|
|
A269874
|
|
Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 41", based on the 5-celled von Neumann neighborhood.
|
|
1
|
|
|
1, 5, 10, 42, 55, 139, 168, 336, 369, 637, 698, 1114, 1167, 1747, 1868, 2616, 2721, 3685, 3870, 5058, 5239, 6739, 6960, 8744, 8965, 11073, 11378, 13858, 14175, 16987, 17424, 20612, 21033, 24649, 25194, 29346, 29815, 34391, 35036, 40160, 40681, 46393, 47206
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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.
|
|
LINKS
|
|
|
MATHEMATICA
|
code=41; stages=100;
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[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|