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A271203
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 313", based on the 5-celled von Neumann neighborhood.
1
3, 1, 27, -19, 75, -67, 147, -131, 247, -207, 367, -371, 547, -511, 695, -623, 827, -835, 1155, -1107, 1367, -1299, 1659, -1667, 2011, -1895, 2259, -2275, 2655, -2555, 3071, -3043, 3475, -3335, 3791, -3719, 4307, -4251, 4779, -4759, 5347, -5279, 5903, -5871
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=313; 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. A271200.
Sequence in context: A317930 A270078 A269875 * A271151 A027495 A269813
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 01 2016
STATUS
approved