 5 2 16 9 13 10 19

Surface/BBVolume,Intersection and Average Leaf Z value Ratio and Ranking

0.26 0.19 0.12 0.05 Distribution of Values

0.05

0.12

0.19

0.26

0.33

0.4

Normal Distribution Plot

Population 7 Results The results indicate a wide variation in the population, when evaluated by the weighed ranking fitness criteria. In many ways this population is a new â&#x20AC;&#x2DC;initialâ&#x20AC;&#x2122; population, as changes to the body plan were first implemented while generating the individuals. A significant amount of these individuals performs rather poorly in at least one of the fitness criteria, beause selection has not had been applied when generating the genome structure.Yet some individuals show promise for high perfomance in all the critera, it is these individuals (selcted using a weighted ranking score) which will be the base for the new generation.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 7

trunk genes trunk genes

Individual Individual

A-2345 A-1234 A-2345 A-5123 A-1234 A-4512 A-5123 A-3451 A-4512 B-2345 A-3451 B-1234 B-2345 B-5123 B-1234 B-4512 B-5123 B-3451 B-4512 C-2345 B-3451 C-1234 C-2345 C-5123 C-1234 C-4512 C-5123 C-3451 C-4512 C-3451 D-2345 D-2345 D-1234 D-1234 D-5123 D-5123 D-4512 D-4512 D-3451 D-3451

surface/ BB rank surface/

Intersection rank Intersection

leaf Z rank leaf Z

weighted rank weighted

BB rank 2 24 13 4 7 13 14 7 9 14 91 11 1 5 11 16 5 17 16 3 17 10 3 6 10 12 6 12 15 15 8 8 20 20 18 18 19 19

rank 11 20 11 14 20 5 14 58 83 17 3 9 17 91 12 16 2 19 16 10 19 12 10 18 12 18 7 7 15 15 6 6 13 13 4 4

rank 18 10 18 17 10 19 17 15 19 6 15 67 78 12 8 14 12 3 14 31 14 45 52 2 16 16 9 9 13 13 10 10 19 19

rank 33 38 33 57 38 38 57 51 38 27 51 26 27 39 26 23 39 48 23 53 48 26 53 34 26 29 34 44 29 44 53 53 40 40 59 59 59 59 61 61

weighted rank =

rank rank

6 68 8

Ab Ab Aa Aa

4 43 3 1 1 2 27 75 5

2*surface/BB rank + Intersection rank + leaf Z rank

Ac Ac

Bb Bb Ba Ba

leaf genes

Bc Bc

A1 A1 A2 A2 A3 A3 A4 A4 B1 B1

Bb Aa Aa

Ac Ac

A2 A2 B3

Ab Ba Ba

Ac Ac

B2 B2 A3 A3

A4 A4

Aa Aa

Ab Ab Bc Bc

8 7

B2 B2 B3 B3 B4 B4

A1 A1 B2 B2 B3 B3 A4 A4

Each breeding pair produces three different offsprings “trunk” and “leaf” genes do not mix during the breeding process

4 3 2 1 8 7 6 5 4 3 2 1

7 6 5 4

All Parents transfer to the next generation with some mutation

3 2 1 8 7 6 5 4

Breeding of four pairs of parents produces twelve offspring

3 2 1

Population 8 Translocation (Trunk + Leaves) + Mutations At this stage, the body plan starts to emerge with a defined form of a tree-like structure and its properties need to be enhanced through ‘controlled mutation’ to produce better performing and fit individuals. Therefore, eight fittest individuals chosen from the preceding population are all mutated for an idealised performance to create eight new, fitter individuals. It is important to note that evolution is controlled at this point and in reality is unlikely to make such a big jump. Also, the other twelve individuals are produced through cross breeding of four pairs, giving rise to three offspring’s per pair. Another critical factor of cross breeding is the distinction in the trunk and leaf genomes. Since the genome is extended in the previous population, visual identification dividing the trunk and leaf parts can be seen. Cross breeding of trunk genes is performed only with the trunk genes of other individuals and the same rule follows for cross breeding of the leaf genes, since both these components have a specific function to perform. 46

Population 8

Sequence 2

1-5-A

29AM 29BM

6A 6B

7A-M

5B 25B

7B-M

2AM 2BM

29AM 29BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

19A 15A

1-5-B 19A 15A 6A 6B 3A 3B 5B 25B 2AM 2BM 2AM 2BM 6A 6B 19A 15A

POP08 - 1-5-A 0.33 861.79 2.47

29AM 29BM 7A-M

19A 15A

7B-M

6A 6B

29AM 29BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

24BM 7A-M

7B-M 29AM 29BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

Emergence

2AM 2BM

19A 15A

6A 6B

5B 25B

2AM 2BM 2AM 2BM 6A 6B 19A 15A 19A 15A 6A 6B 3A 3B 5B 25B

POP08 - 1-5-B 0.24 1218.90 2.47

4-8-B

24AM

2AM 2BM

1-5-C

29AM 29BM 7A-M

5B 25B

7B-M

2AM 2BM

7AM 7BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP08 - 4-8-B 0.28 794.58 2.98

29AM 29BM 7A-M

7B-M 24AM 24BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

2AM 2BM

19A 15A

5B 25B

19A 15A

19A 15A 6A 6B 3A 3B 5B 25B 2AM 2BM 2AM 2BM 6A 6B 19A 15A

POP08 - 1-5-C 0.32 501.64 3.81

4-8-C 2AM 2BM 2AM 2BM 6A 6B 19A 15A 19A 15A 6A 6B 3A 3B 5B 25B

6A 6B

2-6-A

POP08 - 4-8-C 0.38 769.05 3.00

29AMM

6A 6B

29BMM 5B 7A-MM 25B

7B-M 29AM 29BM

2AM 2BM

19A 15A

29BM 7A-M

19A 15A

7B-M

6A 6B

7AM 7BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

5B 25B

2AM 2BM 2AM 2BM 6A 6B 19A 15A 19A 15A 6A 6B 3A 3B 5B 25B

POP08 - 2-6-A 0.14 530.31 2.56

4AM 4BM 4A-M

19AM 15AM 6A 6BM 3A 3B 5BM 25B 2AMM 2BMM 2AMM 2BMM 6A 6B 19A 15A

Name: POP08 - 1-M Surface to Volume Ratio: 0.14 Intersection Length: 1078.67 Average Leaf Z: 2.49

19A 6A 15A 6B 6A 29AM 6B 3A 29BM 5B 3B 7A-MM 25B 5B 25B 2AMM 2AMM 2BMM 7B-MM 2BMM 2AMM 7AM 2BMM 6A 7BMM 19A 6B 15A 19A 15A

Name: POP08 - 5-M Surface to Volume Ratio: 0.21 Intersection Length: 490.04 Average Leaf Z: 4.63

