René Doursat - University of York · 9. ¾. The challenges of complex systems (CS) research. From...

1

EmbryomorphicEmbryomorphicEngineering:Engineering:

From biological development toFrom biological development toselfself--organized computational architecturesorganized computational architectures

René Doursathttp://www.iscpif.fr/~doursat

2

free self-organization

Systems that are self-organized and architectured

(evolutionary) design

decomposethe system

Peugeot Picasso

self-organized architecture / architectured self-organization Peugeot Picasso

makecomponents

evolve

the scientific challenge of

complex systems: how can they

integrate a true architecture?

the engineering challenge of complicated

systems: how can they integrate self-

organization?

3

Architectured systemstrue intrinsic structure: non-trivial, complicated morphology

hierarchical, multi-scale: regions, parts, details, agentsmodular: reuse, quasi-repetitionheterogeneous: differentiation & divergence in the repetition

random at the microscopic level, but reproducible (quasi deterministic) at the mesoscopic and macroscopic levels

Toward programmable self-organizationSelf-organized (complex) systems

a myriad of self-positioning, self-assembling agentscollective order is not imposed from outside (only influenced)comes from purely local information & interaction around each agentno agent possesses the global map or goal of the systembut every agent may contain all the rules that contribute to it

4

1. Toward self-organized and architectured systems

2. Biological development as a two-side challengeHeterogeneous motion vs. moving patterns

3. Embryomorphic engineeringMorphogenesis as a multi-agent self-assembly process

4. Evo-devo engineeringEvolutionary innovation by development

5. Extension to self-knitting network topologies

Embryomorphic EngineeringEmbryomorphic Engineering

5

large number of elementary agents interacting locally

simple individual behaviors creating a complex emergent collective behaviordecentralized dynamics: no master blueprint or grand architect

Complex systems in many domains

Internet& Web

= host/page

insectcolonies

= ant

physical, biological, technical, social systems (natural or artificial)

patternformation

= matter

biologicaldevelopment

= cell

socialnetworks= person

the brain& cognition

= neuron

6

Paris Ile-de-France

LyonRhône-Alpes

National

4th French Complex SystemsSummer School, 2010

CS in geographical space (F)

7

Precursor and neighboring disciplines

dynamics: behavior and activity of a system over time multitude, statistics: large-scale

properties of systems

adaptation: change in typical functional regime of a system

complexity: measuring the length to describe, time to build, or resources to run, a system

dynamics: behavior and activity of a system over time

nonlinear dynamics & chaosstochastic processessystems dynamics (macro variables)

adaptation: change in typical functional regime of a system

evolutionary methodsgenetic algorithms machine learning

complexity: measuring the length to describe, time to build, or resources to run, a system

information theory (Shannon; entropy)computational complexity (P, NP)Turing machines & cellular automata

systems sciences: holistic (non- reductionist) view on interacting partssystems sciences: holistic (non- reductionist) view on interacting parts

systems theory (von Bertalanffy)systems engineering (design)cybernetics (Wiener; goals & feedback)control theory (negative feedback)

CS in conceptual space: a vast archipelago

→ Toward a unified “complex systems” science and engineering?

multitude, statistics: large-scale properties of systems

graph theory & networksstatistical physicsagent-based modelingdistributed AI systems

8

EmergenceThe system has properties that the elements do not have

ex: micro units form macro patterns: rolls, spiral waves, stripes, spotsex: “ignorant” individuals make intelligent collective decisions: insect colonies, neurons, market traders(?)

