Random Recipe

The Cook Book

Recipe for the week of August 21 - 27

A CA run on Penrose Tiles

When my family exalts ' CA rules,' they're not endorsing my line of research. While I visit them for my parents' fiftieth anniversary, Kellie Evans has offered to run the Kitchen. The report that follows describes her experiences at SFI this summer. Thanks Kellie!

This week's soup was generated by running Majority Vote on the fat diamonds and Minority Vote on the skinny diamonds of a Penrose tesselation. In other words, the image was generated by a cellular automaton with two states, on or off. The universe is a Penrose tesselation so each site is either a fat or a skinny diamond. The neighborhood of a diamond consists of four other diamonds, each of which shares one of its edges. A fat diamond will switch state if it sees a majority of its four neighbors which are of the other state. A skinny diamond will switch if it sees a minority of the other state. The additional colors seen in this image are used to indicate the amount of time a diamond has been switched on. The initial state had all of the sites turned off.

The idea for this rule came from a collaboration of students in the Cellular Automata Research Group (CARGO) formed at the 8th Annual Complex Systems Summer School put on by the Santa Fe Institute. Eric Weeks was the master of the code, David Ardell suggested using a Penrose tesselation as the universe for the CA, and Patrik D'haeseleer had the idea to use different rules for the distinct diamonds.

Eric spent a good part of the summer school generating pictures. Well worth seeing is the phase diagram of a finite, nearest neighbor one-dimensional CA. Each point of the diagram represents the average - gamma (0 < gamma < 1) of the 150 site values after 100 time steps. Its two dimensions come from two constants, c (0 < c < 1) and gamma, which determine the rule.

In addition to CARGO, many other research groups were formed during the summer school. Several of the groups continue to collaborate. Other highlights of the summer school with connections to cellular automata included a week of lectures on Genetic Algorithms given by Stephanie Forrest; a demo of Swarm, a software package for multi-agent simulation of complex systems; a lecture on the Evolving CA Project given by Rajarshi Das; and Chris Langton's 'complex' overheads...

Take me higher...
Introduction to the PSK PSK Search Recent Additions CA Archive CA Links Feedback Appreciated !