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A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART III: PREDICTING THE UNPREDICTABLE

Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA

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VALERY I. SBITNEV

Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA

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, and

SOOK YOON

Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA

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https://doi.org/10.1142/S0218127404011764Cited by:49 (Source: Crossref)

Abstract

We prove rigorously the four cellular automata local rules 110, 124, 137 and 193 have identical dynamic behaviors capable of universal computations. We exploit Felix Klein's remarkable Vierergruppe to partition the 256 local rules studied empirically by Wolfram into 89 global equivalence classes of which only 50 may exhibit complex dynamics. We define a 24-element rotation group which induces 30 local equivalence classes of nonlinear difference equations whose parameters can be mapped into each other among members of the same class.

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