These properties cannot be easily inferred or deducedex: liquid water or ice emerging from H2O moleculesex: cognition and consciousness emerging from neurons

Different properties can emerge from the same elements/rulesex: the same molecules of water combine to form liquid or ice crystalsex: the same cellular automaton rules change behavior with initial state

Global properties make local (sophisticated) rules at a higher level→

jumping from level to level through emergence

Counter-examples of emergence without self-organizationex: well-informed leader (orchestra conductor, military officer)ex: global plan (construction area), full instructions (orchestra)

9

The challenges of complex systems (CS) research

From natural to engineered emergence (and back)

Transfersamong systems

CS engineering: designing a new generation of "artificial" CS(harnessed & tamed, including nature):

collective robotics, synthetic biology, energy networks

CS science: understanding & modeling "natural" CS(spontaneously emergent, including human-made):

morphogenesis, neural dynamics, cooperative co-evolution, swarm intelligence

Exportsdecentralizationautonomy, homeostasislearning, evolution

Importsobserve, modelcontrol, harnessdesign, use

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(a) simple/random SO: pattern formation (spots, stripes), swarms (clusters, flocks), complex networks (hubs)...

(d) directdesign(top-down)

mor

e self

-org

aniza

tion

mor

e arc

hite

ctur

e

gap to fill

Most self-organized systems form “simple”/random patterns

... while “complicated” architectures are designed by humans

texture-like order: repetitive, statistically uniform, information-poor – arising from amplification of fluctuations: unpredictable number/position of mesoscopic entities (spots, groups) – OR determined by the environment (trails)

From “statistical” to “morphological” CS

11

artif

icial

natu

ral

(a) natural random self-organization

(d) directdesign(top-down)

(b) naturalself-organizedarchitectures

(c) engineeredself-organization(bottom-up)

. . . .. . . .

mor

e self

-org

aniza

tion

mor

e arc

hite

ctur

e

MESOBIONICS

From “statistical” to “morphological”... to artificial CS

the only natural emergent and structured forms are biological

→

can we reproduce them in artificial systems?

mesoscopic organs and limbs have intrinsic, nonrandom morphologies – development is highly reproducible in number and position of body parts – heterogeneous elements arise under information-rich genetic control

12

?

number of transistors/year

in hardware, software,

number of O/S lines of code/year

?or networks, ...

number of network hosts/year

?

Ineluctable breakup into myriads of modules/components,

De facto complexity of engineering (ICT) systems

13

Self-architecturing in natural systems → artificial systems

Taming complex ICT toward morphogenetic abilities

morphogenetic abilities in biological modelingorganism developmentbrain development

need for morphogenetic abilities in computer science & AI

self-forming robot swarmself-architecturing softwareself-connecting micro-components

http://www.symbrion.eu

need for morphogenetic abilities in techno-social networked systems

self-reconfiguring manufacturing plantself-stabilizing energy gridself-deploying emergency taskforce MAST agents, Rockwell Automation Research Center

{pvrba, vmarik}@ra.rockwell.com

14

From design to “meta-design”

www.infovisual.info

organisms endogenously grow but artificial systems are builtexogenously

could engineers “step back” from their creation and only set generic conditions for systems to self-assemble?

instead of building the system from the top (phenotype), program the components from the bottom (genotype)

systems designsystems"meta-design"

genetic engineering

Toward “evo-devo” engineering

direct (explicit)

indirect (implicit)

15

intelligent “hands-on” designheteronomous order

centralised controldesigner as a micromanager

rigidly placing componentssensitive to part failures

need to control and redesigncomplicated systems: planes, computers

intelligent & evolutionary “meta-design”autonomous orderdecentralised controldesigner as a lawmakerallowing fuzzy self-placementinsensitive to part failuresprepare for adaptation & evolutioncomplex multi-component systems

Pushing design toward evolutionary biology

The meta-design of complexity

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Genotype: rules at the micro level of agentsability to search and connect to other agentsability to interact with them over those connectionsability to modify one’s internal state (differentiate) and rules (evolve)ability to provide a specialized local function

Phenotype: collective behavior, visible at the macro level

The evolutionary “self-made puzzle” paradigma. Construe systems as self-

assembling (developing) puzzles

b. Design and program their pieces (the “genotype”)

c. Let them evolve by variation of the pieces and selection of the architecture (the “phenotype”)

