Bio

Kabir Khanna is an undergraduate student at the Indian Institute of Technology Madras, studying Engineering Design. He is deeply passionate about Physics and Mathematics and would like to pursue further studies in them. His interests currently lie in the field of Dynamical Systems and Cosmology. Kabir believes that education is the key to a lot of India’s problems, and thus has devoted a significant portion of his time teaching kids in rural areas. In his spare time, he likes to play the guitar, go for short runs, or spend time having debates over various philosophical matters with his mother over coffee.

Computational Essay: Fate of the Love Affair?

Project: Aggregation System framework in Mathematica

Goal

Aggregation systems are probabilistic systems analogous to cellular automata that have been known/hypothesized to explain some behaviors like the growth of cities, cancer cells and even wasp colonies. The goal of this project was to build a framework to work with aggregation systems in Mathematica. The next step was to meditate on the rules and look for typical behavioral patterns. Lastly, a novel method of studying these systems was taken up using graphs to test confluence in the rules of the system. There have been hypotheses and studies in the subject, but this was a more general exploration than what was done in the past.

Summary of Results

A function was successfully fabricated to give out the aggregation system given the rule number, initial conditions and the number of iterations (exactly like cellular automaton). Following that, the function was made efficient by precisely fitting it to the frame. Then, certain properties like dimensions, standard deviation and mean were studied, which revealed some behavioral patterns that hint toward natural events like phase changes in a system. Finally, the study of confluence, which is usually done on a deterministic system, was undertaken, giving statistics on the “confluenciality” of a stochastic model of this type.

Future Work

1. Extending the function to include 3D aggregation systems.
2. Extending similar studies to a general space of initial conditions and other rule sets.
3. Looking for interesting patterns by analyzing parameters like fractal box dimension, growth of the system with time, etc.
4. Continuing investigations on confluence in the rule space and looking for stronger results.