2AM 2BM

19A 15A 19A 15A

4B-M 24AM 24BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

19A 15A

2AM 2BM 2AM 2BM 6A 6B 19A 15A 6B 19A 15A 6A 6B 6A 6B 25B

POP08 - 2-6-B 0.34 287.35 4.79

5-M

1-M

2AM 2BM 2AM 2BM 6A 6B 19A 15A 6A 6B 19A 15A 3A 3B 5B 25B

29AM

2AM 2BM

2-6-B

2-M 2AMM 2AM 2BMM 2BM 2AMM 29AM 2BMM 6A 29BM 19A 6B 7A-MM 15A 19AM 15A 6A 19A 6B 7B-M 15A 6A 7AM 6B 19A 7BM 6A 15A 6B 6A 6B

Name: POP08 - 2-M Surface to Volume Ratio: 0.13 Intersection Length: 478.19 Average Leaf Z: 4.33

Population 8

2-6-C

29AM 29BM 7A-M

7B-M 7AM 7BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

2AM 2BM

19A 15A

6A 6B

3-7-A 2AM 2BM 2AM 2BM 6A 6B 6A 6B 19A 15A 6A 6B 19A 15A 6A 6B

POP08 - 2-6-C 0.39 462.99 3.19

29AM 29BM 7A-M

7B-M 29AM 29BM

19A 15A

3-M

6A 19A 6B 15AM 19A 4AM 15A 6A 4BM 19A 6B 4A-MM 15A 6A 6BM 19A 6A 15A 4B-MM 6B 6A 24AM 6B 3A 24BM 5B 3B 25B 5B 25B

POP08 - 6-M 0.19 829.82 1.91

19A 15A

2AM 2BM 2AM 2BM 6A 6B 19A 15A 6A 6B 19A 15A 6A 6B 6A 6B

Name: POP08 - 3-7-A Surface to Volume Ratio: 0.40 Intersection Length: 456.93 Average Leaf Z: 2.89

6-M

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

2AM 2BM

3-7-B

29AM 29BM 7A-M

7B-M 29AM 29BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

2AMM 2AMM 2BMM 2BMM 2AMM 2BMM 6A 19AM 6B 15A 19AM 15A 6A 19AM 6B 15A 6A 6B 19A 6AM 15A 6B 6AM 6B

POP08 - 3-M 0.31 453.78 2.83

7AM 7BM 7A-M

7B-M 29AM 29BM

2AM 2BM

19A 15A

6A 6B

3-7-C 2AM 2BM 2AM 2BM 2AM 2BM 2AM 2BM 6A 6B 19A 15A 19A 15A 6A 6B

Name: POP08 - 3-7-B Surface to Volume Ratio: 0.35 Intersection Length: 171.58 Average Leaf Z: 2.81

29AM 29BM 7A-M

7B-M 7AM 7BM

Name: POP08 - 7-M Surface to Volume Ratio: 0.27 Intersection Length: 547.23 Average Leaf Z: 3.92

2AM 2BM

19A 15A

6A 6B

3A 3B 5B 25B 2AM 2BM 2AM 2BM 6A 6B 19A 15A 19A 15A 6A 6B

Name: POP08 - 3-7-C Surface to Volume Ratio: 0.35 Intersection Length: 348.96 Average Leaf Z: 4.20

7-M 3A 5B 3B 25BM 5B 29AM 25BM 2AMM 29BMM 2AMM 2BMM 7A-M 2BMM 2AMM 2BMM 6A 19AM 6B 7B-M 15A 19AM 7AMM 15A 6A 7BMM 19A 6B 15A 6A 6B

5B 25B

4-8-A

29AM 29BM 4A-M

4B-M 29AM 29BM

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

29BM 7A-M

7B-M 29AM 29BM

19A 15A

8-M

6A 19AM 6B 15A 19A 15A 6A 19A 6BM 15A 6A 6BM 19A 6AM 15A 6B 6A 6BM 3A 5B 3B 25B 5B 25B

Name: POP08 - 4-M Surface to Volume Ratio: 0.27 Intersection Length: 817.57 Average Leaf Z: 2.91

19A 15A

2AM 2BM 2AM 2BM 6A 6B 19A 15A 6A 6B 19A 15A 6A 6B 6A 6B

POP08 - 4-8-A 0.15 484.60 1.74

4-M

29AM

2AM 2BM

4AM 4BM 4A-M

4B-M 24AM 24BM

2AMM 2AMM 2BMM 2BMM 2AMM 2BMM 6A 19AM 6B 15A 19AM 15A 6A 19A 6B 15A 6A 6BM 19A 6A 15A 6B 6A 6B

Name: POP08 - 8-M Surface to Volume Ratio: 0.40 Intersection Length: 383.72 Average Leaf Z: 2.49

Population 8

Sequence 2

Population 8: Aggregated Growth (Increased material and energy) Surface/BBVolume

Surface/BBVolume Ratio Average: 0.28 Standard Deviation: 0.09

0.55 0.46

Individual 1-5-A 1-5-B 1-5-C 2-6-A 2-6-B 2-6-C 3-7-A 3-7-B 3-7-C 4-8-A 4-8-B 4-8-C 1-M 5-M 2-M 6-M 3-M 7-M 4-M 8-M

Surface/ BBVolume

Rank

Intersection Length

Rank

Average leaf z

Rank

0.37

0.33 0.24 0.32 0.14 0.34 0.39 0.40 0.35 0.35 0.15 0.28 0.38 0.14 0.21 0.13 0.19 0.31 0.27 0.27 0.40

8 14 9 19 7 3 1 6 5 17 11 4 18 15 20 16 10 13 12 2

861.79 1218.90 501.64 530.31 287.35 462.99 456.93 171.58 348.96 484.60 794.58 769.05 1078.67 490.04 478.19 829.82 453.78 547.23 817.57 383.72

8 14 9 19 7 3 1 6 5 17 11 4 18 15 20 16 10 13 12 2

2.47 2.47 3.81 2.56 4.79 3.19 2.89 2.81 4.20 1.74 2.98 3.00 2.49 4.63 4.33 1.91 2.83 3.92 2.91 2.49

17 17 6 14 1 7 11 13 4 20 9 8 15 2 3 19 12 5 10 15

0.27 0.18 0.09 0.42

Distribution of Values

Surface/BBVolume,Intersection and Average Leaf Z value Ratio and Ranking

0.09

0.18

0.27

0.37

0.46

0.55

Normal Distribution Plot

Population 8 Results Selective breeding for a higher surface to volume ratio is starting to show its effect, as can be seen in the increase of the average score for that parameter. Average leaf Z value has also improved quite dramatically, showing that optimization of more than one parameter is achievable in this sort of algorithm. The genome structure of this population is slowly becoming more complex as the simluation moves on, slowly evolving beyond our control. Individual genomes are described by 30 different genes, which is much to complicated for our needs. In order to be able to continue from this point some simplification to the genome structure will have to be made.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 8

