Richard Phillips
 Bio [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 Title
Simple basic comments on growth of cellular automata boundaries
Abstract
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 3-color Cellular Automata
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.
|
