Congratulations on your discovery, although temper it with the knowledge that like most great discoveries, it's been around for a while:
The 4d, and higher (I made up to 10d way back in January), have been around since close to the rediscovery of the bulb (someone else was working on them around March of this year, and in fact I think the topic was mentioned in the original thread, although I wasn't aware of any implementation before mine). Here is a 6 dimensional bulb video (crappy, didn't figure out coloring methods yet) I posted on youtube January 24th of this year:
http://www.youtube.com/v/9Jzfdr1Zh6Y&rel=1&fs=1&hd=1 Anyways, there are VERY awesome pseudo-julia that can be created using the correct coloring methods, etc. with the 5d bulb. I posted a thread over in the images forum with a few images from a 5d pseudo-julia. Each iteration creates a great variety of patterns as one zooms straight into the fractal (the pattern changes each iteration as you zoom deeper... it's amazing, although the pseudo-mandel variety r2 modes 1-4 have some variety as well).
Also, for the both of you (Jesse and JosLeys) I'd like to point out that the complex triplex, quadplex, and quintplex (untested, but assumed) math versions I developed are slightly faster for cpu implementations (not sure about gpu implementations). As I've a crappy gpu I can't compare the complex triplex... versions to trig versions on a gpu (many of which I guess to have trigonometric optimizations, but maybe not?).
For example, for the degree 9 (z^9) 4d bulb @ 10 iterations (.2 k value), the trig version took 75.813 seconds and the complex quadplex version took 47.453 seconds: in other words the trig version takes 159.8% longer for the same exact image. This adds up, especially when you render larger images (than these 500x500 test images)...
Now the difference is lower for less iterations... so when you increase iterations (deep zoom) the quadplex version really starts to pay off (at 5 iterations, there is only ~ +120% time for the trig version).
500x500 zoomed in:
21 iter trig: 2:26.172 vs. 21 iter quadplex: 1:21.109 = 180.2% difference!!!!
NOTE: Complex derivatives are fricken simple... and all these should pass
Cauchy Riemann conditions. Derivative of z^n? n*z^(n-1)
I'll start a thread for the pseudo-julias, later tonight or tomorrow. Pretty busy as my brother is arriving in town tonight... but the discovery was very simple (and probably already exists somewhere else, as this thread shows, someone's probably already done it elsewhere in the forums before now).
I just take the starting x, y, and z values, subtract the new values and add in whatever julia seed value I was using. To extend this to 5d, do the same thing with your starting x,y, z, k, and l values, subtract the new values and add in your julia seed. Simply phenomenal.... Check the variety on this 11 iteration 2048x2048 image (done with x,y, and z values sandwiched between the k and l values, you can vary the placement of the 5 dimensions for different images):
http://lh6.ggpht.com/_gbC_B2NkUEo/TIc-2TiNOvI/AAAAAAAAAp8/lwUI1FxYTnw/11%20iter%202048x2048.jpg