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.

Sebastian Rath´s PY4D is a new, alternative way to script with or to code plugins for Cinema4D – without COFFE or C++ – but in Python.

The current beta (v0.9.0001) already makes a fine impression and proves itself easy to get started with.

This video shows a little script that was adapted in a twinkling and controls the particles of a TP-Storm to behave after the three flocking boids rules.
Don has rendered a much prettyer version of the dummy above.

You can download the C4D-scene here.

Update: The file has been updated to work with the R12 version of Cinema 4D.

Cinema 4D offers the function “create outline” to offset a spline as contour.

Sadly it is only accessible while editing a spline in pointmode- so it´s destructive.

Smart Outline offers the same functionality but is animateable, can exclude the sourcespline and works with all types of splineobjects.

Its available for R10 and higher – PC/MAC (supports 64bit) – …and it´s free!

Update: The new version 1.2 now also has an animateable chamfer- option