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A273567
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 793", based on the 5-celled von Neumann neighborhood.
1
3, 9, 15, 21, 32, 27, 33, 39, 77, 51, 57, 63, 89, 51, 57, 63, 209, 99, 105, 111, 137, 99, 105, 111, 245, 123, 129, 135, 221, 51, 57, 63, 641, 195, 201, 207, 233, 195, 201, 207, 341, 219, 225, 231, 317, 147, 153, 159, 725, 267, 273, 279, 365, 195, 201, 207
OFFSET
0,1
COMMENTS
Initialized with a single black (ON) cell at stage zero.
First negative term is a(61) = -141. Georg Fischer, Feb 15 2019
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=793; 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}];
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[on[[i+1]]-on[[i]], {i, 1, Length[on]-1}] (* Difference at each stage *)
CROSSREFS
Cf. A273564.
Sequence in context: A273560 A246388 A272793 * A162486 A067201 A071526
KEYWORD
sign,easy
AUTHOR
Robert Price, May 25 2016
STATUS
approved