Population 6

Translocation Branch Breeding + Mutation (Leaf)

Population 6A

Translocation Branch Breeding + Mutation (Trunk)

Population 7

Genome extended (Trunk + Leaf)

Population 8

Translocation Branch Breeding (Trunk and Leaf) + Mutation fittest individual

Populations 6 -8

Sequence 2

Sequence 1

Sequence 2

gen-1

gen-2

gen-3

gen-4

gen-5

gen-5A

gen-6

gen-6A

gen-7

gen-8

01A 01B 02A 02B 03A 03B 04A 04B 05A 05B 06A 06B 07A 07B 08A 08B 09A 09B 10A 10B 11A 11B 12A 12B 13A 13B 14A 14B 15A 15B

16A 16B 17A 17B 18A 18B 19A 19B 20A 20B 21A 21B 22A 22B 23A 23B 24A 24B 25A 25B 26A 26B 27A 27B 28A 28B 29A 29B 30A 30B

02A 02B 05A 05B 07A 07B 13A 13B 15A 15B 18A 18B 19A 19B 21A 21B 24A 24B 25A 25B 26A 26B 27A 27B 28A 28B 29A 29B 30A 30B

02A 02B 03A 03B 04A 04B 05A 05B 06A 06B 07A 07B 15A 15B 19A 19B 20A 20B 21A 21B 22A 22B 23A 23B 24A 24B 26A 26B 28A 28B

02A 02B 03A 03B 05A 05B 06A 06B 07A 07B 15A 15B 19A 19B 21A 21B

05A 05B 15A 15B 19A 19B 21A 21B

02A-M 02B-M 03A 03A-M 03B 03B-M 05B 06A 06A-M 06B 06B-M 07A-M 07B-M 15A 15B 19A-M 19B-M 21A 21B 25B 29A-M 29B-M

04A-M 04B-M 06A-M 06B-M 07A-M 07B-M 24A-M 24B-M 29A-M 29B-M

02A-M 02B-M 03A-M 03B-M 04A-M 04B-M 06A 06B 07A-M 07B-M 15A 19A-M 24A-M 24B-M 25B 29A-M 29B-M

02A-M 02A-MM 02A-MMM 02B-M 02B-MM 02B-MMM 03A-M 03B-M 04A-M 04B-M 06A 06A-M 06B 06B-M 06B-MM 06B-MMM 07A-M 07A-MM 07A-MMM 07A-MMMM 07B-M 07B-MM 14B 15A 19A 19A-M 19B 19B-M 24A-M 24B-M 25B 25B-M 29A-M 29B-M 29B-MM

gene introducded at generation 1 gene introducded at generation 2 gene introducded at generation 6

2A 3A

4A 4B

7A 7B

19B 20A

19A

20B

21A

15A

21B

15B

23A 22A 22B 22A 22B

23B 24A 24B

15A 15B

19A 19B

26A

05A

26B

05B

21A 21B

Implemeting the Trans Location Breeding strategy causes the gene pool to diminish by the end of Sequence 1 Kill and breeding strategies mean only the fitest survive

28A 28B

Genes from past generations are reintroduced

Gene Pool Observing the gene structure of populations from 1 to 8, indicates that most of the genes which were carried from the initial populations (1 and 2) are killed by this time and most of the genes are present in mutated or multiple mutated forms. The deterioration of the gene pool occurs due to two reasons: first the chosen fitness criteria and kill strategies and second the breeding strategies which continue to reduce the size of the gene pool with every generation. This may be considered a negative step in evolution as far as the genotype is concerned; however it leads to a positive evolution of the phenotype, creating fitter individuals with the performance desired. Overall Performance As can be seen on the charts on the right, our Evolutionary Algorithm seems to display positive results. Surface to Volume ratio has increased consistently through the generations - except in the transition phase between popualtion 6 and 7, where the new body plan and added complexity causes the results to take a sharp decline. Intersection between the pyramids can be seen to increase, which is actually opposite from our desired result, but this is due to our weighting it in the wrong way (high intersection value being interperted as positive) a fact which we will correct for the following simulations. Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Gene Pool and Evolution

