Split-Complex Numbers?

[mjk1093]

I was wondering if anyone here knew anything about the Split-Complex numbers, and if you can make interesting fractals with them.

Thanks in advance,
mjk1093

[kram1032]

http://kram1032.deviantart.com/art/dusty-old-attic-128907426 - this is a Buddhabrot with Split Complex numbers

Nice but not really interesting.

However, playing with it a bit more can lead to quite interesting results

Dual Numbers result in this Fan-pattern:
http://kram1032.deviantart.com/art/sunset-fans-128739482

And if you cycle through complex, split complex and dual numbers, you get quite interesting patterns like this one:
http://kram1032.deviantart.com/art/battlebrot-128916634

[Timeroot]

Neat pics. I'm surprised that the Fan pattern (dual numbers( also produces an interesting image, as the x is independent of the y, and so would always approach either a steady state or infinity... and so y will "almost always" goes to infinity too, if x goes to infinity. If x goes to a steady state, then y will either go to infinity as well (albeit only exponentially fast), or go to a steady state. No, wait... x could be chaotic... never mind. 

My computer is broken, could someone render a quick escape-time picture of dual numbers? It would be appreciated! 

[kram1032]

I also found it kinda surprising
The split complex (at least for the standard Mset) aren't half as interesting as the dual numbers