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Wolfram Summer SchoolFounded in 2003

16th Annual Wolfram Summer School, held at Bentley University June 24–July 13, 2018


Benjamin Walker

Class of 2013


Benjamin Walker is currently one year into his bachelor's degree in Math and Physics at Rensselaer Polytechnic Institute in Troy, NY and he's planning on pursuing a PhD. He is interested in theoretical physics and modeling systems, especially according to artificial biological rules, like artificial neural networks and genetic evolution, in addition to cryptography, especially from a mathematical viewpoint. Ben's hobbies include recreational programming, primarily using Python and C++, and playing the violin. He plans on primarily using Mathematica as a tool for computational solutions to problems in physics.

Project: Analysis of Systems Exhibiting Self-Organized Criticality

An eight-color, two-dimensional cellular automaton can be used to model the effects of a system of self-organized criticality. A pile of a grainy substance, like sand, can hold a slope; however, if the slope is sufficiently steep, it will collapse. Piles of sand can lead to interesting behavior as they automatically even themselves out to a stable organization by continually moving sand away from the steepest areas. The color represents the relative height in each cell, meaning that the darker a cell, the steeper the slope in that cell. Sand pile rules consist of those with a threshold level, above which a cell will collapse into neighboring cells. By looking at rules of this form and the phenomena observed in their execution, the effects of models of this sort can be evaluated.

Sand pile models are not too well explored, so the main goal of this project is to make quantitative and qualitative observations of these cellular automata. The goals of the project will be further developed once initial progress is made. These goals will hopefully include looking at the mechanisms by which self-organized criticality models progress to lead to the overall behavior of the system and the behavior of the model in which one builds up a pile of sand by randomly dropping grains onto it, observing the patterns of constructive and destructive behavior.

Favorite Four-Color, Four State Turing Machine

Rule 12878101947614518977880