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A272092
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 425", based on the 5-celled von Neumann neighborhood.
1
3, 5, 19, -11, 51, -27, 99, -107, 227, -155, 243, -267, 403, -315, 451, -555, 963, -827, 979, -971, 1011, -859, 1059, -1259, 1955, -1627, 1715, -1867, 2131, -1787, 1923, -2475, 3971, -3707, 3987, -3979, 4019, -3739, 4067, -4331, 5219, -4379, 4211, -4747
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=425; 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. A272089.
Sequence in context: A128362 A272283 A053484 * A272019 A270723 A242961
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 19 2016
STATUS
approved