05A

06A

Standard Deviation

0.35

0.29

0.41

0.29

0.38

0.26

0.42

0.13

0.07

0.09

Average

0.50

0.37

0.50

0.67

0.89

0.82

0.84

0.3

0.26

0.28

Population Surface/ Bounding Box Volume

Intersection Length

Leaf Z Value

Standard Deviation

40.07

31.69

53.42

68.85

136.01

267.20

Average

79.54

74.02

98.27

135.07

540.23

598.39

Standard Deviation

1.11

0.72

0.87

Average

1.73

2.87

3.12

1.00

2.5

0.60

0.30 0.20

Surface/ Bounding Box Volume

0.10

Standard Deviation

0.00

500

0.60

400

1.5

300

0.20

Surface/ Bounding Box Volume

0.10

Standard Deviation

700 600 500

0.60

400

1.5

300

200

0.00

Leaf Z Volume

Leaf Z Value

Standard Deviation

0.5

100

200 100

2.5

Standard Deviation

0.5

0.70

0.10

600

2.5

3.5

Surface/ Bounding Box Volume

Leaf Z Value

0.00

0.20

0.70

0.30

0.5

700

3.5

0.40

Surface Area / Bounding Box Volume

0.50

1.5

0.40

0.80

0.70 0.50

0.90

0.80

1.00

3.5

0.90

Intersection Length

Standard Deviation

Intersection Length

Summary of Fitness Criteria

Sequence 2

5(15-19)A

6-07-M 6-(15-19)A

04 5(15-19)B 19 5(15-19)C

19 20 02 21

6-(15-19)B 6-(21-05)B

6A-1

5(15-19)D

6A-3 6A-4

5-15

5-07

5-02

6B-3 6B-4

05 5-06

6B-5

5-03

6A-04-M

26 06

5-21

6A-29-M 6A-(29M-07M)A

5-(21-05)A

6A-(29M-07M)B 6A-(29M-07M)C 6A-(29M-07M)D

5-(21-05)B 26

5-(21-05)D 15

2-6-A

A-3451

2-6-B

B-2345

2-6-C

B-1234

3-7-A

B-5123

3-7-B

B-4512

3-7-C

B-3451

4-8-A

C-2345

4-8-B

C-1234

4-8-C

C-5123

1-M

C-4512

5-M

C-3451

2-M

D-2345

6-M

D-1234

3-M

D-5123

7-M

D-4512

4-M

D-3451

8-M

6A-(04M-24M)C 6A-(04M-24M)D 6A-(04M-24M)E

5-05

Emergence

A-4512

6A-(04M-24M)A 6A-(04M-24M)B

6A-(29M-07M)E 6A-(29M-07M)F

5-(21-05)C

1-5-C

6A-07-M 6A-24-M

25 28

A-5123

6B-6

24 05

1-5-B

6B-1 6B-2

A-1234

6A-5 6A-6

1-5-A

6-(21-05)D

6A-2

21 22

Population 8

Population 6A

6-03-M 6-06-M

A-2345

6-02-M 5-19

Population 7

02 13

Population 6

Sequence 2

Population 5

Population 4

Population 3

Sequence 1

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

6A-(04M-24M)F

Breeding Family Tree Populations 3-8 53

Sequence 3

Gene c

Gene a Gene C

Gene A

Gene d Gene c

Gene b

Gene d Gene c

Gene a

Gene D

Gene d Gene c

Gene b

Gene d Gene c

Gene a

1 primitive Gene C

Gene B 2 primitive

Gene d Gene c

Gene b

Gene d Gene c

Gene a

Gene D 4 primitive

Gene d Gene c

Gene b

Branching Structure

8 primitive

Gene d 16 primitive Genotype Branches

Phenotype representation of the genotype branch structure can be seen on the right as a physically expressed branching system. The genome hierarchy is expressed in the variation of the branch colour, which describes the location of the expressed gene in the genome hierarchy.

Gene c Gene A

Gene C

Gene B

Gene D

1 primitive

2 primitive

Gene a

Gene b 4 primitive

homeobox issues scaling command

Gene d 8 primitive 16 primitive

Simplified Genome Reworking the genome structure into a condensed form allows for better control of the hierarchal structure, enabling simple manipulation of the general scale of each of the branching level using a single command. The new structure has a single pair of genes controlling each level of the phenotype, but it retains most of the complexity generated by the tree structure through splitting the branches into two at each level of the algorithm, and applying a different gene on each of the branches. Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Phenotype

Genome Structure

Typical Leaf Gene

Rotate

Mutated Trunk Gene

Move

Scale

Result

Leaf Only Development Translocation

Move (Z axis only)

Rotate

Scale

Result

Mutated Specialized Genes An observation into the results of the previous simlations realises that a certain mutation of the normal genes diplays qualities the are benficial to our abstract tree model. Mutating the “normal” genes into trunk genes is achieved using translocation of the move and rotate part of the gene, coupled with limiting the move component in the Z axis. These genes show a typical vertical development in three-dimensions, contrary to the “regular” genes which can develop in all directions and tend to create a cluster, and are well suited to forming the trunks of the trees.

Trunk Only Development

Specialized Genes

Sequence 3

Trunk

Leaf

Trunk

Leaf

Trunk

Leaf

Homeobox and Body Plan Abstract â&#x20AC;&#x153;treeâ&#x20AC;? body plan for the genome structure uses a simple homeobox to direct translation points between trunk to leaf genes and the number of times they are repeated. This technique reflects the observation made by W.Bateson in his book Materials for the study of variation(1894) that the most obvious difference between members of a group were in the number and kind of repeated structures (from S.B.Caroll, Endless Forms Most Beautiful, p. 26). Individuals for the 3rd sequence are evenly divided between three different expressions of the homeobox, with different amounts of leaf and trunk genes in each of the types. This behaviour is typically shown in Hox transcription genes which affect how other genes are turned on or off during embryological development. (from S.B.Caroll, Endless Forms Most Beautiful, p. 70-74).

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Geneome Structure

Homeobox

Translocation

Rotation x y 53 z -

Move x y 1.4 z -

Point Mutation

Scale (NonUniform) x 1.5 y z -

Mutation strategy for a single gene (a mutated genome typcally contains up to 50% mutated genes)

Kill Strategy

Mutation Strategy

Kill Strategy Trees with a large amount of disconnected branches are not evaluated or allowed to proceed to the following generations, regrardless of how they perform in the other fitness criteria. Mutation Strategy Mutation of a single gene can occur by either changing the amount or axis of a single translation within the genome (point mutation) or by switching the order of the different translations (translocation).

Kill, Mutate Strategies

Sequence 3

Child 1 (with structure of parent A)

Parent A (higher ranking)

Child 2 (with structure of parent A)

Parent B (lower ranking)

Child 3 (with structure of parent B)

Breeding Algorithm for two Individuals Genome structure of offspring is constructed so trunk genes from the parents are randomly mixed to form the trunk genes of the offspring, while leaf genes are mixed to form the leaf genes of the child. The homeobox structure of the higher ranking parent is conserved in two of the offspring, while the third offspring shows the homeobox structure of the less dominant parent. This strategy alludes to the process of specialization of genes and the creation of homologs which is a typical feature of any natural organism.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population Breeding Strategy

Individual 1T3L-A-M 1T3L-E-M 2T2L-C-M 2T2L-A-M

Surface/ Rank BBVolume Surface/ Individual

1T3L-A-M 1T3L-E-M 2T2L-C-M 2T2L-A-M

1.20 0.98 0.61 0.46

3T1L-A-M 3T1L-A-M 0.39 2T2L-B-M 2T2L-B-M 0.54

BBVolume

Intersection Rank LengthIntersection Rank 244.91

Length

1.20

244.91

0.98

99.34

0.61

0.46

99.34

Average leaf Kill (detached Rank Overall Rank Average leaf Kill (detached Rank z Rank Overall Rank Leaves) z Leaves) 2.04 6 2 19 7

219.52 9 219.52

569.58

0.95 3.23 2.16

2.04

0.95 3.23 2.16

14 3 5

25 27

417.79 417.7912 13

12 4.22

4.22

269.35 269.359 10

9 1.95

1.95

0.54

2 2 5

0.39

3 4

1 2 3 4

5 5 6 6 4 4

6 6

3 3

1 1

1-4A

0.97

0.975

100.51 100.514 5

4 1.27

1.27 12

1-4B

1.54

1.542

170.70 170.705 2

5 1.34

1.34 11

1-4C

0.48

0.4811

247.49 247.498 11

8 2.03

2.03

2-5A

0.97

0.976

675.41

75.41 2

2 1.69

1.69 10

2-5B

1.64

1.641

154.06

54.06 1

1 2.01

2.01

2-5C

0.22

0.2215

15 608.40 608.4015

15 2.87

2.87

3-6A

0.70

13 3.34

3.34

4 4

3-6B

0.69

11 0.94

0.94 15 0.98

0.69

7 445.70 445.7013

5 5

6 6

3-6C

0.35

8 356.83 356.8311

352.33 14 352.33

10 0.98

Three breeding pairs of parents produce nine offspring

2 2 1 1

3 3

All parents transfer to the next generation

Selection and Breeding Strategy for Populations Selection of individuals from parent population is performed by a weighted rank of the three fitness criteria (with surface to Bounding box volume ratio being given a higher influence) and selecting the six fittest individuals. These individuals are then divided into three breeding pairs. The highest ranked individual will mate with the individual ranked fourth. The second highest will mate with the fifth and the third will mate with the sixth. This mixing strategy is employed in order to ensure genetic diversity in the offspring, in the case that similar genotypes arrive at the first two places in the simulation. This strategy is a Comma breeding strategy - no individuals from parent generation pass on unchanged, but their DNA (in both cross bred and mutant form) will make up the new population. Oriented towards improving each subsequent generation, this strategy runs the risk of the population becoming increasingly self similar as a result of discarding all the unfit individuals. In order to make up for a diminished gene pool due to selection, each of the breeding parents will appear as a mutant in the next generation, with 30-50% of its genes mutated as described in the previous diagrams. 60

