proposed

approved

editing

proposed

Cf. A282359, A282361, A282362.

Robert Price, <a href="/A282360/a282360.tmp.txt">Diagrams of first 20 stages</a>

Robert Price, <a href="/A282360/a282360.tmp.txt">Diagrams of first 20 stages</a>

Robert Price, <a href="/A282360/b282360.txt">Table of n, a(n) for n = 0..126</a>

Robert Price, <a href="/A282360/a282360.tmp.txt">Diagrams of first 20 stages</a>

allocated for Robert PriceBinary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 457", based on the 5-celled von Neumann neighborhood.

1, 0, 111, 10, 10011, 11110, 1100111, 1111010, 110010011, 111001110, 11010010111, 10001001010, 1001000000011, 10101110, 101000000010111, 111010011010, 11001010001110011, 11000011010101110, 1110101110010010111, 100110101011001010, 100111100000110000011

0,3

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>

Wolfram Research, <a href="http://atlas.wolfram.com/">Wolfram Atlas of Simple Programs</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 = 457; 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[i, 2 * i - 1]], 10], {i, 1, stages - 1}]

allocated

nonn,easy

Robert Price, Feb 13 2017

approved

editing

allocated for Robert Price

allocated

approved