17

mut

atio

n

mut

atio

n

mut

atio

n

a. Construe systems as self- assembling (developing) puzzles

b. Design and program their pieces (the “genotype”)

c. Let them evolve by variation of the pieces and selection of the architecture (the “phenotype”)

The evolutionary “self-made puzzle” paradigm5

1 208

10

3 92

1

17614

4

7 213

3

0 434

42

2 316

22

10210

differentiation

18







19

Computational, spatially explicit models of development and evolution with possible outcomes toward hyperdistributed, decentralized engineering systems

Replacing biological development in the center

DevoDevo--inspired inspired engineeringengineering

DEVO PROGNET EVOSPACE

Nadi

ne P

eyrié

ras,

Paul

Bour

gine e

t al.

(Emb

ryom

ics &

BioE

merg

ence

s)

genetics evolutiondevelopment

20

more intrinsic, sophisticated architecture

http:/

/www

.bio.f

su.ed

u/fac

ulty-t

schin

kel.p

hp

ant trail

network of ant trails

ant nesttermite mound

http:

//taos

-telec

ommu

nity.o

rg/ep

ow/ep

ow-a

rchive

/ar

chive

_200

3/EPO

W-0

3081

1_file

s/mata

bele_

ants.

jpg

http:/

/cas.b

ellar

mine

.edu/t

ietjen

/Ter

miteM

ound

%20

CS.gi

f

http:/

/pica

sawe

b.goo

gle.co

m/trid

entor

igina

l/Gha

na

From “statistical” to “morphological” CSin social insect constructions

21

From “statistical” to “morphological” CSin inert matter / insect constructions / multicellular organisms

ant trail

network of ant trails

ant nesttermite mound

more intrinsic, sophisticated architecturephysicalpattern formation

biologicalmorphogenesis

social insectconstructions

grains of sand + air insectscells

new inspiration

22

Morphological (self-dissimilar) systemscompositional systems: pattern formation ≠

morphogenesis

“The stripes are easy, it’s the horse part that troubles me”—attributed to A. Turing, after his 1952 paper on morphogenesis

23

reaction-diffusionwith NetLogo

larval axolotl limb condensations

Gerd B. Müller

fruit fly embryoSean Caroll, U of Wisconsin

Physical pattern formation is “free” –Biological (multicellular) pattern formation is “guided”

≠


24

Multicellular forms = a bit of “free” + a lot of “guided”

spots, stripes in skinangelfish, www.sheddaquarium.org

ommatidia in compound eyedragonfly, www.phy.duke.edu/~hsg/54

domains of free patterning embedded in a guided morphologyunlike Drosophila’s stripes, these pattern primitives are not regulated by different sets of genes depending on their position

repeated copies of a guided form, distributed in free patterns

segments in insectcentipede, images.encarta.msn.com

flowers in treecherry tree, www.phy.duke.edu/~fortney

entire structures (flowers, segments) can become modules showing up in random positions and/or numbers


25

FP6 Projects Embryomics, BioEmergencesSubmitted ANR Projects MEC@GEN, SYNBIOTIC

Model embryogenesis ↔ import/export to engineering

RAWembryoimages

MEASUREDcell

coordinates

RECALCULATEDembryonic

development

ARTIFICIALARTIFICIALembryomorphic

engineering

automated observation and reconstruction of developing organisms by image processing and learning/optimization methods

mathematical and computational (agent-based) modeling

simulation of recalculated embryos, real and fictitious

Evo-devo engineering

26

Overview of morphogenesis

Broad principles1. biomechanics → collective motion → "sculpture" of the embryo2. gene regulation → gene expression patterns → "painting" of the embryo+ coupling between shapes and colors

Multi-agent modelsbest positioned to integrate bothaccount for heterogeneity, modularity, hierarchyeach agent carries a combined set of biomechanical and regulatory rules

An abstract computational approach to developmentas a fundamentally spatial phenomenonhighlighting its broad principles and proposing a computational model of these principles

27

Sculpture → forms

Morphogenesis couples assembly and patterning

Painting → colors

the forms are “sculpted” by the self-assembly of the elements, whose behavior is triggered by the colors

new color regions appear (domains of genetic expression) triggered by deformations

Niki de Saint Phalle

“patterns from shaping”

“shape from patterning”

Ádá

m S

zabó

, The

chi

cken

or t

he e

gg(2

005)

http

://w

ww

.sza

boad

am.h

u

28

(a)

α

α3(d)

SA2

α1

α3

α2 . . .

