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

I haven´t written about Py4D for quite a while now…

In the meantime, Maxon has first announced a cooperation with – and now the acquisition of Sebastian Rath´s praised python implementation for Cinema4D.

So finally – Cinema4D meets Python!

Let´s celebrate with some cool experiments!

If you are new to this blog or Py4D – a short introduction:

Py4D enhances C4D with a standard Python interpreter that provides access to the C4D SDK and allows to easily code platform indepentent scripts and plugins that control or extend C4D.

Basicly the same as COFFEE, C4D´s own scripting language, but Py4D has two major advantages:

• It follows the C++ SDK more closely and implements it further than COFFEE does.
• It is a easy to pickup, widely known language with a huge community and tons of existing code and librarys.

While C4D is a mighty tool in itself, this powerful scripting interface enables the user to work with external data, automate processes or build his own tools.

Being more the C++ type when it comes to plugin development and C4D, I enjoy being able to solve small problems just by hacking a few lines of code into the script manager.
I also prototype most of my plugins in Py4D before I start developing in C++ – it´s just more convenient.
The step of compiling for every test takes much more time in the long run.

So here´s the meat:

Four simple examples how to have a good time with Py4D and some particles…

Everyone requires C4D R11.5, the Thinking Particles module and the actual version of Py4D.

Update: All files have been updated to work with the R12 version of Cinema 4D.

Py4D has been through some changes since the open beta started, so I took the time to update the scripts I published in the boids, and strange attractor posts and included them here.

Click the images for a preview.

1. Stars4Py4D

This is a Py4D port of the Sagan experiment I did in flash <- check out this link, it´s fun

A good and simple first step with particles - position vectors get parsed from a CVS database and from a galaxy of suns… “My God. It’s full of stars!”

Hint: this example might be the best to start with, as it includes comments – the others don´t, because they use pretty much the same pattern.

Just download the package, load the scene and change the path to the CSV file within the “file” user data field of the Py4D Tag.

2. Phy4D

A very simple adaptation of a 2D “physic engine” – works only with spheres.
The direction of gravitation is animated to make this a little more interesting.

Have a look at the preview video and scene file.

3. Boids

This is simply a revival of the Py4D Boids post – same beast, but updated to the Py4D release version.
The script creates a flocking boids swarm, that behaves according to the rules outlined by Craig Reynolds.

Checkout this video from Sebastian and get the scenefile.

4. Strange Attractor

Again just the script from the original strange attractor post, but ported to the final SDK.
View the final rendering and the original post – you can use the Strange Attractor Finder to locate your very own, chaotic attractor!

Here´s the scene file.

Conclusion

Python and Cinema4D are a great team and Py4D is THE alternative to COFFEE.

I hope this gives everybody who is interested in Py4D and controlling particles, a small head start, some inspiration or at least something fun to play with


Thanks to Sebastian for suggestions, support – and of course Py4D.

Cheers!

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.