Wolfram Computation Meets Knowledge

Wolfram Summer School


Sai Pavan Kumar Veeranki

Summer School

Class of 2015


Sai is from India and is currently pursuing his PhD at Alpen Adria University, Klagenfurt, Austria. He recently finished a major in information technology with an emphasis on optimization problems in transportation in which he used differential equations to solve the shortest path problem as well as the traveling salesman problem. He is also finishing his second major in the field of health care information technology this year.

His three months of internship at Arsenal Research (Austrian Institute of Technology) motivated him to work on optimization problems in transportation, where he has been investigating several methods that are utilized in real-time scenarios. In his PhD, he plans to apply dynamical system principles to solve some of the challenging optimization problems.

Apart from information technology, he is interested in politics and is an active participant in social events. In the future, Sai would like to get back to his country and make teaching his profession. He is looking forward to using the concepts of A New Kind of Science in practice and using Mathematica intensively during the Summer School, as well for his thesis.

Project: Cellular Automata That Behave Like Differential Equations

Solutions for differential equations can be difficult to compute. But the behavior of a cellular automaton, in contrast, is easy to compute. In this project, we searched for elementary cellular automata (ECA) whose ensemble average densities behave like the solutions to commonly encountered differential equations. We identified several ECA that satisfy this criterion. In particular, we showed that the ensemble average densities of rules 156, 178, and 198 exponentially converge toward equilibrium, and we found mathematical formulas that describe this behavior. We also identified ECA rules, such as 26, 60, 105, and 154, whose ensemble average densities do not resemble the solutions of differential equations.


  • Wolfram, S. (2002). A New Kind of Science. Champaign, IL: Wolfram Media.

Wolfram Summer School | Champaign, IL, USA | July 3 29–July 22, 2022