(c)

PF1α3,3

α3,1

α3,2

(e)

PF2

α

SA1

(b)α3,1

(f)

SA3 . . .

PF3

genotype

Morphogenesis couples assembly and patterningSA = self-assembly (“sculpture”)PF = pattern formation (“painting”)

29

Genetic regulation

PROT A PROT BGENE GENE II

PROT C

“key”

“lock”

after Carroll, S. B. (2005)Endless Forms Most Beautiful, p117

GENE A

GENE B

GENE C

A

B

XY

I

Cellular mechanicsadhesiondeformation / reformationmigration (motility)division / death

tensio

nal in

tegrity

(Ing

ber)

cellu

lar P

otts m

odel

(Gra

ner,

Glaz

ier, H

ogew

eg)

GENE GENE IIDrosophila

embryo

GENE CGENE A

GENE B

r

(Dou

rsat)

(Deli

le &

Dour

sat)

Morphogenesis couples mechanics and regulation

30

Segmentation & identity domains in Drosophilaperiodic A/P band patterns are controlled by a 5-tier gene regulatory hierarchy

intersection with other axes creates organ primordia and imaginal discs (identity domains of future legs, wings, antennae, etc.)

from Carroll, S. B., et al. (2001)From DNA to Diversity, p63

Gene regulatory pattern formation

31

Genetic regulation

Cellular mechanics

gene regulation

differential adhesion

modification of cellsize and shape

mechanical stress,mechano-sensitivity

growth, division,apoptosis

change ofcell-to-cell contacts

change of signals,chemical messengersdiffusion gradients

("morphogens")

Morphogenesis couples mechanics and regulation

32

Collective motion regionalized into patterns

Pattern formation that triggers motion

Nad

ine

Peyr

iéra

s, Pa

ul B

ourg

ine,

Thie

rry

Savy

,B

enoî

t Lom

bard

ot, E

mm

anue

l Fau

re e

t al.

Em

bryo

mic

s & B

ioE

mer

genc

es

zebr

afis

h

Hir

oki S

ayam

a(S

war

m C

hem

istry

)ht

tp://

bing

web

.bin

gham

ton.

edu/

~say

ama/

Swar

mC

hem

istry

/http://zool33.uni-graz.at/schmickl

Morphogenesis couples motion and patterns

Doursat

33







34

grad1

div1

patt1

div2

grad2

patt2div3

grad3

patt3...

Recursivemorphogenesis

genotype

Overview of an embryomorphic system

35r

pA

BV

rr0rerc

div

GSA: rc < re = 1 << r0p = 0.05

36

grad

EW

S

N

EW

WE WENS

37

I4 I6

B4

B3

patt

X Y

. . . I3 I4 I5 . . .

B1 B2 B4B3

wix,iy

GPF : {w }

wki

WE NS

38r

pA

BV

rr0rerc

div

GSA : rc < re = 1 << r0p = 0.05

I4 I6

B4

B3

grad patt

EW

S

N

EW

WE WENS

X Y

. . . I3 I4 I5 . . .

B1 B2 B4B3

wix,iy

GPF : {w }

wki

WE NS

GSA ∪

GPF

39

I9

I1

(a) (b)

(c)

. . . . . .

WE = X NS = Y

B1 B2 B3 B4

I3 I4 I5

X Y

. . . I3 I4 I5 . . .

