Artificial Life VII, August 2000

Creating a Physically-Based, Virtual-Metabolism with Solid Cellular Automata (SOCA)

Alan Dorin

http://www.cs.monash.edu.au/~aland
aland@cs.monash.edu.au

Centre for Electronic Media Art
School of Computer Science & Software Engineering
Monash University, Melbourne, Australia

Outline

Motivation

To model an organism...

• network of self-sustaining, self-bounding, auto/cross-catalytic chemical processes.

  ...in the spirit of Monod, Kauffman, Prigogine, Maturana & Varela.
  
  

Organism components act entirely within the limits imposed by...

• their physical & chemical attributes
  
  
• their local environment

Previous Work (by others)

• Physical Simulation
  (computer animation, weather forecasting, engineering)
  
  
• Cellular Automata
  (study complex dynamical systems, reproducing systems)
  
  
• Self-Assembly
  (nano-technology, cell & bacteriophage development)
  
  
• Distributed A.I.
  (agent simulations, distributed problem solving)
  
  
• Molecular Dynamics / Supra-molecular Inorganic Chemistry
  (chemical modelling, synthesis, visualization)

Introduction to Solid Cellular Automata (SOCA)

The Physical Model

Model of rigid, convex, polyhedra which are:

• suspended in a fluid medium
  
  
• subject to:
  
  
  • Fluid drag
  • Contact forces caused by collisions
  • Internally-generated forces (attract/repel)
  • Externally-generated forces (gravity)

The Cellular Automaton Model

• Polyhedron's faces may be in one of a number of discrete states.
  
  
• States are visualized by colour.
• One state is designated the inert state.

• A polyhedron's environmental conditions consist of the state and range of all non-inert faces on neighbouring polyhedra.
  
  
• A polyhedron's transition table prescribes state changes for a face
  (according to the face's current state and local environmental conditions)
  
  
• A polyhedron's force table dictates forces generated by a face
  (according to the face's current state and local environmental conditions)

Previous work (by the author)

Previous Work: Chaining SOCA elements

short chains

long clumpy chains

long open chains

Previous Work: Size-limited and fracturing clusters of SOCA elements

single cluster	size-limited & fractured clusters

Modelling chemical reactions

Red	+ Blue		Magenta	+ Cyan

Illustration of (contained) reaction	Concentration vs. Time (plot)

Catalyzed reactions

Red	+ Blue	Green/Yellow catalyst	Magenta	+ Cyan

t=0 Red, Blue and a Green/Yellow catalyst	t=100 Red has been pulled towards Green Blue has been pulled towards Yellow	t=120 Red and Blue have been pulled into proximity and react to form Magenta and Cyan which then frees the catalyst

Concentration vs. Time (plot)

Auto-catalysis

Green	Blue catalyst	Blue

t=0 Lots of Green, one Blue (at the back)	t=300 Green turns towards expanding collection of Blue	t=900... Blue collection continues to expand converting more and more Green to Blue

Cross-catalysis

Red	+ Blue	Green catalyst	Inert	+ Yellow
Magenta	+ Cyan	Yellow catalyst	Inert	+ Green

The reactions produce catalyst for each other

t=0 Lots of Blue/Red, Cyan/Magenta, a bit of Yellow & Green	t=900... Blue/Red, Cyan/Magenta pulled towards their respective catalysts to manufacture more catalyst

A model of living systems

Q: Which SOCA topology might potentially be formed from a set of cross-catalytic reactions?

A: The cluster / star is:

• easily assembled
  
  
• robust
  
  
• of recognizable form
  
  
• an ideal candidate!
  
  

Q: How can a cluster / star be produced using virtual cross-catalytic reactions?

A: Yellow & Green catalyst elements produced by cross catalytic reactions (above) may be clustered together to produce a topology which is:

• dynamic
  
  
• maintained by the cross-catalytic reactions
  
  
• robust
  
  
• of recognizable form
  
  
• a (virtual) metabolic system

Red	+ Blue/Grey	Green/Grey catalyst	Inert	+ Yellow/Grey
Magenta	+ Cyan/Grey	Yellow/Grey catalyst	Inert	+ Green/Grey

* Optional forces & transitions for reproduction by fracture

These structures may even fracture (using process explained for fracturing, size-limited structures above) and therefore reproduce whilst maintaining the cross-catalytic reactions.

Dynamic, fracturing clusters formed by (virtual) cross-catalysis

Conclusions & future work

The following SOCA models have been presented:

• chemical reactions essential to living things
  
  
• an organism which:
  
  
  • constructs its materials
  • self-assembles
  • cross-catalyzes
  • regulates its size
  • reproduces by fracture
  
  

  In the future some motile structures which have been constructed using SOCA will be demonstrated.

©Copyright Alan Dorin/Animaland 2000