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A273830
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 950", based on the 5-celled von Neumann neighborhood.
1
4, 4, 16, 12, 16, 12, 44, 32, 32, 28, 52, 40, 48, 28, 108, 64, 64, 60, 84, 72, 80, 60, 132, 88, 96, 76, 132, 88, 112, 60, 236, 128, 128, 124, 148, 136, 144, 124, 196, 152, 160, 140, 196, 152, 176, 124, 292, 184, 192, 172, 228, 184, 208, 156, 308, 200, 224
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=950; 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. A273827.
Sequence in context: A174595 A160020 A273370 * A250069 A333169 A075882
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 31 2016
STATUS
approved