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

  • Previous work (by others)

  • Introducing Solid Cellular Automata

  • Previous work (by the author)
  • Simple chemical reactions

  • Models of catalysis

  • A model of life

  • Conclusions & future work

 


Motivation

To model an organism...

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


Previous Work (by others)


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


Previous work (by the author)

Previous Work: Chaining SOCA elements


Forces

Grey

Blue

Green

Grey

-0.25

0

0

Blue

0

-1

+1

Green

0

+1

-1


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

Forces

Grey

Blue

Green

Red

Grey

-1
-1
-1
0

Blue

-1
-60
-30
-20

Green

-1
-30
+70
-2

Red

0
-20
-2
+70

Transitions

Grey

Blue

Green

Red

Grey

-
-
-
-

Blue

-
-
-
-

Green

-
-
8,Red,0
1,Red,0

Red

-
-
-
10,Green,0




single cluster

size-limited &
fractured clusters


Modelling chemical reactions





Red

+ Blue

 

Magenta

+ Cyan


Forces:

Null (rely on kinetic energy of elements & random collisions)


Transitions

Grey

Red

Blue

Cyan

Magenta

Grey

-
-
-
-
-

Red

-
-
1,Magenta,0
-
-

Blue

-
1,Cyan,0
-
-
-

Cyan

-
-
-
-
-

Magenta

-
-
-
-
-

 

Illustration of (contained) reaction

Concentration vs. Time (plot)


Catalyzed reactions




Red

+ Blue

Green/Yellow catalyst

Magenta

+ Cyan


Transitions:

Blue -> Cyan
Red -> Magenta

(in the presence of Red)
(in the presence of Blue)


Forces

Grey

Green

Blue

Red

Cyan

Magenta

Yellow

Grey

0
0
0
0
0
0
0

Green

0
0
0
+500
0
-500
0

Blue

0
0
0
0
0
0
+500

Red

0
+500
0
0
0
0
0

Cyan

0
0
0
0
0
0
-500

Magenta

0
-500
0
0
0
0
0
Yellow
0
0
+500
0
-500
0
0

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


Forces:

Green >attract< Blue

Blue <repel> Blue

Transitions:

Green -> Blue

(in the presence of 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

Forces:

Blue >attract< Green

Red >attract< Green

Magenta >attract< Yellow

Cyan >attract< Yellow

Transitions:

Red -> Inert

Blue -> Yellow

(in the presence of Blue)

(in the presence of Red)

Magenta -> Inert

Cyan -> Green

(in the presence of Cyan)

(in the presence of Magenta)


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:

 

 

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:

 

 

Red

+ Blue/Grey

Green/Grey catalyst

Inert

+ Yellow/Grey

Magenta

+ Cyan/Grey

Yellow/Grey catalyst

Inert

+ Green/Grey


Forces:

Blue >attract< Green

Red >attract< Green

Magenta >attract< Yellow

Cyan >attract< Yellow

Grey >attract< Grey

Black >attract< Black*

Transitions:

Red -> Inert

Blue -> Yellow

(in the presence of Blue)

(in the presence of Red)

Magenta -> Inert

Cyan -> Green

(in the presence of Cyan)

(in the presence of Magenta)

Grey -> Inert

Grey -> Black*
Black -> Grey*

(in the presence of 3 Grey)

(in the presence of 3 Grey)
(in the presence of 5 Black)

* 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:



©Copyright Alan Dorin/Animaland 2000