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A273370
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 822", based on the 5-celled von Neumann neighborhood.
1
4, 4, 16, 12, 12, 8, 48, 12, 36, 8, 68, 24, 44, -8, 128, -20, 148, 40, 76, 48, 36, -8, 212, -40, 164, -40, 276, -24, 140, -136, 368, -148, 372, 104, 284, -32, 212, 88, 188, -32, 260, -24, 316, 32, 132, -168, 564, -360, 724, 56, 316, -64, 196, -264, 868, -536
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=822; 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. A269918.
Sequence in context: A227074 A174595 A160020 * A273830 A250069 A333169
KEYWORD
sign,easy
AUTHOR
Robert Price, May 27 2016
STATUS
approved