# Strange Attractors

Hi there folks, I am wanting to use the algorithm for a strange attractor (akin to these: [url]https://chaoticatmospheres.com/mathrules-strange-attractors[/url]) to determine the movement of an object (e.g. using a Transform SOP on a Sphere SOP) and running the output through a Feedback TOP network to achieve a nice visualisation.

I have put the equations through the t[xyz] parameters on the Transform SOP but to no avail. Lately I have been trying a combination of Expression CHOPs and a Feedback CHOP, but all my values remain at zero. I have a basic understanding of the math involved in these expressions, but finding a way to make it all happen in TouchDesigner is proving a challenge.

Any ideas? Would love to see examples of chaotic systems being produced in TD!

Hello,
I am also interested to strange attractors and chaotic structures.
I think what you forget is that this kind of mathematic is part of parametric equations, in this case diferential equations.
You have to introduce somewhere the time in the equation (here the Lorenz attractor) :
dx = (a * (y - x)) * dt;
dy = (x * (b - z) - y) * dt;
dz = (x * y - c * z) * dt;
where dx/dt, dy/dt and dz/dt is the speed on each axe.
The position is gift by this formula:
x = x + dx;
y = y + dy;
z = z + dz;
I send you a proposition where each calculus create a new line in a Table DAT, building a polygon with Add SOP.
LorenzAttractorVersion02.toe (141 KB)

2 Likes

Hello there,

Nice to see others interested in this topic!

Like jacqueshoepffner said, time is the essential element you were missing to fully implement the equations.

You can go a long way using the technique of creating points artificially, writing them on a table, and creating a SOP from it, just like jacqueshoepffner has suggested. Attached an image and a little video created in TouchDesigner using a similar approach.

vimeo.com/343428105

This is from a live performance dedicated to chaotic functions called â€śStrange Attractorsâ€ť that I have been working for a while. Here a link with some more documentation: [url]https://darienbrito.com/project/strange-attractors/[/url].

I will make sure to upload a tox with some goodies from it after the premiere, if you guys are interested about it

Hello Darien,
Sure, I am really interested about your research who intersect with my preoccupations.
I am on the way to transfer the Lorenz Attractor from python to GLSL.
If, by chance, you come to Paris, make a sign to take a drink together and speak about procedures and algorithms.
All the best,
Jacques

Hey Jacques,

Great! Will do!

All the best,
Darien

Hi!

One more person interested in strange attractors here.
jacqueshoepffner, thank you for a tox â€” very nice starting point to explore possibilities.
After testing different options for creating thicker objects instead of lines, I found two solutions:
for a realtime attractor growing - send table to CHOP and Limit SOP afterwards with a Tube output option (orient to path, apply texture)
for complex shapes - create attractor first, and then Limit CHOP as polyline - seconds input of Sweep SOP with Skin On (Text SOP as an first input works nice).

Here is my render of Hadleyâ€™s attractor:

```dx = (-(y1*y1) - (z1*z1) - (a*x1) + (a*c)) * dt dy = ((x1*y1) - (b*x1*z1) - y1 - d) * dt dz = ((b*x1*y1) + (x1*z1) - z1) * dt```

Hi there,

i love this kind of stuffâ€¦ just scratching the surface of Touchâ€¦ soo this is way above my headâ€¦ but i still want to see some .tox files dear Darien â€¦some beautifull stills you got there, love the blurriness

Greets Jeffrey

Merci Jacques ! I used your patch this morning as a basis for this thing I posted today for #genuary. I couldnâ€™t find you on social media (good for you!) so I wanted to say thanks here have a great day everyone - L.