t * sin (t) ≈ Christmas tree - exploring a famous Reddit discussion

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 Vitaliy Kaurov 13 Votes I noticed that a discussion about programming a lighted Christmas Tree from a simple equationt*Snt[t]became very popular on Reddit. It is connected to a project a programmer developed. I thought how fast we can make it with Wolfram language? Here is the result with slight flickering ;-) Note a very special care needs to be paid to the dimming of the lights at a larger distances, and pretty shadowing. Function f(t, f) is rescaling sampling rate of driving parameter t of parametric curve so points are distributed uniformly. f is basically phase shift.Parameter PD is just average distance between pointsThis .GIF file has 100 frames. Enjoy! And in the spirit of holidays don't forget to read: “Happy Holidays”, the Wolfram Language Way PD = .5; s[t_, f_] := t^.6 - f; dt[cl_, ps_, sg_, hf_, dp_, f_] := {PointSize[ps], Hue[cl, 1, .6 + sg .4 Sin[hf s[t, f]]],                                      Point[{-sg s[t, f] Sin[s[t, f]], -sg s[t, f] Cos[s[t, f]], dp + s[t, f]}]}; frames = ParallelTable[        Graphics3D[Table[{dt[1, .01, -1, 1, 0, f], dt[.45, .01, 1, 1, 0, f],                       dt[1, .005, -1, 4, .2, f], dt[.45, .005, 1, 4, .2, f]}, {t, 0, 200, PD}],          ViewPoint -> Left, BoxRatios -> {1, 1, 1.3}, ViewVertical -> {0, 0, -1},     ViewCenter -> {{0.5, 0.5, 0.5}, {0.5, 0.55}}, Boxed -> False,     PlotRange -> {{-20, 20}, {-20, 20}, {0, 20}}, Background -> Black],      {f, 0, 1, .01}];Export["tree.gif", frames]
Answer
4 years ago
4 Replies
 BoB LeSuer 4 Votes Beautiful.  The shading solution, especially with the subtle differences between large and small points, is very elegant.
Answer
4 years ago
 Silvia Hao 10 Votes Beautiful tree!A festoon lamp ornamented one  PD = .5; s[t_, f_] := t^.6 - f dt[cl_, ps_, sg_, hf_, dp_, f_, flag_] :=  Module[{sv, basePt},         {PointSize[ps],          sv = s[t, f];          Hue[cl (1 + Sin[.02 t])/2, 1, .3 + sg .3 Sin[hf sv]],          basePt = {-sg s[t, f] Sin[sv], -sg s[t, f] Cos[sv], dp + sv};          Point[basePt],         If[flag,            {Hue[cl (1 + Sin[.1 t])/2, 1, .6 + sg .4 Sin[hf sv]], PointSize[RandomReal[.01]],             Point[basePt + 1/2 RotationTransform[20 sv, {-Cos[sv], Sin[sv], 0}][{Sin[sv], Cos[sv], 0}]]},            {}]        }]frames = ParallelTable[                       Graphics3D[Table[{                                         dt[1, .01, -1, 1, 0, f, True], dt[.45, .01, 1, 1, 0, f, True],                                         dt[1, .005, -1, 4, .2, f, False],                                          dt[.45, .005, 1, 4, .2, f, False]},                                        {t, 0, 200, PD}],                                  ViewPoint -> Left, BoxRatios -> {1, 1, 1.3},                                   ViewVertical -> {0, 0, -1},                                  ViewCenter -> {{0.5, 0.5, 0.5}, {0.5, 0.55}}, Boxed -> False,                                  PlotRange -> {{-20, 20}, {-20, 20}, {0, 20}}, Background -> Black],                       {f, 0, 1, .01}];Export["tree.gif", frames]
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4 years ago
 Silvia, this is absolutely stunning. To me it gives a perfect feel of reflective flickering.
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4 years ago
 Max Sakharov 1 Vote Great work! thanks for sharing!
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4 years ago