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> The main problem by introducing the fourth dimension in the calculation is the enormous increase of processing needs and the difficulties of selecting an adeq
by bryan0 4y ago
> The main problem by introducing the fourth dimension in the calculation is the enormous increase of processing needs and the difficulties of selecting an adequate projecting surface.
This article was written over 10 years ago and this is no longer true. Recently I wrote a simple program which can explore the CxC space of Mandelbrot and Julia sets. I don’t know why there aren’t better visualizer which do this.
- Jarmsy 4y agoCan you share a link?
- bryan0 4y agoI actually just dusted this code off, and unfortunately the code is way too crappy to share as a fun learning and POC using TypeScript and React. but here is the basic idea: start with the standard mandelbrot equation: Zn+1^2 = Zn^2 + c where Zn and c are complex numbers. You can think of these as 4 real dims: (Z0_re, Z0_im, c_re, c_im) Now associate the X dimension of the display window to one of these and the Y dim to another. The other dims can be set to arbitrary constants. This can get you all orthogonal slices of the 4D space. For example the standard mandelbrot set would just be mapping: Z0_re->0, Z0_im->0, c_re->X, c_im->Y But you can also generate every combination of mandelbrot and julia sets in this space. As the paper mentioned though, you want to choose any arbitrary 2d slice, not just orthogonal ones, but really this shouldnt be much harder to implement. If I could do a POC of this in TS and React this should be easy to do for real.