Population Breeding Strategy

Sequence 3

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP9 -1T3L-A 1.16 174.23 2.13

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP9 -1T3L-B 2.25 69.82 1.67

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP9 -1T3L-C 0.76 421.29 0.85

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP9 -1T3L-E 0.83 155.9 0.47

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP9 -2T2L-A 0.45 304.9 2.37

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP9 -2T2L-B 0.43 298.57 2.09

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

POP9 -1T3L-D 1.11 117.22 1.32

POP9 -2T2L-C 0.36 285.08 3,23

Population 9

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP9 -2T2L-D 0.29 178.17 1.95

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP9 -2T2L-E 0.73 247.82 3.15

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP9 -3T1L-A 0.22 353.15 4.31

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP9 -3T1L-C 0.14 530.19 2.65

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP9 -3T1L-D 0.16 816.78 2.33

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP9 -3T1L-E 0.11 655.37 2.69

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

Population 9

POP9 -3T1L-B 0.19 540.89 2.17

Sequence 3

Surface/ BBVolume

Rank

Intersection Length

Rank

Average leaf z

Rank

Overall Rank

1T3L-A

1.16

174.23

2.13

1T3L-B

2.25

69.82

1.67

1T3L-C

0.76

421.29

0.85

1T3L-D

1.11

117.22

1.32

1T3L-E

0.83

155.90

0.47

2T2L-A

0.45

304.90

2.37

2T2L-B

0.43

298.57

2.09

2T2L-C

0.36

285.08

3.23

2T2L-D

0.29

178.17

1.95

2T2L-E

0.73

247.82

3.15

3T1L-A

0.22

353.15

4.31

3T1L-B

0.19

540.89

2.17

3T1L-C

0.14

530.19

2.65

3T1L-D

0.16

816.78

2.33

655.37

2.69

Individual

3T1L-E

0.11

Individuals assessed to three criteria and ranked with weighting towards Surface/BBVolume

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 9

2.32

981.99

1.75

769.09

4.15

1.18

556.19

3.19

0.61

343.29

2.23

0.04

130.39

1.27

0.53

-82.51

0.31

-1.10

-295.41

-0.65

-1.10

0.53

0.04

0.61

Surface Area / BB Volume Average: 0.61 Standard Deviation: 0.57

1.18

1.75

2.32

-295.41

-82.51

130.39

343.29

Intersection Length Average: 343.29 Standard Deviation: 212.90

556.19

769.09 981.99

-0.65

0.31

1.27

2.23

3.19

4.15

Average Leaf Z Average: 2.23 Standard Deviation: 0.96

Population 9 Results A large number of â&#x20AC;&#x153;deadâ&#x20AC;? individuals appear due to random generation of trunk genes, and the change of the hierarchal structure (each subsequent branch is scaled by 50-75%). Some correlation exists between individuals with high surface/volume ratios and individuals with low intersection lengths. High Leaf Z values are typically exhibited by different individuals.

Population 9

Sequence 3

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -1T3L-A-M 1.2 244.91 2.04

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -1T3L-E-M 0.98 99.34 0.95

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -2T2L-C-M 0.61 219.52 3.23

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -2T2L-A-M 0.46 569.58 2.16

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -3T1L-A-M 0.39 417.79 4.22

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -2T2L-B-M 0.54 269.35 1.95

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -1-4A 0.97 100.51 1.27

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -1-4B 1.54 170.7 1.34

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 10

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -1-4C 0.48 247.49 2.03

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -2-5A 0.97 75.41 1.69

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -2-5B 1.64 54.06 2.01

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -3-6A 0.70 445.7 3.34

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -3-6B 0.69 356.83 0.94

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP10 -3-6C 0.35 352.33 0.98

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

Population 10

POP10 -2-5C 0.22 608.4 2.87

Sequence 3

Surface/ BBVolume

Rank

Intersection Length

Rank

Average leaf z

Rank

Overall Rank

1T3L-A-M

1.20

244.91

2.04

1T3L-E-M

0.98

99.34

0.95

2T2L-C-M

0.61

219.52

3.23

2T2L-A-M

0.46

569.58

2.16

3T1L-A-M

0.39

417.79

4.22

2T2L-B-M

0.54

269.35

1.95

1-4A

0.97

100.51

1.27

1-4B

1.54

170.70

1.34

1-4C

0.48

247.49

2.03

2-5A

0.97

75.41

1.69

2-5B

1.64

54.06

2.01

2-5C

0.22

608.40

2.87

3-6A

0.70

445.70

3.34

3-6B

0.69

356.83

0.94

3-6C

0.35

352.33

0.98

Individual

Individuals assessed to three criteria and ranked with weighting towards Surface/BBVolume

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 10

4.96 1.66

630.59

3.99

1.23

456.36

3.02

0.80

282.13

2.05

0.37

107.9

1.08

-0.06

-66.33

0.11

-0.49

-240.56

-0.86

-0.49

-0.06

0.37

0.80

Surface Area / BB Volume Average: 0.78 Standard Deviation: 0.43

1.23

1.66

-240.56

-66.33

107.9

282.13

Intersection Length Average: 282.13 Standard Deviation: 174.23

456.36

630.59

-0.86

0.11

1.08

2.05

3.02

3.99

4.96

Average Leaf Z Average: 2.07 Standard Deviation: 0.97

Population 10 Results Since most of the population shares some part of the genome, the standard distribution of all three parameters is reduced, causing the normal distribution graph to be more similar to the desired â&#x20AC;&#x153;bell curveâ&#x20AC;?. There is a marked overall decrease in the size of average size of individuals in this population. Gene specialization has also shown some results, as can be seen in the reduction in the number of individuals with fallen leaves, since the leaf genes who resulted in disconnected parts have not been passed to this generation.