B1 B2 B4B3

wiX,YGPF

wki

Programmed patterning (patt): the hidden embryo mapa) same swarm in different colormaps to visualize the agents’ internal

patterning variables X, Y, Bi and Ik (virtual in situ hybridization)b) consolidated view of all identity regions Ik for k = 1...9c) gene regulatory network used by each agent to calculate its expression

levels, here: B1 = σ(1/3 −

X), B3 = σ(2/3 −

Y), I4 = B1 B3 (1 − B4 ), etc.

Virtual gene atlas

40

Morphological refinement by iterative growthdetails are not created in one shot, but gradually added. . .

. . . while, at the same time, the canvas grows

from Coen, E. (2000)The Art of Genes, pp131-135

Hierarchical morphogenesis

41

I4 I6

E(4)

W(6)

I5I4

I1

N(4)

S(4)W(4) E(4)

rc = .8, re = 1, r0 = ∞r'e = r'0 =1, p =.01GSA

SAPF

SA4PF4

SA6PF6

Hierarchical embryogenesis

42

I4 I6

E(4)

W(6)

I5I4

I1

N(4)

S(4)W(4) E(4)

rc = .8, re = 1, r0 = ∞r'e = r'0 =1, p =.01GSA

SAPF

SA4PF4

SA6PF6

all cells have same GRN, but execute different expression paths → determination / differentiation

microscopic (cell) randomness, but mesoscopic (region) predictability

Hierarchical embryogenesis

43







44

Development: the missing link of the Modern Synthesis...

Purves et al., Life: The Science of Biology

evolutionmutation

"When Charles Darwin proposed his theory of evolution by variation and selection, explaining selection was his great achievement. He could not

explain variation. That was Darwin’s dilemma."

—Marc W. Kirschner and John C. Gerhart (2005)The Plausibility of Life, p. ix

"To understand novelty in evolution, we need to understand organisms down to their individual building blocks, down to their

deepest components, for these are what undergo change."

?? ??

Evolutionary innovation by development

45

Nathan Sawayawww.brickartist.com


The self-made puzzle of “evo-devo” engineering

“To understand novelty in evolution, we need to understand organisms down to their individual building blocks, down to their

deepest components, for these are what undergo change.”

Amy L. Rawsonwww.thirdroar.com macroscopic,

emergent level

microscopic,componential

level

46

Nathan Sawayawww.brickartist.com


The self-made puzzle of “evo-devo” engineering

Amy L. Rawsonwww.thirdroar.com

generic elementary rules of self-assembly

macroscopic,emergent level

microscopic,componential

level

Genotype Phenotype“Transformation”

more or less direct representation

≈ ≈( )

47

Quantitative mutations: limb thickness

Multi-agent evolutionary development (evo-devo)

GPF

GSA

3×31, 1

p = .05g = 15

4 6

disc

GPF

GSA

1×1

tip p’= .05g’= 15

GPF

GSA

1×1

tip p’= .05g’= 15

GPF

GSA

3×32, 1 4 6

disc p = .05g = 15

GPF

GSA

1×1

tip p’= .05g’= 15

GPF

GSA

3×30.5, 1 4 6

disc p = .05g = 15

(a) (b) (c)

wild type thin-limb thick-limb

body planmodule

limbmodule

4 6

48

Quantitative mutations: body size and limb length


(a) (b) (c)

GPF

GSA

3×31, 1

p = .05g = 8

4 6

disc

GPF

GSA

1×1

tip p’= .05g’= 8

GPF

GSA

1×1

tip p’= .05g’= 10

GPF

GSA

3×31, 1 4 6

disc p = .05g = 15

GPF

GSA

1×1

tip p’= .05g’= 40

GPF

GSA

3×31, 1 4 6

disc p = .05g = 15

small long-limb short-limb

49

(a) (b) (c)antennapedia duplication

(three-limb)divergence

(short & long-limb)

