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

Ideas
, ,
1

tree.gif

I noticed that a discussion about programming a lighted Christmas Tree from a simple equation

t * sin(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 :wink: 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 points

This .GIF file has 100 frames. Enjoy!

PD = .5; s[t_, f_] := t^.6 - f;
dt[cl_, ps_, sg_, hf_, dp_, f_] := {PointSize, 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]
14 Likes
The "Mathy" Arts of Coding Postcards
2

Beautiful. The shading solution, especially with the subtle differences between large and small points, is very elegant.

4 Likes
3

Beautiful tree!
A festoon lamp ornamented one :slight_smile:

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]

tree.gif

14 Likes
4

Silvia, this is absolutely stunning. To me it gives a perfect feel of reflective flickering.

5

Great work! thanks for sharing!

1 Like
6

Beautiful! Absolutely a damn good presentation and good work.