
Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal - hassy
http://www.skytopia.com/project/fractal/mandelbulb.html
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anigbrowl
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?

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davi
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/>

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anigbrowl
Ooh, very interesting - thanks!

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benhoyt
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?"

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

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jacquesm
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!

~~~
davi
page 2: <http://www.skytopia.com/project/fractal/2mandelbulb.html>

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

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wglb
This could lead to some _serious_ procrastination.

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

~~~
sp332
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>

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algorias
Could that same logic of using shaders also apply to flames?

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sp332
I suppose so, yes. It's been possible to do a "reasonable" flame effect since
the nvidia 5900 at least [0], and there's been a lot of work on fluid dynamics
(including fire [1]) since then.

[0] <http://http.developer.nvidia.com/GPUGems/gpugems_ch06.html>

[1] <http://www.youtube.com/watch?v=ZgoDypGMV50>

~~~
algorias
Oops, should have been more explicit. I meant fractal flames:

<http://en.wikipedia.org/wiki/Fractal_Flames>

Loved that video, though.

~~~
sp332
Oh yeah, I actually wondered about that after I posted :) I was on the fence
about this, but all the examples I can find use CUDA, so I guess CUDA is the
way to go: <http://www.google.com/search?q=flame+fractal+on+GPU> That makes
sense, because it's more about huge matrices (flames are just big histograms)
and less about textures on polygons.

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algorias
Yes, there are CUDA implementations such as flam4, but I'm always interested
in new possible approaches to the problem, since I'm writing a flame editor
and CUDA doesn't play all that nicely with it.

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

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chasingsparks
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.

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flatline
I don't see why this should daunt your 2D efforts - it still sounds like
something fun to play around with;)

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wwalker3
Indeed -- the whole point of projects like that is they make you a better
programmer. The program itself is just a nice side effect.

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bjelkeman-again
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...](http://www.newscientist.com/article/mg20427335.600-tomorrows-
weather-cloudy-with-a-chance-of-fractals.html)

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rbanffy
Thank you for sharing this. Absolutely wonderful.

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b-man
The little beast looks like a virus. Hmmmm...

