IEICE Transactions on Information and Systems
Online ISSN : 1745-1361
Print ISSN : 0916-8532
Regular Section
Evolution of Cellular Automata toward a LIFE-Like Rule Guided by 1/ƒ Noise
Shigeru NINAGAWA
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Volume E93.D (2010) Issue 6 Pages 1489-1496

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Abstract

There is evidence in favor of a relationship between the presence of 1/ƒ noise and computational universality in cellular automata. To confirm the relationship, we search for two-dimensional cellular automata with a 1/ƒ power spectrum by means of genetic algorithms. The power spectrum is calculated from the evolution of the state of the cell, starting from a random initial configuration. The fitness is estimated by the power spectrum with consideration of the spectral similarity to the 1/ƒ spectrum. The result shows that the rule with the highest fitness over the most runs exhibits a 1/ƒ type spectrum and its transition function and behavior are quite similar to those of the Game of Life, which is known to be a computationally universal cellular automaton. These results support the relationship between the presence of 1/ƒ noise and computational universality.

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© 2010 The Institute of Electronics, Information and Communication Engineers
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