After seeing this picture on Flickr:
I decided to see if I could model the bastard child of an escalator and a circular staircase:
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I think that it works pretty well.
I’ve recently been playing with Chaoscope, software for rendering 3D strange attractors. Here is an example of a render of a type A polynomial as rendered by Chaoscope:
If you are interested in replicating this image, use the following factors: p0=0.271, p1=1.594, p2=1.122.
While the images that Chaoscope renders are quite interesting, they are based around an orthographic camera model - there is no vanishing point perspective. I decided that I should try to replicate these attractor systems in Blender. I modified some python code that I found here with the formulas that Chaoscope uses to produce this:
Later I want to modify this by adding more of the formulas that Chaoscope uses, especially the “Unravel” one, and to animate, both by moving through space, and by changing the attractor’s coefficients through time.
This tutorial requires basic knowledge of Blender.
Background
Blender’s three-dimensional rectilinear grid allows for easy creation of cube-based objects. But what do you do if you want to create a tetrahedron, a regular polyhedron with four equilateral triangle faces? My initial attempts at this involved trying to create one face on the X-Y plane and rotating a copy up. This turned out to be a lot more trouble than it’s worth because you have to deal with some very specific angles.
After playing with a magnetic toy in the shape of a tetrahedron I realized that it could be inscribed neatly in a cube, with each of its vertexes in a corner of the cube, and each of its edges running along the diagonal of one of the cube’s faces.
In short the coordinates for the vertices of a tetrahedron are:
(+1, +1, +1)
(−1, −1, +1)
(−1, +1, −1)
(+1, −1, −1)
Constructing the Tetrahedron
Create a cube, switch to vertex select mode and rotate the scene so that you can see and select any of its vertices. The image below already has a tetrahedron inscribed in it which should help you locate the new faces you will add. Each vertex of the cube is labeled “A” to “H”:
You now have a tetrahedron inscribed inside the original cube. Let’s cut away the cube:
Select B, C, H & E. Delete these vertices.
You are now left with a tetrahedron: