Wolfram Computation Meets Knowledge

Wolfram Summer School


Mauricio Bustamante

Summer School

Class of 2005


Mauricio Bustamante is currently studying towards a physics undergraduate degree at Pontificia Universidad Católica del Perú, in Lima, Peru. Together with César Guerra (also in attendance at the NKS 2005 Summer School) and another physicist, he has been studying complex systems theory, particularly cellular automata, and doing NKS research for about two years. He is currently interested in statistical mechanics, specially in how self-organisation and other emergent features can be incorporated into the existing theory.

Project: Finding Clusters of CA Rules with Similar Behavior

In this work, I have tried to group CA rules into classes that exhibit the same kind of behavior. The criterion chosen for clustering was the rules’ stability against slight perturbations in the initial conditions. Four different classes are found (related to Wolfram’s). Also, a numerical measure of stability is proposed for the periodic and linear-growth classes. The experiments carried out have shown that most CA can be grouped in one of the following stability classes: stable, periodic, chaotic, and linear-growth. Rules that belong to a particular stability class will remain in that class for almost any initial condition that they are provided with. The stability of linear-growth difference patterns for a particular rule is very uniform across a large sample of initial conditions; i.e., it is possible to assign a stability figure to a rule.

Favorite Four-Color, Nearest-Neighbor, Totalistic Rule

Rule chosen: 5824

I chose this rule becomes it resembles the well-known seashell pattern, more closely than ECA rule 30.