Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal

http://www.skytopia.com/project/fractal/mandelbulb.html

by hassy • 17 years ago

200 23 17 years ago

skytopia.com

jacquesm2• 17 years ago

Thank you hassy, that really made my day!

Wonderful how mathematics can turn up such incredibly complex stuff from such simple numbers.

be sure you don't miss page 2!

davi2• 17 years ago

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

good link from page 2: http://www.bugman123.com/Hypercomplex/index.html

wglb• 17 years ago

This could lead to some serious procrastination.

jacquesm2• 17 years ago

Let me help you there, how about some CUDA implementation of a real time viewer :) ?

sp3323• 17 years ago

I've been working (slowly) on a real-time viewer for a 2D and maybe eventually 3D Lyapunov fractal[0] viewer, and I think implementing the algorithms as a shader program is more practical than using CUDA. After all, CUDA is meant to get around the limitations of using graphics hardware for non-graphics applications, which isn't necessary when you are doing a graphics application.

[0] http://en.wikipedia.org/wiki/Lyapunov_fractal

rbanffy• 17 years ago

Thank you for sharing this. Absolutely wonderful.

chasingsparks2• 17 years ago

I've slowly been building a Javascript 2D canvas library that renders lots of well known fractals. This just demolished my motivation: 3D is just too damn sexy.

WilliamLP• 17 years ago

Good luck with that JS canvas raytracer that handles surface gradients from iterating arbitrary functions.

chasingsparks2• 17 years ago

The JS library was 2D only. I have no intention of writing a ray-tracer in JS. This project erased the motivations on my original project; it didn't persuade me to play with 3D. I'll leave that to someone whose itch needs more scratching than mine.

bjelkeman-again• 17 years ago

New Scientist has this recent article on how weather patterns may actually best be modelled with 3D fractals. And when you look at some of the pictures on Skytopia you can see where that comes from, some of the really look like cumulonimbus clouds.

http://www.newscientist.com/article/mg20427335.600-tomorrows...

anigbrowl2• 17 years ago

Awesome! I knew something like this had to exist, but never acquired the math skills or the time to dig seriously for it, though I did have a lot of fun render quaternions along the way. I wonder if the techniques used for this could help us in reverse-engineering of DNA (stay with me here...).

Some years ago I came across the Romanesco Broccoli, sometimes referred to as a broccoflower - the first time I saw I got badly startled, thinking I was experiencing some sort of LSD flashback. But it's real, quite edible (and tasty), and Mrs Browl has since grown several of them in the garden. Check it out here: http://en.wikipedia.org/wiki/Romanesco_broccoli and http://www.fourmilab.ch/images/Romanesco/

There are many other instances of logarithmic spirals in nature, but few so striking as this one, given its compound structure. Irritatingly, I've had little luck finding any serious analysis of this structure - it turns up on quite a few pages, but mostly with a comment of 'yup, that's fractal all right' or mention of it as a teaching aid for introducing mathematical concepts. The only papers mentioning its genome seem concerned with agricultural considerations like yield and disease resistance. I can't understand why it's not the subject of feverish interdisciplinary study, since it practically screams 'analyze me'. Any thoughts from mathematically-inclined HNers?

davi2• 17 years ago

I think the usual idea is that during development, cell division patterns in the plant apical meristem [1] implement some Lindenmayer system [2]. I don't know if anyone has looked into genetic & molecular mechanisms whereby cell division could be regulated so as to implement an L-system in this way.

[1] http://en.wikipedia.org/wiki/Meristem

[2] http://en.wikipedia.org/wiki/L-system

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edit: lots of stuff here: http://algorithmicbotany.org/papers/

anigbrowl2• 17 years ago

Ooh, very interesting - thanks!

benhoyt• 17 years ago

I showed my two-year old daughter the Mandelbrot set, then this pic: http://en.wikipedia.org/wiki/File:Mandelbrot_zoom.gif

She said, "Is that all Mandelbrot's friends?"

modeless• 17 years ago

Here's the 7500x7500 image of it in Seadragon: http://seadragon.com/view/fnr

b-man• 17 years ago

The little beast looks like a virus. Hmmmm...

Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal

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