There are those popular structures we all know and love because they simply look fascinating from every angle – like the Sierpinski triangle, the Pythagoras tree or the Menger sponge.
Generative geometry is one more proof that math is beautiful no matter how basic.

Recently I stumbled upon a new pattern that is also phenomenally simple but produces rather complex shapes – the “Binary Kite”.

I first saw it in Mikael Hvidtfeldt Christensen’s ‘Structure Synth‘ – an ingenious tool for exploration of generative 3D structures.

Basically it’s a 3D array of randomly black/white colored cubes that slightly scale(linear) and rotate(noise) per iteration on one axis.
What makes it look so interesting is that each items transformation matrix is subordinated to its predecessor on that axis.

Initially, I played around with the kite in Unity 3D but quickly discovered that it can´t be animated at high iterations.


So I fired up C4D and wrote a simple Py4D generator.

The results

I did end up with this gorgeous picture of a 30*30*500 cubes kite (5400000 polygons) (fullsize):

Here is a closeup from the same viewpoint (fullsize):

Last but not least I rendered this short animation of a 5*5*150 kite growing:

Want to render your own kite with even more cubes? Grab the scene file here.

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

Hint:
Remember to uncheck “Optimize cache” in the Python Generator´s properties if you want to animate the parameters.

Conclusion

While Structure Synth is awesome, Cinema 4D and Py4D are a great way to visualize generated geometry too as Cinema’s render instances enable you to work with millions of objects.


Cheers

Smart PRS is a Cinema4D tag that allows to record position, rotation and scale of one or multiple objects to key frames.

This is especially useful for all, who want to bake Thinking Particel setups and don’t own the MOCCA module.

Take a look at the demonstration Video.



Recently I tried to use the AfterEffects export Option from Cinema4D to pass a simple particle animation to AE.

Unfortunately this didn´t work out – the issue is that all animation capable export formats/plugins rely on key frames, and objects animated via Xpresso/Thinking Particles are most times not even present in the timeline as they get generated as “Particle Geometry”.

While this can be easily fixed by creating them manually and linking the particle positions to them, it´s still impossible to export that animation without key frames.

Cinema4D offers the option to “bake” certain motions to key frames, but not from simulations.
Actually there is a plug-in called “Cappuccino” within the MOCCA module that allows this, but if you are not into character animation, chances are you don´t have it handy.


SmartPRS makes those animations export-and editable by recording them as key frames while the simulation is running.
After that, the Xpresso setup can be removed from the scene and the animation edited or exported.

The plug-in even allows to capture the position of an object that gets moved in real-time by the mouse.

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.

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