STATUS
proposed
approved
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Decimal 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 358", based on the 5-celled von Neumann neighborhood.
(history; published version)
(history; published version)
STATUS
editing
proposed
NAME
allocated for Robert PriceDecimal 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 358", based on the 5-celled von Neumann neighborhood.
DATA
1, 3, 4, 14, 17, 59, 68, 238, 261, 909, 1105, 3803, 4096, 14336, 17408, 60928, 66816, 232832, 282688, 973024, 1049936, 3673976, 4461572, 15611406, 17121553, 59597755, 72422416, 249280056, 268697924, 940442478, 1141965845, 3996880447, 4383331648, 15257763296
OFFSET
0,2
COMMENTS
Initialized with a single black (ON) cell at stage zero.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
LINKS
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>
MATHEMATICA
CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code = 358; 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]], 2], {i, 1, stages - 1}]
KEYWORD
allocated
nonn,easy
AUTHOR
Robert Price, Jan 19 2017
STATUS
approved
editing
NAME
allocated for Robert Price
KEYWORD
allocated
STATUS
approved