Population 10

Sequence 3

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -1T3L-AMM 1.18 194.89 2.16

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -1-4BM 1.53 140.11 1.23

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -2-5AM 1.09 58.53 1.99

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -1T3L-E-MM 0.94 89.55 1.19

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -1-4-A-M 0.95 50.78 1.39

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -2T2L-C-MM 0.69 258.25 3.09

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -1-4A 0.94 170.63 1..43

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -1-4B 1.05 141.43 2.29

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 11

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -1-4C 1.34 268.36 1.84

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -2-5A 1.25 192.72 1.73

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -2-5B 0.84 135.35 0.54

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -3-6A 0.99 137.58 1.36

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -3-6B 0.82 75.82 2.00

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

POP11 -3-6C 0.49 220.68 3.35

Name: Surface to Volume Ratio: Intersection Length: Average Leaf Z:

Population 11

POP11 -2-5C 1.18 181.47 1.3

Sequence 3

Surface/ BBVolume

Rank

Intersection Length

Rank

Average leaf z

Rank

Overall Rank

1T3L-A-MM

1.18

194.89

2.16

1-4B-M

1.53

140.11

1.28

2-5A-M

1.09

58.53

1.99

1T3L-E-MM

0.94

89.55

1.19

1-4A-M

0.95

50.78

1.39

2T2L-C-MM

0.69

258.25

3.09

1-4A

0.94

170.63

1.43

1-4B

1.05

141.43

2.29

1-4C

1.34

268.36

1.84

2-5A

1.25

192.72

1.73

2-5B

0.84

135.35

0.54

2-5C

1.18

181.47

1.30

3-6A

0.99

137.58

1.36

3-6B

0.82

75.82

2.00

3-6C

0.49

220.68

3.35

Individual

Individuals assessed to three criteria and ranked with weighting towards Surface/BBVolume

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Population 11

1.80

356.61

3.98

1.54

289.21

3.25

1.28

221.81

2.52

1.02

154.41

1.79

0.76

87.01

1.06

0.50

19.61

0.33

0.24

-47.79

-0.40

0.24

0.50

0.76

1.02

Surface Area / BB Volume Average: 1.02 Standard Deviation: 0.26

1.28

1.54

1.80

-47.79

19.61

87.01

154.41

Intersection Length Average: 154.41 Standard Deviation: 67.40

221.81

289.21

356.61

-0.40

0.33

1.06

1.79

2.52

3.25

3.98

Average Leaf Z Average: 1.80 Standard Deviation: 0.73

Population 11 Results Exhibits an even smaller amount of “dead” individuals appear due to the disappearance of “problematic” genes (ones with high move values of over which would cause disconnection form the trunk). The population decreases again in terms of overall size of individuals in the population, due to the stressing of the bounding box volume criteria for natural selection.

Population 11

Sequence 3

2L 2L 2L 2L 2L 1L 1L

GM 2T2L IM2T2L H 2T2L J2T2L 2T2L I 2T2L JM 3T1L 2T2L IM a 2T2L J 3T1L aM 3T1L 2T2L JM aMM 3T1L 3T1L a b 3T1L 3T1L aM bM b bMM bM c 0.80 c cM cM d 0.60 d dM e e 0.40 400.00 eM eM f eMM 350.00 0.20 fM fM g fMM 300.00 0.00 gM g 250.00 gMM gM Surface/ Boundingh Box gMM 200.00 Volume hM gMMM Standard Deviation 150.00 i h 400.00 Surface / Bounding iM Box Volume hM 100.00 350.00 j hMM jM i 50.00 300.00 jMM iM 0.00 250.00 iMM j 200.00 jM jMM 150.00 2.50 jMMM 100.00 2.00 50.00 1.50 0.00

1T3L 1T3L 1T3L 1T3L 1.20 1T3L 2T2L1.00 2T2L

a b 0.80 c d 0.60 e f 0.40 g h 0.20 i j 0.00

1T3L 1T3L 1T3L 1T3L 1T3L 1T3L 2T2L 2T2L

a b c d e f g h i j

GM IM fM 0.00 H J I JM Surface/ Bounding Boxg IM a Volume gM J aM gMM Standard Deviation JM aMM h a b 400.00 aM bM hM b bMM i 350.00 bM c iM c cM 300.00 cM d j d dM jM 250.00 e Bounding e Box Surface/ jMM eM eM Volume f eMM 200.00 Standard fM Deviation fM g fMM 150.00 gM g gMM 100.00 gM h gMM hM gMMM 50.00 i h iM hM j 0.00 hMM jM i Intersection Length jMM iM iMM Standard Deviation j 2.50 jM Intersection Length jMM 2.00 jMMM

eMM fM 0.00 fMM g gM 400.00 gMM 350.00 gMMM 300.00 h 250.00hM 200.00hMM i 150.00 iM 100.00 iMM 50.00 j 0.00 jM jMM jMMM 2.50

50.00 0.00

2.50 2.00

Intersection Length Standard Deviation

1.50

Stand

Standard 1.00 Deviation

0.50 0.00

2.00 1.50

Leaf Z Value

1.00

Standard Deviation

Average Leaf Z

0.50 0.00

1.50

Leaf Z Value

1.00

Standard Deviation

Intersection Length

Leaf Z

Intersection Length

Standard Deviation

0.50 0.00

Leaf Z Value Standard Deviation

1.00 Intersection Length

2.50

0.50 Standard Deviation

2.00

0.00

1.50

Leaf Z Value

1.00

Standard Deviation

0.50 0.00

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Evaluation

POP-10 POP-10 POP-11 POP-11 POP-09 POP-09 POP-10 POP-10 POP-11 POP-11 POP-09 POP-09 A AA AA A 1T3L 1T3L 1T3L 1T3L 1T3L 1T3L B BB BAM AM 1T3L 1T3L 1T3L 1T3L 1T3L 1T3L C CBM BMB B 1T3L 1T3L 1T3L 1T3L 1T3L 1T3L D DC CBM BM ECM CMC C 1T3L 1T3L 1T3L 1T3L 1T3L 1T3L E F FD DCM CM 1T3L 1T3L 1T3L 1T3L 1T3L 1T3L G GE ED D 2T2L 2T2L 1T3L 1T3L 1T3L 1T3L H HEM EM DM DM I IF FF F 2T2L 2T2L 2T2L 2T2L 1T3L 1T3L J JG GI I 2T2L 2T2L 2T2L 2T2L 1T3L 1T3L a aGM GMIM IM 2T2L 2T2L 2T2L 2T2L 1T3L 1T3L b bH HJ J 2T2L 2T2L 2T2L 2T2L 1T3L 1T3L c c I I JM JM d d IM IM a a 3T1L 3T1L 2T2L 2T2L 1T3L 1T3L e eJ JaM aM 3T1L 3T1L 2T2L 2T2L 1T3L 1T3L f f JM JM aMM aMM 3T1L 3T1L 2T2L 2T2L 1T3L 1T3L g ga ab b h haM aMbM bM 3T1L 3T1L 3T1L 3T1L 2T2L 2T2L i i b bbMM bMM 3T1L 3T1L 3T1L 3T1L 2T2L 2T2L j j bM bMc c Distribution of the c ccM cM Different Structures cM cMd d d ddM dM e ee e eM eMeM eM f feMM eMM fM fMfM fM Summary and Evaluation g gfMM fMM gM gMg g An increase in the Surface to Bounding Box Volume ratio over the generations indicates the general success of the genetic algorithm, gMM gMM gM gM and similar success shown by the decrease of intersection length. Decrease in leaf-Z values (and thus a decrease in overall tree h hgMM gMM height) originates in the weighting of the fitness criteria being balanced in favour of the surface to volume ratio - the results can be hM hM gMMM gMMM compared to “bushes” that are highly efficient in material, but do not need to compete over exposure to the sun. i i h h This result can be seen as a form of directed evolution, where one of the parameters takes precedent due to environmental pressure. iM iMhM hM j jhMM hMM jM jM i i Gene Summary jMM jMMiM iM iMM iMM Looking at homeobox structure of the population one can see that the 1 trunk, 3 leaf variety has almost completely overtaken the entire j j jM jM population. This is probably due again to the surface to volume criteria being overstressed, as trunk genes tend to generate more jMM jMM height thus increasing the bounding box volume. In the number and type of genes in the genes in the simulation one can see that a jMMM jMMM high amount of mutation has caused an increase in the total amount of genes in the new population, with a shift to the dominance of

