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.

Unfortunately I had to discover that the bottleneck at C4D wasn´t the rendering of vast amounts of vertices but the allocation of many particle objects.

I managed to render a maximum of 50.000 particles with the R11 before C4D outmaxed my systems ram (4GB).

Thats less than a sixth of what can be rendered realtime with flash.
Admitted that comparison is unfair for many reasons, still… there is a point.

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.

Sadly I was limited to 300.000 points so I 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).
Also its worth mentioning that the viewport can actually draw more particles that C4D is able to render.

It would be interesting to see how for example POVRay or Blender would perform when faced with this task.

If you are interested you can download the szenefile here.
(Remember to activate render instances in the PShape node of the XPresso tag when using the R11.5).

Update:

I already knew that 3D Studio Max and Softimage could handle several millions of particles but i was surprised to hear that Maya seams to have similar problems like C4D.
I also gave Blender a shot and managed to preview and render over a million with ease.

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.
So I can find more fascinating attractors for further experiments (most likely with blender) and you can use it to generate parameters for the PY4D script aswell.