# Wolfram Summer SchoolFounded in 2003

17th Annual Wolfram Summer School, held at Bentley University

Alumni

# César Guerra

Class of 2005

## Bio

César Guerra was born in Huancayo, a little city in the Andes of Peru. He studied physics at Pontificia Universidad Católica del Perú (PUCP), and obtained his M.S. in quantum optics and quantum computing. Other fields that caught his attention are particle physics, cosmology, and computer science. While developing a package for doing calculations in quantum physics, he started using Mathematica. Later, two colleagues at PUCP introduced him to NKS. They formed a complex systems research group and have focussed on NKS approaches to understanding nature. At nights, and when time permits some relaxation, he very much enjoys playing the guitar.

## Project: Sequential Substitution Systems That Perform Some Simple Calculations

Sequential substitution systems that perform some simple calculations are investigated. To this aim, the input for a certain calculation is encoded as a string of characters, then transformation rules are applied sequentially until evolution of the system reaches a fixed point. At this point, the output should be decoded from the evolved string. The NKS approach is followed by doing exhaustive searches over a subspace of the infinite possible transformation rules that can be applied to the input string. The main results of these experiments are the discovery of transformation rules that perform simple adding and subtraction in unary coding. What searches have shown us is that there are in fact several ways in which they can be performed. They have also shown that the unary encoding is not a good choice for other types of calculations, such as multiplication or finding primes. Possible directions are to look for rules of greater length and colors, and to envisage other ways to encode and decode the input and output, respectively.

## Favorite Four-Color, Nearest-Neighbor, Totalistic Rule

Rule chosen: 32042

Although I didn't try all four-color totalistic cellular automata (too many rules), I found several ones that are interesting. One of them is rule number 32042. It's quite funny how in a background of little, white, randomly distributed strings, several simple geometric figures like rhombuses live, and how inside each rhombus, evolution stops its complexity and decides to go periodically.