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A271019
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 251", based on the 5-celled von Neumann neighborhood.
1
4, 4, 32, -20, 80, -52, 136, -124, 248, -212, 352, -316, 480, -388, 536, -524, 776, -740, 1008, -972, 1264, -1156, 1424, -1388, 1744, -1636, 1976, -1868, 2216, -1924, 2104, -2092, 2600, -2564, 3088, -3052, 3600, -3492, 4016, -3980, 4592, -4484, 5080, -4972
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=251; 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. A271016.
Sequence in context: A130188 A270676 A270625 * A271003 A217310 A298681
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 28 2016
STATUS
approved