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Inspired by this (please use Chrome or Firefox), I tried to simulate it, but I couldn't do it. I'm not familiar with Dynamic. Here is my simple code:

Dynamic[
 Graphics[{Hue[Random[]], PointSize@Large, 
   Point[{0, Dynamic[Clock[{0, 5, 0.5}]]}]}, Axes -> 1, PlotRange -> 5]
 ]
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2 Answers 2

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Here you have a toy to start playing with:

Edit preventing the animation running at different speeds in different machines by using Clock[] and DynamicWrapper[] (due credit to @jVincent)

n = 500; (*number of managed  particles*)
x[i_][t_] := (vx0[i] (t - delay[i])) UnitStep[t - delay[i]];
y[i_][t_] := Module[{k},  If[(k = (-#^2 + vy0@i #) UnitStep@#) < 0 &[t - delay@i], 
                              delay[i] = t + RandomReal[{0, 5}], k]];
vcols = RandomReal[{0, 1}, n];
Table[vx0@i = RandomReal[{-1, 1}]; vy0@i = RandomReal[{10, 12}]; 
                                 delay@i = RandomReal[{0, 12}], {i, n}];

points[s_] := Table[{x[i][s], y[i][s]}, {i, n}];

DynamicModule[{t}, DynamicWrapper[
     Framed@Graphics[Dynamic@Point[points[t], VertexColors -> Hue /@ vcols], 
                     PlotRange -> {{-10, 10}, {0, 40}}, ImageSize -> 200], 
  t = Clock[10^6]]]

belisarius's x-rated effusion

enter image description here

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16
  • 2
    $\begingroup$ Wow!.. this is cool.. +1 $\endgroup$
    – Murta
    Jan 26, 2013 at 13:34
  • 1
    $\begingroup$ GroosooooooooOO $\endgroup$
    – Rojo
    Jan 26, 2013 at 14:25
  • 1
    $\begingroup$ hm, I should have been faster :) +1 $\endgroup$
    – acl
    Jan 26, 2013 at 17:00
  • 1
    $\begingroup$ @Mr.Wizard, sure $\endgroup$
    – Rojo
    Jan 26, 2013 at 19:41
  • 1
    $\begingroup$ @cormullion - you mean "if you don't like" ;-). $\endgroup$
    – stevenvh
    Jan 26, 2013 at 20:00
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Here is a modification @belisarius asked me to post. I was playing around and made a 3D version. Putting Dynamic inside Graphics3D lets you rotate the fountain.

n = 100;
width = 10;
x[i_][t_] := (x0[i] + vx0[i] (t - delay[i])) UnitStep[t - delay[i]];
y[i_][t_] := (y0[i] + vy0[i] (t - delay[i])) UnitStep[t - delay[i]];
z[i_][t_] := (k \[Function] 
     If[k < 0, 
      If[Abs[x[i][t]] > width || Abs[y[i][t]] > width, (* wait until over the edge *)
       delay[i] = t + RandomReal[{0, 12}], 0.01], 
      k])[(-#^2 + vz0@i # + z0[i]) UnitStep@# &@(t - delay[i])];
Table[x0@i = y0@i = z0@i = 0;
  vx0@i = RandomReal[{-1, 1}];
  vy0@i = RandomReal[{-1, 1}];
  vz0@i = RandomReal[{10, 12}];
  delay@i = RandomReal[{0, 12}], {i, n}];
points[s_] := 
  Table[{x[i][s], y[i][s], z[i][s]}, {i, n}]~Join~
   Table[{x[i][s], y[i][s], 0}, {i, n}];
{Graphics3D[
  GraphicsComplex[
   Dynamic@points[Clock[\[Infinity]]], {Point[Range[n], 
     VertexColors -> Hue /@ (Range[n]/n)], LightGray, 
    Point@Range[n + 1, 2 n]}], 
  PlotRange -> {{-width, width}, {-width, width}, {0, 40}}], 
 Dynamic[Clock[\[Infinity]]]}

Some output

Edit: Garden Hose

Here's a variation that uses ViewPoint and ViewVector to keep gravity pointing screen-down no matter how the graphics are rotated. The hose is gratuitous; but I ran into a bug with BezierCurve, so I used BezierFunction instead. The hose droops, too, according to the current gravity.

droplets = 200;
dist = 25;
hoseHeight = 5 - dist;

pos[t_, p0_, v0_, gravity_, delay_, droplets_] := 
  Table[p0[[i]] + (gravity #^2 + v0 [[i]] #) UnitStep@# &@(t - delay[[i]]), {i, droplets}];
p0 = ConstantArray[{0., 0., hoseHeight + 3.}, droplets];
v0 = MapThread[{#1 Cos[#2], #1 Sin[#2], #3} &,
      {RandomReal[{0, 1}, droplets], RandomReal[{0, 2 \[Pi]}, droplets], RandomReal[{10, 12}, droplets]}];
delay = RandomReal[{0, 13}, droplets];
points[s_] := (gravity = Normalize[(vv\[Cross]vp)\[Cross]vp]; 
   MapIndexed[(If[Max[Abs[#]] > dist, 
       delay[[First[#2]]] = s + RandomReal[{0, 4}]]; #) &,
    pos[s, p0, v0, gravity, delay, droplets]]);
hoseFn := 
  With[{offset = 
     5 Normalize[{gravity[[1]], gravity[[2]] + 1.`*^-6, 0}]},
   BezierFunction[{offset + {0, 0, hoseHeight - 5} + 2 dist gravity, 
     offset + {0, 0, hoseHeight - 5}, {0, 0, hoseHeight - 5}, {0, 0, 
      hoseHeight}}]];
vp = {1.8, -2.8, 0}; vv = {0., 0., 1.}; (* ViewPoint, ViewVertical *)

Graphics3D[{
  GraphicsComplex[
   Dynamic@points[Clock[\[Infinity]]], {Specularity[White, 10],
     {Hue[0.45 + #/(4 droplets), 0.7, 1], Sphere[#, 0.25]} & /@ Range[droplets]
    }],
  {Thickness[0.0075], LightGray, 
   Line[{{0, 0, hoseHeight}, {0, 0, hoseHeight + 3.1}}], Darker@Green,
    Dynamic@Line[Table[hoseFn[t], {t, 0, 1, 0.05}]]}
  },
 PlotRange -> dist, PlotRangePadding -> {{0, 0}, {0, 0}, {0, 0}}, 
 ViewPoint -> Dynamic@vp, ViewVertical -> Dynamic@vv, 
 SphericalRegion -> True, ImageSize -> 400, Background -> Black]

Sprinkling hose animation

In one respect it is not like a garden hose. When the graphics are rotated, the water droplets change their trajectories. In real life, you could only rotate the hose.

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2
  • 1
    $\begingroup$ Nice use of GraphicsComplex! $\endgroup$ Jan 27, 2013 at 2:50
  • $\begingroup$ mmmm... skittles! $\endgroup$
    – rm -rf
    Jan 27, 2013 at 4:08

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