

A282388


Decimal representation of the xaxis, from the origin to the right edge, of the nth stage of growth of the twodimensional cellular automaton defined by "Rule 462", based on the 5celled von Neumann neighborhood.


4



1, 3, 3, 15, 3, 15, 51, 255, 3, 15, 51, 255, 771, 3855, 13107, 65535, 3, 15, 51, 255, 771, 3855, 13107, 65535, 196611, 983055, 3342387, 16711935, 50529027, 252645135, 858993459, 4294967295, 3, 15, 51, 255, 771, 3855, 13107, 65535, 196611, 983055, 3342387
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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



MATHEMATICA

CAStep[rule_, a_] := Map[rule[[10  #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code = 462; 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]], 2], {i , 1, stages  1}]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



