Strange Attractors Case Study

Final Image

My first project for Virtual Entertainment uses Processing to visualize a mathematical system called a strange attractor.  Strange attractors create a cloud of points based on a quadratic map, a series of letters which the program translates into numbers which control its movement.  For example, the final image used the pattern “AMTMNQQXUYGA”.

While there are a huge number of combinations that can be created, most of them seem to move  fairly continuously in one direction, and don’t create an interesting pattern.  A computer program can figure out which patterns work and which don’t, but luckily my atrophied math skills got a break from having to figure this one out, as other people have already done it.

The basic attractor renders out a cloud of points:

Cloud of Points

I then explored several options for connecting the points, initially with straight lines:

Lines

Then with Curves:

Curves

At the same time, I modified the file to output a PDF, so that everything was in vector and can be scaled to any size.

Finally, I connected all of the points with a continuous spline.  Unfortunately, this narrowed my options for which attractors I could use, as it caused several patterns to look pretty lame:

Boring

Finally, I added color, by having processing grab colors out of an image file, resulting in the final image at the beginning of the post.  I also ended up with a few other images that I thought were cool.

I also explored some other options for this project, which didn’t turn out badly, but still need some more work.

[Download Processing Code]

References

• Strange Attractors at Wolfram Research Mathworld
• Julien C. Sprott on Strange Attractors