proposed

approved

editing

proposed

Cf. A274216, A274224, A274473.

Robert Price, <a href="/A274060/a274060.tmp.txt">Diagrams of first 20 stages</a>

Robert Price, <a href="/A274060/a274060.tmp.txt">Diagrams of first 20 stages</a>

Robert Price, <a href="/A274060/b274060.txt">Table of n, a(n) for n = 0..126</a>

Robert Price, <a href="/A274060/a274060.tmp.txt">Diagrams of first 20 stages</a>

allocated for Robert PriceBinary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 22", based on the 5-celled von Neumann neighborhood.

1, 11, 100, 1100, 10000, 110000, 1000100, 11001100, 100000000, 1100000000, 10001000000, 110011000000, 1000000010000, 11000000110000, 100010001000100, 1100110011001100, 10000000000000000, 110000000000000000, 1000100000000000000, 11001100000000000000

0,2

Initialized with a single black (ON) cell at stage zero.

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>

<a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

<a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>

<a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];

code=22; 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}];

Table[FromDigits[Part[ca[[i]][[i]], Range[1, i]], 10], {i, 1, stages-1}]

allocated

nonn,easy

Robert Price, Nov 10 2016

approved

editing

allocated for Robert Price

recycled

allocated

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allocated for Thomas Curtright

allocated

recycled

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editing

allocated for Thomas Curtright

allocated

approved