Further adventures with 3D Strange Attractors

After the original new 3D Strange Attractor formulas I found here I have been playing with alternate formulas and came up with these 5 new types.

Here are the formulas used and some sample images of each type. The a3da[] values are parameters between -1 and +1 that control the shapes.

Rampe 6
xnew=z*sin(a3da[0]*x)-cos(a3da[1]*y)
ynew=x*sin(a3da[2]*y)+cos(a3da[3]*z)
znew=y*sin(a3da[4]*z)-cos(a3da[5]*x)



Rampe 7
xnew=z*sin(a3da[0]*x)-cos(a3da[1]*y)
ynew=x*cos(a3da[2]*y)+sin(a3da[3]*z)
znew=y*sin(a3da[4]*z)-cos(a3da[5]*x)



Rampe 8
xnew=z*sin(a3da[0]*x)-cos(y)
ynew=x*cos(a3da[1]*y)+sin(z)
znew=y*sin(a3da[2]*z)-cos(x)



Rampe 9
xnew=y*sin(a3da[0]*x)-arccos(a3da[1]*y)+sin(a3da[2]*z)
ynew=z*sin(a3da[3]*x)-arccos(a3da[4]*y)+sin(a3da[5]*z)
znew=x*sin(a3da[6]*x)-arccos(a3da[7]*y)+sin(a3da[8]*z)



Rampe 10
xnew=y*sin(a3da[0]*x)-cos(a3da[1]*y)+arcsin(a3da[2]*z)
ynew=z*sin(a3da[3]*x)-cos(a3da[4]*y)+sin(a3da[5]*z)
znew=x*sin(a3da[6]*x)-cos(a3da[7]*y)+sin(a3da[8]*z)



All of the above formulas are now implemented in the latest version of Visions Of Chaos.

I have more ideas to expand new attractor formuals in future versions of Visions Of Chaos. Firstly is to get a decent formula compiler implented so the user can try formulas easily by typing in the 3 formulas for xnew, ynew and znew. Once that works the next obvious evolution is to get it to genetically evolve and mutate the formulas like I have done for Genetic Art in the past.

Jason.

6 responses to “Further adventures with 3D Strange Attractors

  1. i shared this page from your blog in my fb without asking you. hope u dont mind. thanks for sharing your work and pictures from math formula are beautiful.

    • There is no OBJ export at the moment. These images are created by calculating a “point cloud” of millions of points and then rendering them.

      Would an OBJ file containing millions of points be helpful to you?

      Regards,
      Jason.

      • Hi Jason,
        Sure that might be cool. I was hoping to import them into something like Meshlab or Blender

        cheers,
        CS

      • OK, I added in OBJ export for the 3D Strange Attractors.

        I did some tests importing the OBJ files (approx 3 million points) into both MeshLab and Blender and they worked fine. I don’t know how to create meshes or solid objects from the point clouds, so if you do get some nice results I would like to see them. I was able to use MeshLab to simplify the points, but any marching cube options I tried crashed Meshab.

        Download the latest Visions Of Chaos here (or if you already have it installed, select the Help -> Check For Updates menu to get the latest version).

        Follow these steps to get an OBJ file;

        1. Start Visions Of Chaos
        2. Select Mode->Attractors->3D Attractors
        3. Find a sample you want to export (click Search a bunch of times or load a sample)
        4. Check the OBJ checkbox and then click OK to start rendering
        5. After a few million points have been calculcated (or however many you want) click Stop.
        6. The OBJ file will be written to disk and when done you will get a message telling you the location.

        Let me know if you have any problems with it.

        Jason.

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