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A273579
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 803", based on the 5-celled von Neumann neighborhood.
1
4, 16, 12, 44, 28, 48, 8, 124, 60, 80, 40, 144, 56, 112, -72, 380, 124, 144, 104, 208, 120, 176, -8, 432, 152, 208, 24, 416, 40, 240, -520, 1276, 252, 272, 232, 336, 248, 304, 120, 560, 280, 336, 152, 544, 168, 368, -392, 1392, 344, 400, 216, 608, 232, 432
OFFSET
0,1
COMMENTS
Initialized with a single black (ON) cell at stage zero.
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=803; 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. A273577.
Sequence in context: A223864 A223987 A224123 * A147560 A266973 A029659
KEYWORD
sign,easy
AUTHOR
Robert Price, May 25 2016
STATUS
approved