A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART III: PREDICTING THE UNPREDICTABLE
Leon Ong Chua, Valeriy I. Sbitnev, Sook Yoon · International Journal of Bifurcation and Chaos · 2004
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.