login
A271601
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 390", based on the 5-celled von Neumann neighborhood.
1
4, -1, 16, -11, 24, -20, 52, -45, 72, -47, 64, -64, 112, -100, 168, -144, 176, -204, 120, -64, 208, -188, 284, -225, 256, -256, 312, -268, 432, -356, 488, -452, 520, -648, 552, -472, 544, -448, 640, -560, 584, -532, 696, -688, 808, -644, 1008, -1128, 952
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=390; 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. A271598.
Sequence in context: A374098 A272088 A271135 * A271068 A272509 A272279
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 10 2016
STATUS
approved