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A270723
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 201", based on the 5-celled von Neumann neighborhood.
1
3, 5, 19, -11, 63, -52, 105, -69, 177, -169, 276, -239, 423, -395, 519, -444, 653, -661, 845, -753, 1053, -1045, 1253, -1125, 1349, -1285, 1589, -1453, 1789, -1701, 1985, -1961, 2361, -2193, 2592, -2655, 3183, -2872, 3189, -3221, 3776, -3671, 3995, -3867
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=201; 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. A270720.
Sequence in context: A053484 A272092 A272019 * A242961 A025046 A305700
KEYWORD
sign,easy
AUTHOR
Robert Price, Mar 22 2016
STATUS
approved