June 24–July 13, 2018

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Wolfram Summer School

June 24–July 13, 2018
Bentley University, Waltham, MA


Emmanuel Garcés Medina

Class of 2006


Emmanuel Garcés Medina was born in a southeastern town in Mexico City, and has been programming computers since he was eleven years old. He has a bachelors degree in computer science from the National Autonomous University of Mexico (UNAM) and has also taken many courses on complex systems and nonlinear dynamics at the Autonomous University of Mexico City. He currently is working towards his master's degree in computer science at UNAM.

His main scientific interests include mathematical biology, origin of complex structures, evolution, equivalence between systems, and universality. In order to do research into those topics, he would like to investigate his ideas about complex systems, algorithms, logic, and computational geometry in an NKS direction.

Project: Tree Structures in Replacement Turing Machines

It is known that some systems can be emulated with other systems. In the NKS book some transformations are shown. The purpose of the project is to give a mechanism that will eventually be able to simulate many of the most used systems by using simple rules. The idea for this consists in extending the definition of a Turing machine with a list-replacing mechanism proposed by Richard Phillips. The mechanism and transformation behavior will be studied. Another future extension could give the head the ability to know the symbols in its neighborhood.

Favorite Four-Color, Radius-1/2 Rule

Rule chosen: Rule chosen: 2452419801

This cellular automaton generates many small colored structures that are propagated to the right by changing their velocity in a curved fashion. Also, they never collide with one another, so they are preserved in time.