

A271300


First differences of number of active (ON,black) cells in nth stage of growth of twodimensional cellular automaton defined by "Rule 347", based on the 5celled von Neumann neighborhood.


1



4, 0, 39, 39, 104, 93, 197, 200, 323, 299, 455, 459, 639, 603, 832, 841, 1077, 1052, 1347, 1339, 1644, 1617, 1937, 1921, 2329, 2328, 2663, 2583, 3028, 3025, 3509, 3533, 4037, 3949, 4441, 4473, 5073, 5017, 5593, 5560, 6043, 5931, 6587
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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.


LINKS



MATHEMATICA

CAStep[rule_, a_]:=Map[rule[[10#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=347; 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+1n, k1+n]], {j, k+1n, k1+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



KEYWORD

sign,easy


AUTHOR



STATUS

approved



