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A270224
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 131", based on the 5-celled von Neumann neighborhood.
1
4, 0, 28, -20, 80, -68, 136, -108, 232, -220, 352, -324, 488, -452, 576, -476, 728, -716, 976, -948, 1240, -1204, 1456, -1364, 1720, -1684, 2000, -1916, 2264, -2156, 2320, -1980, 2488, -2476, 2992, -2964, 3512, -3476, 3984, -3892, 4504, -4468, 5040, -4956
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=131; 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. A270221.
Sequence in context: A358653 A270281 A270728 * A270692 A282918 A282979
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 13 2016
STATUS
approved