A272745 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 526", based on the 5-celled von Neumann neighborhood.
4, 4, 8, 0, 16, 12, 24, -8, 24, 12, 24, 0, 48, 36, 72, -32, 48, 12, 24, 0, 48, 36, 72, -24, 72, 36, 72, 0, 144, 108, 216, -104, 120, 12, 24, 0, 48, 36, 72, -24, 72, 36, 72, 0, 144, 108, 216, -96, 144, 36, 72, 0, 144, 108, 216, -72, 216, 108, 216, 0, 432, 324
Offset: 0
References
- S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
Links
- Robert Price, Table of n, a(n) for n = 0..127
- N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015
- Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
- S. Wolfram, A New Kind of Science
- Index entries for sequences related to cellular automata
- Index to 2D 5-Neighbor Cellular Automata
- Index to Elementary Cellular Automata
Crossrefs
Cf. A272742.
Programs
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Mathematica
CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}]; code=526; stages=128; rule=IntegerDigits[code,2,10]; g=2*stages+1; (* Maximum size of grid *) a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *) ca=a; ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}]; PrependTo[ca,a]; (* Trim full grid to reflect growth by one cell at each stage *) k=(Length[ca[[1]]]+1)/2; ca=Table[Table[Part[ca[[n]][[j]],Range[k+1-n,k-1+n]],{j,k+1-n,k-1+n}],{n,1,k}]; on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *) Table[on[[i+1]]-on[[i]],{i,1,Length[on]-1}] (* Difference at each stage *)
Comments