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(* :Title: Collatz Visualization *)
(* :Author: halirutan *)
(* :Mathematica Version: 10+ *)
CollatzSequence::usage = "CollatzSequence[list] creates a Collatz sequence.";
CollatzSequence[list_] := Module[{memory, tmp, chain, result = Internal`Bag[]},
memory[1] = False;
memory[n_] := (memory[n] = False; True);
Do[
chain = Internal`Bag[];
tmp = l;
While[memory[tmp],
Internal`StuffBag[chain, tmp];
tmp = If[EvenQ[tmp], tmp/2, 3 tmp + 1];
];
Internal`StuffBag[chain, tmp];
Internal`StuffBag[result, chain],
{l, list}];
Internal`BagPart[#, All] & /@ Internal`BagPart[result, All]
];
Graph[
Flatten[(Rule @@@ Partition[#, 2, 1]) & /@
CollatzSequence[Range[50000]]],
PerformanceGoal -> "Speed",
GraphLayout -> {"PackingLayout" -> "ClosestPacking"},
VertexStyle -> Opacity[0.2, RGBColor[44/51, 10/51, 47/255]],
EdgeStyle -> RGBColor[38/255, 139/255, 14/17]]
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