PF

SA

1×1

tip p’= .05

GPF

GSA

3×3

p = .05

4 2

disc

6

PF

SA

1×1

tip p’= .1

PF

SA

1×1

tip p’= .03

GPF

GSA

3×3

p = .05

4 2

disc

6

GPF

GSA

1×1

p’= .05tip

GPF

GSA

3×3

p = .05

4 2

disc

GPF

GSA

1×1

p’= .05tip

42

6

Qualitative mutations: limb position and differentiationantennapedia homology by duplication divergence of the homology


50

Qualitative mutations: number of limbs


51

GPF

GSA

4×2

p’= .05tip3 4

GPF

GSA

1×1

tip

GPF

GSA

3×3

p = .05

4 6

disc

GPF

GSA

4×2

tip

(a) (b) (c)

GPF

GSA

3×3

p = .05

4 6

disc

GPF

GSA

4×2

p’= .05tip3 4

GPF

GSA

1×1

tip

GPF

GSA

3×3

p = .05

4 6

disc

GPF

GSA

1×1tip

GPF

GSA

4×2

p’= .15tip3 4 7 8

GPF

GSA

1×1

tipdigit

module

34

3 4

7

84

3

Qualitative mutations: 3rd-level digits


52

Artificial phylogenetic treeproductionproduction

of structuralof structuralinnovationinnovation


53

(Deli

le, D

oursa

t, Pey

riera

s)

More accurate mechanics3-Dindividual cell shapescollective motion, migrationadhesion

Work toward more accurate biological modeling

Better gene regulationrecurrent linksgene reusekinetic reaction ODEsattractor dynamics

switchcombo 1

switchcombo 2

afte

r Dav

id K

ings

ley,

in C

arro

ll, S

. B. (

2005

)En

dles

s Fo

rms

Mos

t Bea

utifu

l, p1

25

54

More work toward functional ECWhat is missing...1. the function/purpose/behavior of a developed organism

depending on the problem domain2-D/3-D modular robotics: move, grab, build, etc.N-D networks: communication dynamics, collective computation

2. a fitness measureassessing the value of the above function

3. a systematic explorationby random, automated mutationswith statistics over many runs

4. a comparisonwith other, non-developmental (or non-self-organized) approacheson the same problems or benchmarks

55

Questions that need to be addressed...modularity?

modularity of the genotype vs. phenotype

compactness?repetitiveness: reuse of genes and gene regulation modulesvs. heterogeneity and uniqueness of structures

innovation?how fine-grained development fosters the emergence of new structures

open-ended evolution?don’t set a specific goal, harvest from surprising organisms

Discussion

56







57

de facto complex systems with spontaneous collective behavior that we don’t quite understand or control yet

time to design new collaborative technologies to harness this decentralisation and emergence

Harnessing complex networks

Programmable techno-social networks

ubiquitous computing & communication capabilities create entirely new myriads of user-device interactions from the bottom up

explosion in size and complexity of techno-social networks in all domains: energy, education, healthcare, business, defense

58

single-nodecomposite branching

clusteredcomposite branching

iterative lattice pile-up

From "scale-free" to architectured networks

59

Not random, but programmable attachment

a generalisation of morphogenesis in n dimensions

Self-knitting networks

the node routines are the "genotype"of the network

60

no intrinsic morphology – complete adaptation to the environment

intrinsic morphologies that are non-trivial andadapt dynamically to their environment

strong intrinsic morphology – no influence from the environment

Self-organized programmable networks

61

Order influenced (not imposed) by the environment

62

freely growing structure

Evolution“wildtype”ruleset A

ruleset A(b) (b)

ruleset A’

ruleset A”

Polymorphism

Development

63Slide from Jake Beal’s course on Spatial Computing, 2009 (CSAIL, MIT)

64

Methodologies and toolsan original, young field of investigation without a strong theoretical framework yet – but close links with many established disciplines, which can give it a more formal structure through their own tools

cellular automata, pattern formationcollective motion, swarm intelligence (Ant Colony Optim. [Dorigo])gene regulatory networks: coupled dynamical systems, attractors

