Wolfram Computation Meets Knowledge

Wolfram Summer School


Richard Phillips

Summer School

Class of 2003


Choosing Mathematics, Physics, Chemistry, and Cell Biology in the first year of the Natural Sciences Tripos at the University of Cambridge, UK, Richard went on to gain his BA in Physics and Theoretical Physics in 1995. He has since been awarded an MSc in Computer Science from Bristol University, UK, for work that involved the creation of a computer language and a system to run it across multiple computers. Computer programs written in this language directly express parallelism, communication and the dynamic movement of programs between computers, allowing the programming of distributed systems in a vastly simpler way than current technology. Richard has also done research work in optimizing compiler technology. More recently he has independently pursued research into the sorts of simple computer programs that form the core of A New Kind of Science. At present he is a Visiting Scholar at Wolfram Research where he is working on building the Wolfram Atlas of Simple Programs.

Project: Simple basic comments on growth of cellular automata boundaries

This project looks at the problem from the Open Problems book “What growth rates for patterns can be achieved by simple cellular automata”, and part of “Study k=3, r=1/2 cellular automata”.

We consider k-color, r =1/2 CAs starting from simple seeds on a background of all 0s. (Growth is considered to happen from right to left.) Fixed right-hand-side boundary conditions will also be considered.

An important observation is that by biasing the CA rule in simple ways (eg. saying that a k-subset of the rule cases must map to 0s) it is found that the proportion of rules that show complex-looking growth increases in random samples of rules.

Favorite Three-Color Cellular Automaton

Rule Chosen: 21252

Reason: When started from randomness using elements Random[Integer,{0,2}] (or anything which gives a uniform sprinking of 2s) the behaviour is strictly speaking class 2. The 2s create walls that isolate fixed regions of behaviour, implying each region cycles and the overall behaviour must be class 2. However we do get transients of rule-30 activity that die away to the right. One can prove simply from the rules why the transients die away to the right.