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.
Softology's Blog 
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.
Not a problem.
Jason.
Hello, great work. Is there a way to export these as an OBJ file or similar?
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.