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Wolfram Summer SchoolFounded in 2003

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


Pranav Krishnan


Class of 2016


Pranav Krishnan is a graduating student from the International Baccalaureate program in India. He's also been a research fellow at the Centre for Fundamental Research and Creative Education. His previous research was on investigating relativistic alternative theories of gravitation in the weak field limit using post-Newtonian parameters. His major research interests lie in quantum gravity, cosmology and the foundations of quantum mechanics. Apart from his zeal for physics, he also has a deep enthusiasm for mathematical research, philosophy, data science and machine learning.

His nonacademic interests include quantitative trading, sports, photography, quizzing and traveling.

Project: Topology of Three-Dimensional Cellular Automata

The primary objective of this project is to ascertain the topological characteristics of three-dimensional cellular automata. Cellular automata are algorithms that describe the spatial and temporal evolution of complex systems by applying local switching rules to the discrete cells of a regular lattice. The evolution of such discrete dynamical systems leads to an emergence of global complexity by the repeated interaction of simple local rules. In this project, we only consider totalistic three-dimensional cellular automata.

The topological analysis of cellular automata can determine whether a structure is made of a single connected mass or separated into multiple parts by quantifying the number of holes or cavities in a given cellular automaton. The Euler number χ has a characteristic value for each topological configuration and is affected by the number of objects, holes and cavities.

The implications of this study have wide-ranging applications in the fields of optimization modeling and topological dynamics, where the versatility of cellular automata to reciprocate physical and biological systems can provide crucial information about the evolution of such systems, and subsequently help predict their outcomes.

Favorite 3-Color 2D Totalistic Cellular Automaton

Rule 95554293