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
Automata Research Group (CARGO) formed at the
Complex Systems Summer School put on by
the Santa Fe Institute.
Eric Weeks was the master of the code,
Ardell suggested using a Penrose tesselation as the universe for the
Patrik D'haeseleer had the idea to use different rules for the
- 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
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