

A287632


Decimal representation of the diagonal from the corner to the origin of the nth stage of growth of the twodimensional cellular automaton defined by "Rule 324", based on the 5celled von Neumann neighborhood.


4



1, 0, 1, 0, 0, 0, 3, 0, 9, 0, 0, 0, 19, 0, 7, 0, 51, 0, 135, 0, 387, 0, 227, 0, 1991, 0, 899, 0, 8135, 0, 3971, 0, 40903, 0, 3971, 0, 4039, 0, 40835, 0, 69575, 0, 237443, 0, 2035655, 0, 987011, 0, 499655, 0, 200579, 0, 26808263, 0, 40835, 0, 25169863, 0
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OFFSET

0,7


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 = 324; 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}]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



