Mapping the Cellular Automata Rule Spaces

Rodrigo A. Obando

TSYS Department of Computer Science
Columbus State University
http://csc.colstate.edu/obando

A Rendering of the Rule Space

This is the resulting map for k=2, r = 1  (1/2)

Constraining the primitives to isotone and antitone boolean functions

Constraining the primitives to isotone and antitone boolean functions (Cont...)

The Elementary Cellular Automata

This is a partial mapping of the ECA Rule Space.  This includes only the isotone and antitone primitives.

Exploring the space for r=1 (1/2)

This mapping contains only two explored quadrants.  The other two are blank but left in place for reference.

Automatic Detection of class behavior (less Class 4)

ECA automatic mapping of the partial space.

Automatic Detection of class behavior (less Class 4) (Cont...)

Automatic mapping of the partial space Cellular Automata r=1 (1/2)

Automatic Detection of class behavior (less Class 4) (Cont...)

Automatic mapping of the partial space Cellular Automata r=2

Side by Side Comparison

Class Behavior location seems to remain localized when going from one space rule to the next.

Primitive Input Space (r = (1/2))

Primitive Input Space (r = 1)

Primitive Input Space (r = 1 (1/2))

Primitive Input Space (r = 2)

Conclusions

Partition of the rules in the define primitives is a good way to create a map of the rule spaces.
The location of class behaviour seems to be invariant when going from one rule space to another and it may be used as a predictor of where to find rules of a particular class.
Further research is necessary to explore the 6-dimensional space instead of just the 'slice' (surface) shown in this presentation.