N-dimensional complex numbers(alenspage.net)
alenspage.net
N-dimensional complex numbers
http://www.alenspage.net/ComplexNumbers.htm
15 comments
A reinvention of quaternions and Clifford Algebra?
There is also a very good book by David Hestenes about the application of Clifford Algebra in 3-D space (http://www.springer.com/de/book/9789027716736).
Curious to see the 3D and 4D Mandelbrot using this method. Should look something like the last visualization on this page http://www.skytopia.com/project/fractal/mandelbrot.html but with more bulbs?
The Mandelbrot set is already 4-dimensional, sort of. It's called a Julibrot or Juliabrot fractal. In the definition of Mandelbrot and Julia sets (which use the same formula), Mandelbrot maps C to the output axes and Z starts at zero. For Julia, it's the other way around, but C is some constant rather than always zero, so there are lots of julia sets (although not all are interesting).
If you combine these and make both Z and C variables, you go from 2 dimensions to 4. If you count the escape iterations, that gives you 5.
This is basically the set of all Julia fractals, which also happens to contain the original Mandelbrot set across the hyperplane where Z=0.
If you combine these and make both Z and C variables, you go from 2 dimensions to 4. If you count the escape iterations, that gives you 5.
This is basically the set of all Julia fractals, which also happens to contain the original Mandelbrot set across the hyperplane where Z=0.
Lont time ago when I was in high school I had a fascination for quaternions and wrote a mandelbrot implementation for them in a weird c like language on the Amiga. Unfortunately it turned out that the 4d mandelbrot set was just the normal one swept around the two new axes.
Now that I actually know how to program and it doesn't take hours to render an image it might be time to revisit this!
Now that I actually know how to program and it doesn't take hours to render an image it might be time to revisit this!
"weird c like language on the Amiga"
Was that BCPL?
Was that BCPL?
I think it was called E!
https://en.wikipedia.org/wiki/Amiga_E
https://en.wikipedia.org/wiki/Amiga_E
On mobile I can't read this article. Paragraphs end midway.
The sections seem to be positioned absolutely with pixel offsets.. Ugh.
I never understood why mobile browsers don't allow you to force-scroll (and force-zoom out) to solve such issues.
Mobile-friendly view sort of works in Chrome.
I viewed this in Chrome and Firefox (mobile), it's horrible in both cases.
Here is sample paragraph from Chrome:
First column:
Here is sample paragraph from Chrome:
First column:
"...This answer indicates that a straightforward"
"This notion of notion of mathematical impossibility..."
Clifford Algebra are century hold. Why would you need a new one...?
He has a weird antifeminist essay on that site, with a jab at transgender identity at the end: http://www.alenspage.net/Man.Woman.htm