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A271090
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 270", based on the 5-celled von Neumann neighborhood.
1
4, 3, 13, -1, 8, 8, 40, 0, -28, 24, 52, -12, 33, 23, 116, 0, -172, 56, 84, -4, 56, 36, 92, -36, -44, 32, 168, -64, 148, 84, 424, -100, -512, 176, 192, 28, -64, 72, 216, -104, 80, 108, 212, -96, 44, 212, 240, -52, -120, 104, 248, -164, 140, 120, 308, -144
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=270; 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. A271087.
Sequence in context: A141826 A178756 A271696 * A271284 A272312 A272117
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 30 2016
STATUS
approved