Inverse Fourier Transform of Swarm Data September 24th, 2009
Patrick Stein

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.

Beautiful Random FFTs September 22nd, 2009
Patrick Stein

Neil Baylis emailed me a program he had put together that puts a few random numbers in a grid and does the inverse FFT of them. His program cycles the values placed in the grid between -1 and 1 to animate some different effects. I like just regenerating random ones over and over again or tweaking which cells of the grid are in use. [You may already be on the same page as I am here, but I’ve got an idea kicking around now that I just have to try…. watch for it in a day or two.]

blob_thing Here is one of the nifty designs that I generated with his program. I encourage you to download it and play around a little bit. It is really great to see in real-time how activating certain frequencies affects the output.

For reference, blob_thing_grid here are the frequencies that I had activated for the above picture.

There are gorgeous specular features and shading in his output images. He could have just it left it flat-colored, but he went the extra distance to add a lighting model. The results are stunning. You should click on the above image to see it full-size. And, you should check out the the example on Neil’s page.

 

Blur and Edge Detect your Fourier Transforms September 21st, 2009
Patrick Stein

I have now added convolutions to my FFT Paint application. Here, I started with the following image (again, magnitude on the left and phase on the right):

conv_orig_m  conv_orig_p

From there, I took the Fourier Transform:

conv_pre_m  conv_pre_p

Then, I did a horizontal Sobel operator on it to get this:

conv_post_m  conv_post_p

From there, I did the Inverse Fourier Transform to obtain this:

conv_final_m  conv_final_p

Enjoy!

Do Radial Gradients on your FFT September 16th, 2009
Patrick Stein

I have now added radial gradients to my FFT Paint application. Here, I wiped out an image entirely and painted my own data using only the new gradient tool to come up with this starting point:

mag_grad  phase_grad

This is what it looks like if I do the inverse FFT of that data. It’s not an incredibly interesting result, but it does show the power.

mag_inv  phase_inv

Here is another example of a starting point made entirely with the gradient paint tool:

conc_tm  conc_tp

And, its resulting image when I do the inverse transform:

conc_rm  conc_rp

Simple Function Plotting in Javascript September 15th, 2009
Patrick Stein

graphRather than work more on my FFT Paint program yesterday, I took a break to make a simple function plotter. There are lots of useful Java applets out there that do more than what I’ve done here. And, certainly, gnuplot is much more complete and useful.

On the other hand, if you just want to quickly plot something that you can save as an image, you either have to re-learn gnuplot (every time I use it, I have to sift through the help to figure out how to set up my tics and labels and output size and output filename) or you have to do screen grabs from one of the Java applets.

With the plotter that I wrote yesterday, you click on the Snapshot button, then right-click to save the image or copy it to your clipboard.

Enjoy.

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