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A272580
First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 502", based on the 5-celled von Neumann neighborhood.
1
4, 3, 16, 5, 19, 8, 49, -29, 72, -7, 103, -99, 99, 56, 97, -53, 104, 13, 139, -103, 148, 43, 188, -159, 207, 8, 181, -105, 248, 76, 40, 53, 171, -20, 357, -337, 408, 117, 35, -168, 561, -81, 132, -79, 287, 341, 116, -393, 668, 181, -193, 9, 611, -35, 167
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=502; 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. A272577.
Sequence in context: A270908 A269781 A322144 * A065679 A223925 A062776
KEYWORD
sign,easy
AUTHOR
Robert Price, May 03 2016
STATUS
approved