Understanding the Convergence in Alpha-Asynchronous Cellular Automata
Authors: Bheemakonda Raja Maheswar & Revanth D. Rampal
Mentor: Souvik Roy
Presented at: Ian Summer School on Cellular Automata (August 29, 2022)
RGUKT-AP, RK Valley & IIEST, Shibpur
Abstract
This paper explores the factors of convergence and the behavior of attractors in Alpha-Asynchronous Cellular Automata (CA). Focusing on 2-state, 1-dimensional CA under periodic boundary conditions, the research experimented with 88 minimal rules across alpha values ranging from 0.1 to 1.0. A specialized program was developed to track evolution, successfully identifying 47 specific rules (including Rule 0, 2, 4, 90, 150, etc.) that demonstrate complete convergence to a fixed point. The study further concluded that specific attractors cannot be reliably recorded; due to the stochastic nature of the alpha-asynchronous randomizer ($Random < \alpha$), the cellular evolution path and resulting configurations differ with every execution cycle.