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I've experimented with the "Mandelbar" (sometimes called the "tricorn") fractal over the split-complex numbers: https://imgur.com/PkzY7B6 https://imgur.com/PkzY
by ogogmad 4y ago
I've experimented with the "Mandelbar" (sometimes called the "tricorn") fractal over the split-complex numbers: https://imgur.com/PkzY7B6 https://imgur.com/PkzY7B6
The result isn't completely trivial, but isn't particularly impressive either.
Anybody want to try Burning Ship over the split-complex numbers? It looks like you only need to replace the complex "i" with the split-complex "j".
- ogogmad 4y agoHere it is. Split-complex burning ship using Xaos: https://imgur.com/a/tBTuUDV https://imgur.com/a/tBTuUDV This is my first time using that program. It doesn't look too bad. Same thing, but with the dual numbers: https://imgur.com/a/kTU5ztn https://imgur.com/a/kTU5ztn
- ogogmad 4y agoA follow-up question, not easily answered using Xaos: The dual numbers can be pictured as lines in the Euclidean plane instead of points (details here: https://en.wikipedia.org/wiki/Laguerre_transformations https://en.wikipedia.org/wiki/Laguerre_transformations). What would the above "dual number burning ship" look like?