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A270637
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 185", based on the 5-celled von Neumann neighborhood.
1
3, 5, 23, 1, 59, -27, 111, -123, 263, -203, 319, -243, 359, -264, 517, -501, 728, -608, 852, -796, 1012, -816, 1168, -1164, 1504, -1340, 1648, -1512, 1852, -1616, 2108, -2060, 2456, -2292, 2848, -2824, 3208, -2876, 3476, -3324, 3768, -3488, 4072, -3852, 4308
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=185; 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. A270634.
Sequence in context: A376002 A178377 A270621 * A064187 A112686 A318443
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 20 2016
STATUS
approved