2021/07/10 by Maurice Margenstern, Margenstern, Maurice · 1 citation
Computer Science · Physics and Astronomy · #68R05 #Cellular Automata and Lattice Gases (nlin.CG) #Discrete Mathematics (cs.DM) #F.2.2 #FOS: Computer and information sciences #FOS: Physical sciences #acm:68R05 #cs.DM #msc:68R05 #nlin.CG
paper · pdf · doi:10.48550/arxiv.2107.04843
49 pages, 23 figures. arXiv admin note: substantial text overlap with arXiv:2104.01561
arxiv created 2021/07/10 · arxiv updated 2021/07/13
In this paper, we prove that there is a strongly universal cellular automaton in the dodecagrid, the tesselllation 5,3,4 of the hyperbolic 3D space, with four states but, it is not rotation invariant as the automaton of arXiv:2104.01561 is with five states. The present paper is not an improvement of arXiv:2104.01561. The reduction to four states of the automaton of the present paper results from a relaxation of the condition of rotation invariance. However, the relaxation is not complete: the rules are invariant with respect to rotations of the dodecahedron which leave it globally invariant which also leave invariant a couple of opposite faces of the dodecahedron. As there are twenty five such rotations, it can be considered that the reduction to four states is significant although the relaxation it implied.