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?

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/

Ooh, very interesting - thanks!

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?"

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

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!

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

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

This could lead to some serious procrastination.

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

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

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

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

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

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

Loved that video, though.

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.

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.

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.

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

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.

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

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

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...

Thank you for sharing this. Absolutely wonderful.

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