Mandelbrot Set stuff.

[foxgrrl]

I fixed the mistake that I had made (see: here (Warning: large)) with regard to the quaternion Mandelbrot set. It's actually much more boring than I though — basically a rotation of the set around the real axis. I found out that the set that I really wanted, was actually generated by the polynomial: z_n→z³_n-1-3a²z+b but I'm not sure whether a and b are scalars, complex vectors, or quaternion vectors. I'll probably figure it out through trial and error. I haven't had time to code that one yet...

I rendered a quick animation so you can see what I mean about the Mandelbrot set in Hilbert space. The white plane is, a white plane, about 0.1 units from the origin (I think, if I bothered to look it up); The surface of the set will shrink down from a sphere. This is the iteration count, stepping up higher by +1. Each one of these surfaces exactly corresponds with one of the bands of color you see around the two dimensional (Complex plane) Mandelbrot set (When you're doing the regular escape-time diagram, nothing weird.) So, imagine this as being like a single band of color, color-cycling around a typical textbook Mandelbrot set image.




Update: LiveJournal is doing something weird, there's supposed to be an image – http://www.arclight.net/~julia/lj/2006_Mar/mandelbrot_crosssection.gif – appearing above this line.

Comments

[soltice.livejournal.com]

Was there an image? I'm not getting anything over here. :-/

[foxgrrl]

It was broken, for not obvious reason. I messed around with the html in the post, and now it works.

[elf]

Forgot to check--are you familiar with Jonathan Coulton's song, Mandelbrot Set? If not, you should definitely check it out.