Title: Split-Complex Numbers? Post by: mjk1093 on March 10, 2010, 02:53:05 PM 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 Title: Re: Split-Complex Numbers? Post by: kram1032 on March 10, 2010, 04:14:59 PM 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 Title: Re: Split-Complex Numbers? Post by: Timeroot on March 11, 2010, 01:02:58 AM 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. :embarrass:
My computer is broken, could someone render a quick escape-time picture of dual numbers? It would be appreciated! :) Title: Re: Split-Complex Numbers? Post by: kram1032 on March 11, 2010, 06:40:57 PM I also found it kinda surprising :) The split complex (at least for the standard Mset) aren't half as interesting as the dual numbers :) |