Wolfram Computation Meets Knowledge

Wolfram Summer School


Gianpiero Cea

Summer School

Class of 2012


Gianpiero Cea is currently finishing his studies at the Science and Math High School in Bitetto, Italy. He is a 17-year-old student interested in mathematics and IT. He started by learning programming on his own at the age of 12. Gianpiero has worked with 3D modeling programs, which he has used to make several science projects for his school by using live animations. Since he has discovered NKS, he has been learning Mathematica in order to explore the world of simple programs.

Project: Simple Program Controlled Cellular Automaton

One of the main properties of standard CAs is that at each time step, we always apply the same rule. Instead the idea of my project is to let another simple program choose which rule to apply from a given array of rules according to a convention. My project will study three different systems to determine which cellular automata rules will be used. We could use the evolution of a neighborhood independent substitution sytem with the symbols {30,90} to decide which rules (rule number 30 or rule number 90) to apply at each time step. We can also use a Turing machine as a “controller” where the direction of movement of the head determines which rule will be used. Lastly we can use another cellular automaton to determine the rule to be used on the color of the cell of the center row at a certain point. The goal is then to find general behaviors for such large spaces and to try to understand what happens when we combine different types of rules.

Favorite Four-Color, Four State Turing Machine

Rule 654284170828991479950528