login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Number of distinct excluded blocks of length n in the evolution language of width 1 (i.e., time series) generated by the elementary cellular automaton of Rule 110, which has the capability of a universal Turing machine.
0

%I #6 Jul 26 2017 20:54:10

%S 1,3,3,5,6,12,16,17,38,42,73,112,198

%N Number of distinct excluded blocks of length n in the evolution language of width 1 (i.e., time series) generated by the elementary cellular automaton of Rule 110, which has the capability of a universal Turing machine.

%D Zhi-Song Jiang, Hui-Min Xie, Evolution Complexity of the Elementary Cellular Automaton Rule 18, Complex Systems, 13 (2002) 271-195

%D Stephen Wolfram, Computation theory of cellular automata, Commun. Math. Phys. 96 (1984) 15-57

%D Huimin Xie, Grammatical Complexity and One-Dimensional Dynamical Systems, World Scientific, Singapore, 1996

%e For length 5 binary blocks, only one block, 11101, cannot be found in the time series generated by the elementary cellular automaton of Rule 110.

%K nonn

%O 5,2

%A Huimin Xie (szhmxie(AT)pub.sz.jsinfo.net), Jul 13 2004