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A273605
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 805", based on the 5-celled von Neumann neighborhood.
1
7, 13, 23, 25, 44, 32, 55, 49, 79, 69, 92, 48, 115, 89, 99, 73, 175, 117, 175, 97, 155, 105, 163, 117, 231, 157, 219, 117, 227, 189, 211, 133, 287, 301, 223, 193, 271, 189, 295, 133, 367, 341, 355, 197, 287, 285, 303, 237, 411, 361, 419, 213, 411, 285, 419
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=805; 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. A273602.
Sequence in context: A236312 A301691 A163676 * A273641 A214794 A043104
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 26 2016
STATUS
approved