Wolfram Computation Meets Knowledge

Wolfram Summer School


Wiktor Macura

Summer School

Class of 2005


Wiktor Macura was born in Poland in March 1990. He is currently a junior at the University of Maryland, Baltimore County, majoring in mathematics and computer science. Beside his interest in programming languages, computer graphics, and artificial intelligence, he also plays the flute and has a black belt in Tae Kwon Do.

Project: Combining Elementary Cellular Automata

Suppose you could define an operator, ⊕, for combining the rules of cellular automata to get another cellular automaton, in analogy to generalized additivity. We wish the operator to resemble our well-known plus operation, so ⊕ must be commutative and associative. There are many trivial ways to combine such CAs, but I will perform an exhaustive search for the so-called inequivalent commutative monoids by looking at all possible monoids. If there are ways rules can be combined to yield output that is equivalent to existing rules, many interesting discussions can be started. Like what are some fundamental rule sets, through which we can get all other rules? Can we define a form of multiplication? If so, how would an algebra of sorts look?

Favorite Four-Color, Nearest-Neighbor, Totalistic Rule

Rule chosen: 100059