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A271098
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 278", based on the 5-celled von Neumann neighborhood.
1
4, 3, 12, -4, 28, -12, 56, -44, 88, -72, 136, -107, 168, -157, 232, -167, 260, -265, 352, -263, 388, -405, 488, -375, 580, -593, 664, -531, 768, -805, 848, -716, 952, -956, 1100, -1000, 1208, -1167, 1356, -1249, 1484, -1464, 1628, -1471, 1792, -1765, 2020
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=278; 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. A271095.
Sequence in context: A204291 A270324 A271888 * A269718 A099377 A121844
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 30 2016
STATUS
approved