the leaf genes for all the reasons mentioned above. 74

Distribution of Trunk and Leaf Genes

Data Structures Data structures are an abstract way of using Object Oriented Programming, in a high level language such as python, C++ or java in order to implement a general structure for genetic algorithms. Classes are defined to be containers of data encapsulating the information necessary for them to function, passing to a higher level only the minimal information needed to run the simulation. This type of implementation allows programmer to define the code in a structured, logical system. The distinction between Genotypes and Phenotypes is Inherent in the data structure and actually helps to understand the algorithm. Since the Classes are written in different files, it makes cooperation between several people working simultaneously possible, as access functions can be defined at the design stage and defined in an API (Application Programming Interface) that is the â&#x20AC;&#x153;logical mapâ&#x20AC;? for the entire code. It seems that the data structures shown here are generic for implementing a genetic algorithm of this type, and can be described as a common basis for all of the simulations in advance.

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Data Structures

Class Gene:

Class Genome:

data:

move(axis,amount) rotate(axis,amount) scale(axis,amout) type (trunk,branch)

Class Population:

geneList[] switchLevel

data:

methods:

createNewGenome(trunkGenes,leafGenes,switch) setGeneAt(location,Gene) getGeneAt(location):returns Gene getSwitch():return Switch seSwitch(Switch) createIndvidual(): returns Indvidual

methods:

createRandomGene(type) createCopyGene(Gene other) setMove(Mx,My,Mz) setRotation(Rx,Ry,Rz) setScale(Sx.Sy,Sz) setType(t)

methods:

Gene Gene Gene

Primitive Primitive Primitive

Class Primitive: data:

center [x,y,z] axis[Vx,Vy,Vz] scale[Sx,Sy,Sz]

methods:

setCenter(x,y,z) getCenter(): return center setAxis(Vx,Vy,Vz) getAxis(): returns [vec3D Vx,Vy,Vz] setScale(Sx,Sy,Sz) getScale():returns[Sx,Sy,Sz] rotate(int ax,int ang) move(int ax,int amount) scale(int ax, int amount) draw()

genomeList[] indList[] surfaceToBBList[] leafZList[] intersectionList[] surfaceToBBRank[] leafZRank[] intersectionRank[] totalRank()

Class Individual:

init() appendGenome(Genome A) createIndividuals() fillRankLists() calculateTotalRanks() getHighestRankingIndividual():returns Individual[]

data:

Primitive primitives[][][][][] int surfaceArea int BBvolume int averageLeafZ int intersectionLength

methods:

init() (empty constructor) init(surface,volume,leafZ) addPrimitive(Primitive p, int level) getPrimAtLevel(int level):returns Primitive[] calcSurfaceArea() calcBBVolume() calcAvgLeafZ() getSurfaceArea():returns surface getBBvolume():returns BBvolume getAvgLeafZ():returns leafZ draw() Individual

Individual

Data Structures

create trunkGeneList from 10 random genes

create leafGeneList from 10 random genes

Trunk Genes

Leaf Genes

create 15 genomes from the gene lists: 5 from type T-L-L-L 5 from type T-T-L-L 5 from type T-T-T-L

convert the genomes into individuals, store in population 1

Genomes of First Population

evaluate all individuals, storing the result in population 1, kill unwanted individuals breed genomes of population 1 -> population 2

repeat last step until reaching fitness goal

convert population 2 into individuals, evaluate population 2 Individuals of First Population Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Algorithm Part I

create trunkGeneList from 10 random genes

Breed( Population1): returns Population2 breeders = Pop1.getHighestRankInd() breeders.removeDeadIndividuals() ResultPop.appendGenome(breedGenome(breeders[0],breeders[3])) ResultPop.appendGenome (breedGenome(breeders[1],breeders[4])) ResultPop.appendGenome (breedGenome(breeders[2],breeders[5])) for all I in Breeders ResultPop.appendGenome (mutateGenome(I))

create leafGeneList from 10 random genes

create 15 genomes from the gene lists: 5 from type T-L-L-L 5 from type T-T-L-L 5 from type T-T-T-L

breedGenome(Genome A, Genome B):returns Genome[1,2,3] Child1=new Genome(with structure of A) Child2=new Genome(with structure of A) Child3=new Genome(with structure of B) trunkGenePool = A.trunkGenes + B.trunkGenes leafGenePool = A.leafGenes + B.leafGenes for all children : add genes from trunkGenePool until switch add genes from leafGenePool after switch return children

convert the genomes into individuals, store in population 1 Individual

evaluate all individuals, storing the result in population 1

breed genomes of population 1 -> population 2

convert population 2 into individuals, evaluate population 2

repeat last step until reaching fitness goal

Overall Rank

1 2

1T3L-A-M

1T3L-E-M

2T2L-C-M

2T2L-A-M

3T1L-A-M

2T2L-B-M

1-4A

1-4B

1-4C

2-5A

2-5B

2-5C

3-6A

3-6B

3-6C

2 3 4 5 6 1 2

Population breeding and mutation strategy

Genome breeding strategy

Algorithm Part II

GENE NAME

01A 01B 01BM(i) 01BM(i)M 01BM(i)MM 01BMM(e) 01BMM(e)M 01BMM(e)MM 02A 02A-M 02A-MM 02A-MMM 02B 02B-M 02B-MM 02B-MMM 03A 03A-M 03B 03B-M 04A 04A-M(c) 04A-M(c)M 04B 04B-M(d) 04B-M(d)M 05A 05B 06A 06A-M 06B 06B-M 06B-MM 06B-MMM 07A 07A-M(g) 07A-M(g)M 07A-M(g)MM 07A-M(g)MMM 07A-MM 07A-MMM 07A-MMMM 07B 07B-M 07B-MM(h) 07B-MM(h)M 07B-MM(h)MM 08A 08B 09A 09B 10A 10B 11A 11B 12A 12B 13A 13B 14A 14B 15A 15B 16A

