Strange Attractors

Hi everybody,

I have started a ‘Strange Attractor’ series and I wanted to share some images with you guys.

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Those images are fantastic!
I have a limited understanding of the “Strange Attractor” phenomenon, but I really enjoy visuals such as these. Nice work!

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Very attractive !

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This is great stuff! There are not so many ship building softwares around that you can also use for this kind of projects!

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Can you please share the gradient map you are using by the Dadras-Momeni attractor? Thank you.

Lorentz attractors. Basic display of chaotic systems.

Im impressed at the visual quality of the lines.

Did you make tubes to render or are they colored lines with gradients?

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Hi, beautifull images. My prefered is the “03_08”, it looks like a sci-fi interstellar vehicule. Amazing. Can you share the rhino/gh files ? thks

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wow, they are all very nice!

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@Peugeot All the attractors are included in the Chimpanzee plug-in :stuck_out_tongue_winking_eye:

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Thank you! They are really simply in practice. Just a bunch of 3 equations to compute the (x,y,z) coordinates of each point. Then interpolate.

They are mesh tubes, made from an interpolated curve. I imported the curve into Blender to make a pipe out of it because Rhino just could not manage to do it fast enough. I then imported the resulting mesh into Rhino again and colored using Grasshopper with the ‘Gradient’ and Mesh Colours’ components following the original curve as an axis for the color gradient. The material is the generic one from Vray with the diffuse being the vertex colors of the mesh.

I have to say, beautiful job on the Chimpanzee plug-in Matouš! Although I did not use it to create these, it has definitely been an inspiration. It has also been very useful as some sort of library. Oddly enough there aren’t complete lists of attractors on the internet.

I actually coded these myself as an exercise. Although once I nailed the first one, it then was a matter of replacing the formulae so not that much learning after the first. This the C# code for the Dadras Attractor.

private void RunScript(bool iEnable, int iCount, double a, double b, double c, double d, double e, ref object Opoints)
  {
    // empty list
    List <Point3d> Points = new List<Point3d>();

    // initial valeus
    double x = 1;
    double y = 1;
    double z = 0;
    double t = 0.002;

    // loop
    for (int i = 0; i < iCount; i++)
    {
      // formulas
      double x0 = x + t * (y - a * x + b * y * z);
      double y0 = y + t * (c * y - x * z + z);
      double z0 = z + t * (d * x * y - e * z);

      // re-assign result of formulas to 'initial values'
      // this means the result of formulas is used for the next iteration
      x = x0;
      y = y0;
      z = z0;

      Points.Add(new Point3d(x, y, z));
    }

    //output
    Opoints = Points;
  }

You mean this?


Here you go!
gradient_01.gh (14.5 KB)

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@ramsena Thank you for the gradient map.

It’s nice to hear that the Chimpanzee plug-in was an inspiration for you. The current version includes the most common strange attractors and discrete maps but there are many related attractors with slight variations. In my blog posts I usually reference the resources. If you are interessted in any particular attractor I might have the equations.

But if you are interessted in more complicated attractors there are a lot of papers about encryption, robotics, etc. but they are usually not for free. I have some papers on my list I wish for Christmas. :sweat_smile:

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Im all for more fractals!

Big fan since 30+ years! Not enough time to explore…

I would love to see Lyapunov structures in the monkey - Rhino might not be happy about it though. The graphics could be amazing.

Check the animation at the end.

Thank you for the feedback. Chimpanzee 0.4 (coming soon) will not include the Lyapunov fractal. But I will put it on a to do list for Chimpanzee 0.5.

Chimpanzee 0.4 will however include some interesting features for deep zoom, coloring.

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you sure got the color dimensions right!

nice JOB , keep going :100: :100: :dizzy: :dizzy: