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Strange attractors are fractals that emerge at certain, sensitive parameters within the three-or more dimensional phase space.

They are are researched since the early 70s and strongly related to the chaos theory as they allow to watch the transition from chaos to order/geometry.

Good things first: see the result and try the chaotic attractor finder!

The 3D visualization of a strange attractor is quite resource intensive as points race around the attractors on chaotic trajectories – so it needs many iterations or particles to see a shape emerge from that chaos.

There are already some great flash experiments so I turned to Cinema 4D and PY4D as an advanced renderer would easily allow to raytrace and shadow the results – and to calculate even more particles of course.

This small PY4D script creates a strange attractor that Dr. Clifford Pickover had published 1990.

I managed to render a maximum of 50.000 particles with the R11 on my machine.

But with the new R11.5 release Maxon introduced render instances to C4D allowing now to calculate up to millions of particles – depending on the system.

I went with a number of 300.000 points, seeded the attractor parameters and rendered four transparent animations that could be combined to a 1.2 million particle video.

The preparation time for each frame was ~1min while PY4D took less than a second of that duration to perform five sinus/cosinus operations for each point.
Rendering itself took about five seconds per frame (CPU:Q6600).

If you are interested you can download the szenefile here.
(Remember to activate render instances in the PShape node of the XPresso tag).

Update:
The scene file has been updated to the R12.

When I learned that you can actually identify strange attractors using the Lyapunov exponent and found John Holder´s programm ‘lyapdemo.c’, I took a few minutes to port it to AS3.

You can use it to generate parameters for the PY4D script.