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A273152
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 598", based on the 5-celled von Neumann neighborhood.
1
4, 4, 12, -4, 36, -12, 44, -52, 68, 4, 76, -100, 164, -76, 172, -276, 132, 4, 140, -132, 420, -268, 428, -628, 324, 4, 332, -484, 676, -332, 684, -1236, 260, 4, 268, -260, 804, -524, 812, -1076, 836, 4, 844, -1380, 1444, -588, 1452, -2708, 644, 4, 652, -644
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=598; 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. A273150.
Sequence in context: A079315 A229253 A272789 * A322785 A189545 A326993
KEYWORD
sign,easy
AUTHOR
Robert Price, May 16 2016
STATUS
approved