Wolfram Computation Meets Knowledge

Wolfram Summer School


Pedro Antonio Martínez Mediano

Summer School

Class of 2013


Pedro is currently a student of Physics at Universidad de Valencia, Spain. He has taken part for two years as a summer student in the NEXT experiment, Valencia, which aims to prove the tiny neutrino to be a Majorana particle through double-beta decay.

His interests are in a wide-ranging variety of fields, from Quantum Statistics to Neuroscience to Big Data. He never loses a chance to explore, code, and simulate everything his hands land on. Recently he is turning his attention to new areas like Chaos, Information Theory, and the frontiers between Physics and Computer Science.

When not programming, you might find Pedro playing bass or climbing a mountain. An enthusiast of music, nature, and martial arts, he is always open to a new challenge.

Project: Conserved Quantities in Elementary Cellular Automata

My goal, in short, is to find conserved quantities in ECAs. I will do that by exploring the state space for several rules and inspecting the structures formed in it when the system evolves. I will consider finite-length tapes and periodic boundary conditions.

Then I will try to find out what states in a certain region of the state space have in common, and what makes them different from states in other regions. For this part I will need all sorts of techniques, from simple visualization and trial-and-error to machine learning algorithms.

Along the way, I have found that this problem is closely related to the issue of how cellular automata handle information. If a cellular automaton traverses several states as a transient toward a steady cycle, could it possibly retain any connection with those states?

In the best-case scenario, we should discover some relationships between rules and the quantities they conserve, some sort of an analogy to energy or momentum for physical systems.

Favorite Four-Color, Four State Turing Machine

Rule 259853317401642231317