Rotate X Y Z 62 62 42 42 42 56 56 56 38 38 38 38 76 76 76 76 59 59 44 62 19 19 19 12 12 12 77 59 90 90 20 20 20 20 48 48 48 48 48 48 48 48 41 41 41 41 41 11 84 18 56 90 65 66 71 42 53 80 0 70 45 20 90 62

Emergence

GENE CODE Move X Y Z 0.7 1.1 1.0 0.2 0.2 1.0 1.0 0.9 1.3 1.3 1.3 1.3 1.3 1.3 1.3 2.0 0.7 0.7 0.7 0.7 1.4 1.6 0.6 1.4 1.4 1.4 0.4 0.8 0.7 0.7 1.2 1.2 1.2 1.2 1.6 1.6 0.7 0.6 0.6 1.6 1.6 1.6 1.2 1.2 4 1.7 0.6 2.0 0.6 0.5 2.0 0.8 1.4 0.8 1.2 2.0 2.0 0.5 0.9 2.0 1.7 1.1 0.8 1.7

GENE NAME

GENERATIONS Scale X Y Z 1.4 2.0 1.7 1.7 1.7 1.7 5.0 1.2 1.2 0.8 0.8 0.8 0.8 0.8 0.8 1.4 1.4 1.4 1.4 1.5 1.5 1.6 1.6 1.8 1.9 1.9 1.1 1.6 0.6 1.8 1.1 0.5 0.5 0.5 0.5 2.2 0 0.6 1.0 1.0 1.5 1.5 1.5 1.5 1.6 2.0 3.0 1.4 1.4 3 0.5 0.5 2.9 1.1 1.7 1.9 1.9 1.7 2.1 1.7 0.5 2.5 3.0 1.5 2.5 2.7 0.8 0.9 2.0

5 5A 6 6A 7

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

9 10 11 16B 17A 17B 18A 18B 19A 19A-M 19B 19B-M 20A 20B 21A 21B 22A 22B 23A 23B 24A 24A-M(a) 24A-M(a)M 24A-M(a)MM 24A-M(j) 24A-M(j)M 24A-M(j)MM 24A-M(j)MMM 24B 24B-M(b) 24B-M(b)M 24B-M(b)MM 25A 25B 25B-M 26A 26B 27A 27B 28A 28B 29A 29A-M 29B 29B-M(f) 29B-M(f)M 29B-M(f)MM 29B-MM 30A 30B A B BM C CM D DM E EM F G GM H I IM J JM

Rotate X Y Z 65 30 40 130 65 30 30 25 45 50 15 140 150 170 65 120 121 170 0 0 0 0 0 0 0 75 17 17 17 67 134 70 4 179 91 126 141 42 56 56 127 140 140 140 140 135 68 1.3 1.4 1.4 0.7 0.7 0.2 1.1 1.1 1.1 1 0.9 0.9 0.3 1.2 1.2 1.2 1.1

GENE CODE Move X Y Z 1.3 1.8 1.7 1.2 1.0 0.4 0.4 1.2 1.2 2.4 1.7 0.2 1.3 1.2 1.4 1.6 1.2 0.7 0.7 0.7 1 0.8 0.3 0.5 0.9 0.8 0.8 0.8 1.4 0.6 1 1 0.4 0 0.3 1 0.4 1.1 0.6 1 1.7 1.7 1.7 0.9 1.7 0.5 1.9 30 -25 -25 -30 15 -22 -22 -21 -30 30 30 15 -30 -30 -30 -30 -30

GENERATIONS Scale X Y Z 1 2.0 2.4 3.0 5.0 0.6 0.2 1.5 0.5 0.5 1.5 1.4 0.3 0.2 2.3 0.6 0.7 0.6 2.0 3 1 1 1.8 1.8 1.8 1.8 2.3 2.3 1.6 1.6 5 3.8 3.8 2 2.2 2.6 3.6 0.3 2.7 2.7 5 1.4 3.0 1.5 1.5 4 3.2 3.9 1.4 2.2 2.2 2.2 2.6 2.6 2 2 1.1 1.1 1.8 1.8 1.4 1.4 1.4 1.4 2.8 3 2.5 2.8 2.8 2.8 2.8

5 5A 6 6A 7

9 10 11

Library and trace of genes used in the simulation for all populations created

Different Genes in the Simulation

Conclusions In this exercise we have tried to implement a basic evolutionary algorithm, as well as develop an initial approach towards embryological development and possible body structures. While developing the different populations we had a chance to experiment with different genome/ homeobox structures, breeding strategies and fitness criteria, and we feel that an outline of an implementable algorithm has been formulated. One of the subjects which was not explored to its full potential was the effect of competition within members of a single population for limited resource, which was hinted at by our fitness criteria but not developed to a model where differentiation within the population might increase the “survivability” of the population as a whole. Another subject which could be expanded would be specialization within the gene population and the refinement of the body plan and the homeobox that activates it. A class of “branch” genes added to the existing “trunk” and “leaf” classes is one such example, as well as adding real physical limitations originating from the world of trees. Since operations were computed “manually” on many parameters of the simulations, our assumptions remain invalidated theories. Much larger populations and many further generations would needed in order to methodically test our notions. This can only be achieved by constructing a fully computerized model to run the simulation and asses its strengths and weaknesses. Typical genetic algorithm work on populations of thousands of individuals, with generations nubering in hundreds. Time consuming as this effort may be, we feel that it might have gained us further insight into genetic programming strategies and scripting experience. 80

Conclusions

Articles E.M. De Robertis, Evo-Devo: Variations on Ancestral Themes. Cell 132, January 25, 2008, Elsevier Inc. E.M De Robertis et Al. Homeobox Genes and The Vertebrate Body Plan. Scientific American, July 1990 Books Steven Johnson. Emergence - the connected lives of ants, brains, cities and software. England: Penguin Books, 2002 Sean B. Carroll. Endless Forms Most Beautiful-the New Science of Evo Devo and the Making of the Animal Kingdom. London: Quercus, 2011 Michael Hensel, Achim Menges and Michael Weinstock. Emergent Technologies And Design-Toward a biological paradigm for architecture. New York: Routledge, 2010

Emergence

Guy Austern | Lei Liu | Christopher Hill | Sushant Verma

Bibliography