login
A272220
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 438", based on the 5-celled von Neumann neighborhood.
1
4, 3, 12, 12, 8, -4, 64, 13, -1, 28, 52, 32, 20, 12, 96, 28, 60, 32, 56, 12, 12, 36, 112, 16, 160, 36, 204, -68, 4, 24, 372, -15, 127, -60, 353, -17, 88, -116, 324, 52, 212, -172, 280, 252, -64, 41, 499, -351, 283, 121, 343, 145, -133, -103, 615, 73, 7, 109
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=438; 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. A272217.
Sequence in context: A323931 A205371 A270633 * A231427 A215942 A054908
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 22 2016
STATUS
approved