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A270976
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 233", based on the 5-celled von Neumann neighborhood.
4
1, 4, 13, 32, 21, 68, 40, 157, 84, 248, 157, 392, 121, 516, 205, 632, 309, 920, 401, 1100, 401, 1408, 541, 1632, 681, 1948, 877, 2284, 825, 2628, 977, 2856, 1273, 3404, 1457, 3836, 1497, 4296, 1561, 4636, 1969, 5396, 2113, 5752, 2385, 6436, 2497, 6868, 2885
OFFSET
0,2
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=233; 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}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
CROSSREFS
Sequence in context: A372377 A218958 A226839 * A272510 A036487 A184632
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 27 2016
STATUS
approved