Simple Attractors
Published on 26 May 2008
This little experiment lets you visually explore two very simple attractor equations that generate very unexpected and aesthetically pleasing results.
It was coded in Actionscript 3.0 and wrapped into an Adobe Air application so that you can export the rendered imaged as PNGs.
The two simple attractor equations are credited to Peter de Jong:
x' = sin(a * y) - cos(b * x)
y' = sin(c * x) - cos(d * y)
And Cliff Pickover:
x' = sin(a * y) + c * cos(a * x)
y' = sin(b * x) + d * cos(b * y)
Start with a random point x, y and plot a semi-transparent pixel at the calculated x', y' point. Plug the new x', y' values back into the equations to get the next point, and so on for a few hundred thousand iterations. Vary the a, b, c, d constants to give wildly different results.
View the gallery for more renderings.
Download the application and get the source code.
Note: you will need the Adobe Air runtime installed first.
Last updated: 5 October 2008
2 Comments
Links & further reading
- The Simple Attrator Gallery
- Download Adobe Air application
- Download source code
- Peter de Jong Attractor
- Clifford Attractor
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I don't know why... but... man... The picture above makes me think about like... bottom of humans body... =\
it's very interesting. in fact easy to calculate, but it seems impossible at first. Thank you very much for your sharing. it will be very useful for me.