Decentralized Network EngineeringDecentralized Network Engineering

evolution: genetic algorithms, computational evolution [Banzhaf]Iterative Function Systems (IFS) [Lutton]

→

goal: going beyond agent-based experiments and find an abstract description on a macroscopic level, for better control and proof

spatial computing languages: PROTO [Beal] and MGS [Giavitto] (top-down compilation)

PROTO

65

Formation of a specific, reproducible structurenodes attach randomly, but only to a few available ports

1. Chains2. Lattices3. Clusters4. Modules

Details:Details: an abstract model of self-made network

66

Simple chaininglink creation (L) by programmed port management (P)

“slo

wer

” lin

k cr

eatio

n

1 2 2 13 00 3

0 2 1 12 0

0 1 1 0

1 3 2 23 10 4 4 0

0 0port X port X’x x’

t = 4

t = 3

t = 1

t = 2

t = 0

Abstract model of self-made network

“fast”

grad

ient u

pdate

t = 3.0

t = 2.3

t = 2.2

t = 2.1ports can be “occupied” or “free”, “open” or “closed”

67

Simple chainingport management (P) relies on gradient update (G)

3 0

2 0

1 2 1 1 2 00 3

1 2 2 1 2 00 3

1 2 2 1 3 00 3

0 2 1 1 2 00 0

+1+1 +1

“fast”

grad

ient u

pdate

t = 3.0

t = 2.3

t = 2.2

t = 2.1


G → P → Lif (x + x’ == 4) {

close X, X’} else {

open X, X’}

X x x’ X’

each node executes G, P, L in a loopP contains the logic of programmed attachment

68

Abstract model of self-made networkSimple chaining

69

Lattice formation by guided attachmenttwo pairs of ports: (X, X’) and (Y, Y’)


1 10

0

1 10

1

0 20

02 0

0

0

2 01

0

0 00

1

0 21

0port X

X’

x y

Y’

Y

y = 0

y = 8y = 15

y = 0

x = 0x = 0 x = 20x = 10

without port management P, chains form and intersect randomly

70

Lattice formation by guided attachmentonly specific spots are open, similar to beacons on a landing runway


Y’Y

if (x == 0 or(x > 0 & Y’(x−1, y) is occupied))

{ open X’ }else { close X’ }

X X’

. . .

latticegrowing in waves

71

Cluster chains and latticesseveral nodes per location: reintroducing randomness but only within the constraints of a specific structure


1 1

2 00 2X’

2 01 10 2

0 22 0

X

C

1 1

0 2 1 12 0

new intra- cluster port

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Cluster chains and lattices


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Modular structures by local gradientsmodeled here by different coordinate systems, (Xa, X’a), (Xb, X’b), etc., and links cannot be created different tags


0 0

10

1 10 2 2 0

01

1 20 3 2 1

00 3 0

1 00 1

X’a

Xa1 1

0 2 2 0

00

Xb

X’b

11

1 20 3 2 1

02 3 0

20

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Modular structures by local gradients


5 0

11

1 40 5 2 3

02 3 2

20

4 10

31

2

21

3 0

X’c

Xc. . .

the node routines are the “genotype” of the network

close Xaif (xa == 2) { create Xb, X’b }if (xa == 4) { create Xc, X’c }if (xa == 5) { close X’a } else { open X’a }close Xbif (xb == 2) { close X’b } else { open X’b }close Xcif (xc == 3) { close X’c } else { open X’c }

X X’

75Thank youThank you

http://iridia.ulb.ac.be/ants2010→ Special Session on Morphogenetic Engineering

Exporing various engineering approaches to theartificial design and implementation of autonomous systems capable of

developing complex, heterogeneous morphologies

+ Springer book in preparation

Morphogenetic Engineering, ANTS 2010, BrusselsMorphogenetic Engineering, ANTS 2010, Brussels

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René Doursat - University of York · 9. ¾. The challenges of complex systems (CS) research. From...

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