z -> z^n + c

[Ichingcarpenter]

And the addition term in z -> z^n + c is similar to standard complex addition, and is simply defined by:

{x,y,z}+{a,b,c} = {x+a, y+b, z+c}


Which can give you this.




Geeky Math Equation Creates Beautiful 3-D World
The quest by a group of math geeks to create a three-dimensional analogue for the mesmerizing Mandelbrot fractal has ended in success.

They call it the Mandelbulb. The 3-D renderings were generated by applying an iterative algorithm to a sphere. The same calculation is applied over and over to the sphere’s points in three dimensions. In spirit, that’s similar to how the original 2-D Mandelbrot set generates its infinite and self-repeating complexity.

If you were ever mesmerized by the Mandelbrot screen saver, the following images are worth a look. Each photo is a zoom on one of these Mandelbulbs.


More photos and links here
http://www.wired.com/wiredscience/2009/12/mandelbulb-gallery/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+wired%2Findex+%28Wired%3A+Index+3+%28Top+Stories+2%29%29

[Adsos Letter]

1. Unbelievable! Thanks for posting this.

[ClayZ]

2. Wow!

K and R

[annabanana]

3. Amazing.. Some of the pics remind me of an Aran Isle Sweater. .

cable-knit

Now we have to get someone to put some of these equation images in motion. . .

[Occulus]

4. You mean.... like THIS?

http://www.youtube.com/watch?v=LxsniUIVfEM

Or perhaps, even better, THIS?

http://www.youtube.com/watch?v=In3d329JFTU&feature=related

:D

[annabanana]

7. Oh YES.. That second one... and a couple called Gigabrocolli

work in Progress I and II.

http://www.youtube.com/watch?v=PFr-cEEb8y0&feature=related

and

http://www.youtube.com/watch?v=xF4mTGyskr0&feature=related

What fun!

[glitch]

5. This is the type of thing I browsed the web for before the coup of 2000

Thanks for the reminder!

[inna]

6. Wow, thanks for this!

:wow:

[muriel_volestrangler]

8. Amaxing how some look 'organic', while some look like decorative sculpture

Take a look at the one on the left here (very pic-heavy page):

http://www.skytopia.com/project/fractal/2mandelbulb.html#variations

It lloks like a 19th century ceiling ornament to me.

[Commie Pinko Dirtbag]

9. Fuck, this is nightmarish. Awesome.