Interactive line chart of Collatz sequence values for a user-chosen starting integer. The famous 3n+1 conjecture is explored by iterating even-halving and odd-tripling rules. Enter a number, view the step graph, sequence length, highest value, and full sequence path to 1.
The Collatz conjecture is one of the most famous unsolved problems in mathematics. Given any positive integer:
- If the number is even, divide it by 2
- If the number is odd, multiply it by 3 and add 1
Input
Statistics
Sequence Length: -
Highest Value: -
Steps to Reach 1: -
Visualization
Sequence
Collatz Visualization in Mathematica
Mathematica Code for the image
SetAttributes[Collatz, {Listable}];
Collatz[n_, e_, a_, f_] := Module[{nn = n, bag = Internal`Bag[]}, While[nn =!= 1, Internal`StuffBag[bag, nn]; nn = If[EvenQ[nn], nn/2, 3 nn + 1] ];
Internal`StuffBag[bag, nn];
With[{seq = Reverse[Internal`BagPart[bag, All]]}, AnglePath[Transpose[{seq/(1 + seq^e), a*(f - 2 Mod[seq, 2])}]]]];
astroIntensity[l_, s_, r_, h_, g_] :=
With[{psi = 2 Pi (s/3 + r l), a = h l^g (1 - l^g)/2}, l^g + a*{ {-0.14861, 1.78277}, {-0.29227, -0.90649}, {1.97294, 0.0} }.{Cos[psi], Sin[psi]}];
Manipulate[
DynamicModule[{seq},
seq = ControlActive[Collatz[Range[5000, 5020], e, a, f], Collatz[RandomInteger[1000000, {n}], e, a, f]];
Graphics[{Opacity[o], Thickness[ControlActive[0.01, 0.003]],
Line[seq,
VertexColors -> (Table[
astroIntensity[l, s, r, h, g], {l, 0, 1,
1/(Length[#] - 1)}] & /@ seq)]}, ImageSize -> 500]
]
, "Colors", { {s, 2.49}, 0, 3}, { {r, 0.76}, 0, 5}, { {h, 1.815}, 0, 2}, { {g, 1.3}, 0.1, 2}, { {o, 0.5}, 0.1, 1},
Delimiter,
"Structure", { {e, 1.3}, 0.9, 1.8}, { {a, 0.19}, 0.1, 0.3}, { {f, 0.7}, 0.1, 1.5}, {n, 300, 5000, 1} ]
code
(note: parameters in the code might differ from the ones in simulation results below)-
Link to code(This simulation is interactive, written in JavaScript, see the source code of this page at the link) -
Link to code(C++ code for the simulation)