Wolfram Computation Meets Knowledge

Wolfram Summer School


Jiang Zhang

Summer School

Class of 2007


Jiang (“Jake”) Zhang from Beijing is a postdoctoral researcher at the Complex Systems Research Center of the China Academy of Sciences. He spent six years studying civil engineering and received his master’s degree from Beijing Jiaotong University, but then changed his major to management science. While pursuing his PhD, his interests migrated to complex systems and multi-agent modeling, both of which inspired his current postdoctoral work. He has also done some part-time work as a software developer and consultant for several companies in Beijing.

His diverse research interests include modeling complex systems, artificial intelligence and life, NKS, and other computational theories. Currently, he is concentrating on energy flows in food webs and the relationship between population dynamics and biological evolution. He also maintains a website to propagate scientific ideas to the general public.

Project: Complexity and Universality of Iterated Finite Automa

Iterative finite automata (IFA) are interesting computational models presented by Stephen Wolfram as a way of studying cellular automata. The rule for the IFA has the general form (current state, input) -> (next state, output). Consider such an automaton with a reading head and s internal states moving on a fixed-size tape with k colors. In each time step, the moving head updates its own state and the color of the next cell according to the input from the tape and the previous state. When the reading head moves to the right-hand side of the tape, it will restart from the left-hand side with the initial state as the first turn. These results can be displayed in the same way as a 1D cellular automaton is displayed.

The simplest case of two states and two colors has already been investigated by Wolfram. The cyclic behavior, fixed value behavior, and nested behavior can all be produced in this very simple case. In my project I will expand this into a study of three states and two colors with more complex rules. Some initial experiments that I have done showed that there were IFAs that can exhibit complex class behaviors.

Favorite Outer Totalistic Three-Color Rule

Rule chosen: 6875542

My favorite outer totalistic CA is 6875542 because from different backgrounds and center cell colors I can obtain similiar complex patterns. For instance, CellularAutomaton[{6875542, {3, {3, 1, 3}}}, {{1}, 0}, {50, All}] can produce the exact pattern that CellularAutomaton[{6875542, {3, {3, 1, 3}}}, {{2}, 1}, {50, All}] produced just after two steps.

You can also get the same pattern with CellularAutomaton[{6875542, {3, {3, 1, 3}}}, {{0}, 2}, {50, All}].

Backgrounds {{1}, 2} and {{2},0} can produce the same pattern.

These patterns are also complex and symmetric.