Animating N points

Question

So I'm trying to create an animation of N interacting particles in two dimensions confined in a box. Generating the data is fine and it's being stored in a text file with two columns for each particle; one for its x coordinate and one for y. At the moment this is the code I've got to animate 4 particles, so a file with 8 columns:

data = Import["many_particles.txt", "Table"];
Animate[Graphics[{PointSize[0.025], Red, 
   Point[{data[[i, 1]], data[[i, 2]]}], PointSize[0.025], Blue, 
   Point[{data[[i, 3]], data[[i, 4]]}], PointSize[0.025], Green, 
   Point[{data[[i, 5]], data[[i, 6]]}], PointSize[0.025], Pink, 
   Point[{data[[i, 7]], data[[i, 8]]}]}, Axes -> False, 
   PlotRange -> {{-4, 4}, {-4, 4}}, Frame -> True], {i, 1, 3000, 1}, 
   AnimationRate -> 30, AnimationRunning -> True]  

And that gives me a visual result that I like, but I'd like to be able to import a data file with any number of columns (so any number of particles), and be able to animate them without writing a ridiculously long animate function to account for every one.

Any help is appreciated, thanks :)

Harry

Answer 1

The previous method I posted used ListPlot to generate the frames for the animation, but this is a very slow way to do it if you want to animate thousands of frames. A much quicker way is to just use graphics primitives like in the original post.

Here is a very fast function that will animate an unknown number of particles. I found that using ListAnimate slowed down the execution considerably over Animate, so that is what is used here. Keep in mind, it's usually better to use ListAnimate as it compiles the entire animation before showing it to you so it can handle errors better. When toying around here, I had initially neglected to have Animate only vary the parameter n by integer values, and this made my notebook nearly unresponsive. It's also possible that ListAnimate and Animate use different amounts of memory, but I'm not certain of that.

animation[datalist_, plotopts : OptionsPattern[]] := 
 Module[{point, data2, nparticles, colorlist, imglist, opts, prange},

  (*A simple function to create the graphics primitives*) 
  point[color_, coords_] := {PointSize[0.025], color, Point[coords]};

  (*Partition the data into the right dimensionality*)

  data2 = Partition[#, 2] & /@ datalist;

  (*Generate a list of distinct colors for every particle*)

  nparticles = Length@data2[[1]];
  colorlist = Hue /@ Range[0, 1., 1./nparticles][[2 ;;]];

  (*Generate the list of images*)

  prange = {#, #} &@Through[{Max, Min}[datalist]];
  imglist = 
   Graphics[point @@@ Transpose[{colorlist, #}], 
      Evaluate[FilterRules[{plotopts}, Options[Graphics]]], 
      PlotRange -> prange] & /@ data2;

  (*Animate the list of images - 
  the slower `ListAnimate` is commented out in favor of the more primitive `Animate` *)
  (*ListAnimate[imglist]*)
  Animate[imglist[[n]], {n, 1, Length@imglist, 1}, 
   AnimationRate -> 30, AnimationRunning -> True]
  ]

This can work on OP's data set in about 0.06 seconds on my machine (versus about 50 seconds for the ListPlot solution)

opdata = Import["http://pastebin.com/raw.php?i=6sccqHr8", "Table"];

animation[opdata, BaseStyle -> 20, FrameLabel -> {"x", "y"}, 
  Axes -> False, Frame -> True] // AbsoluteTiming

You can even apply it to a list with 60 particles, and still less than half a second

randomdata = 
  Transpose[
   Table[Accumulate[
     Prepend[RandomReal[{-0.2, 0.2}, {3000}], 
      RandomReal[{-10, 10}]]], {2*60}]];
animation[randomdata, BaseStyle -> 20, FrameLabel -> {"x", "y"}, 
  Axes -> False, Frame -> True] // AbsoluteTiming

Of course, if you want to export the animation for viewing outside the notebook, I would definitely recommend exporting the individual frames as image files and converting them using another program. Mathematica is not great at outputting movie files in my experience.