Wolfram Computation Meets Knowledge

Wolfram Summer School


Vitaliy Kaurov

Summer School

Class of 2010


Vitaliy Kaurov received his PhD in physics from The City University of New York. He teaches mathematics and physics at the College of Staten Island, incorporating Wolfram|Alpha and Mathematica into his classroom. He also uses Mathematica extensively for his research in the field of ultracold quantum gases. Becoming a contributor to the Wolfram Demonstrations Project attracted him to the field of NKS. His hobbies include cross-country biking, yoga, photography, and poetry. He writes about this and other interests at kaurøv bløg.

Project: Basic Properties of Composite 2D Rules

A composite 2D rule is a 2-color CA with a 9-cell square neighborhood whose update is given by sequential application of two ECAs. The first ECA is run horizontally on every row, followed by the second ECA, which is run vertically on every column. The space of the 2^16 composite rules was investigated with several statistical, analytical, and visualization techniques.

  • Rule indexes of subclasses were mapped onto general class. Composite, totalistic, and outer totalistic subclasses overlap at no more than 10 rules. Some rules common to all subclasses are additive class 3 rules.
  • Asymmetry of composite rules often results in anisotropy of CA patterns and separates different classes of CA behavior into different spatial dimensions.
  • 19-62 composite rule (class-2 ECAs) is equivalent to the universal 110 ECA rule in a single spatial-temporal layer. Polynomial formulation of ECA rules was used to prove this result. More layers couple and produce particles similar to 110 ECA evolving in several layers simultaneously.
  • Complex domain walls behaviors are found, e.g. composite 94-94.
  • Density dependent phase transitions are found, e.g. composite 33-33.

Favorite Four-Color Totalistic Cellular Automaton

Rule 400547