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A272283
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 457", based on the 5-celled von Neumann neighborhood.
1
3, 5, 19, -7, 71, -35, 111, -103, 179, -163, 271, -255, 439, -371, 491, -423, 659, -671, 903, -847, 1155, -1071, 1315, -1251, 1499, -1483, 1907, -1763, 2031, -1839, 2063, -1935, 2275, -2403, 3011, -2855, 3279, -3167, 3559, -3431, 3835, -3783, 4415, -4047
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=457; 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. A272280.
Sequence in context: A270894 A272317 A128362 * A053484 A272092 A272019
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 24 2016
STATUS
approved