Inspired by Neil Baylis‘s Blob Thing program that I talked about previously, I made some Fourier Transform art of my own.
Take a leader-bee in five-dimensional space. Give him a place to go in five-dimensional space. When he gets close to his destination, move his target spot. Have ten follower-bees try to follow him. The follower-bees can fly faster than the leader bee. They are also super eager. They always accelerate at their maximum possible acceleration.
Now, for each follower-bee, consider how far away it is along each axis from the leader-bee. Interpret those deltas as an amplitude, a horizontal frequency, a vertical frequency, a horizontal phase angle, and a vertical phase angle. Compute the inverse 2-D Fourier transform of those components from the follower-bees.
Color code the output by the height. Add in some specular highlights. Animate through time.
Fourier Swarm from Patrick Stein on Vimeo.
I have used a similar technique in the past to generate ambient music. There, I made twenty follower-bees in thirty-two dimensions and used the average distances along each axis to the leader-bee as the volume of the note (each axis had a different pitch). Here, the results are visual instead of aural. I also cannot generate them in realtime except for very tiny sizes. *shrug*
Here is the Lisp source code. It depends on Zach’s ZPNG library for output.
Hah! Very cool.
Doh, I had meant to mention that I was inspired by your Blob Thing. I forgot to throw that in in the rush to get this out the door before my volleyball game tonight. I have now added an opening paragraph about that inspiration.
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I Totally want this as my screensaver, or an iTunes plug-in.
At the moment, it takes about 2-seconds per frame, so it’s not so useful in real-time. *shrug*
That’s brilliant, thank you very much. Do love visualising the higher dimensions