login
A271296
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 345", based on the 5-celled von Neumann neighborhood.
1
3, 1, 39, -39, 99, -91, 191, -183, 319, -315, 471, -463, 639, -627, 863, -839, 1103, -1119, 1391, -1359, 1679, -1679, 1987, -1943, 2351, -2315, 2727, -2759, 3103, -3003, 3511, -3515, 4091, -4139, 4603, -4535, 5135, -5131, 5703, -5643, 6211, -6183, 6863
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=345; 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. A271293.
Sequence in context: A270090 A293940 A103242 * A270132 A050817 A125082
KEYWORD
sign,easy
AUTHOR
Robert Price, Apr 03 2016
STATUS
approved