SGU Science Picture of the Week: Mandelbulb
What you’re seeing is not an ornate structure built by an advanced alien civilization. It’s not even a sub-microscopic image of some bug’s private parts. It’s a MandelBulb.
A mandelbulb is a three-dimensional representation of the classic Mandelbrot set, which is the most famous fractal of all time. The hallmark of any fractal is that it’s self-similar. As you zoom in, the smaller pieces resemble the whole. These shapes are found throughout nature from trees and coastlines to clouds and the branching of capillaries. The most interesting mathematical fractals are quite extraordinary in that no matter how deep you zoom in, weird and wonderful structures reveal themselves, all based on that initial shape. It’s like looking closely at a twig on a branch on a tree, only to find sub-twigs which are also composed of sub-sub twigs (twiggies?) and so on for countless iterations and variations.
As beautiful as the Mandelbrot is, it’s only two dimensional. There’s no depth, no light-source to create interesting shadows. Turning a 2d mandelbrot set into a 3d mandelbulb is not easy though; in fact it hasn’t entirely been accomplished and may never be. This is because a mandelbrot is constructed from complex numbers. There is no way mathematically to transform these complex numbers directly into a 3d analogue. This has not stopped people from trying however to find this holy grail of fractals. Perhaps the essence of the shape of a mandelbrot doesn’t rely on a field of complex numbers.
Any disappointment I felt because the mandelbulb is not a true 3d mandelbrot was quickly dispelled though because the images and zooms are so arresting and detailed and beautiful. Tell me if you agree.
Special thanks to the following people:
Rudy Rucker who began the journey to find what he called the Mandelbulb
Daniel White who later and independently conceived the same idea, came up with a formula, and created the images on this page.
Other Mandelbulb images
DO YOU SEE FACES IN HERE TOO?
Image Credit: Daniel White: http://www.skytopia.com/project/fractal/mandelbulb.html#renders
I’m sorry. This is too much like something so totally alien that it would not hesitate to digest a human being. Not at all my idea of ‘a thing of beauty’. I want to grab a flame thrower and hit it with a good healthy dose of BTU’s.
To see some 3D flybys of fractals checkout Magellan by Farbrausch. The whole thing is worth watching, but the fractal starts a 2:57.
https://www.youtube.com/watch?v=J-Gnr2gfFpU
“There is no way mathematically to transform these complex numbers directly into a 3d analogue.”
But there’s a 4D analogue with quaternions, and you can take 3D cross-sections of it.
https://www.youtube.com/watch?v=AyLvyrU9SMU
Hi Max.
I came across this Quaternion approach in my research.
Regarding this, David White (who I link to in my post) had the following to say as he was discussing his method:
“It’s been almost two years since we last wrote about the potential for a real 3D equivalent to the famous 2D Mandelbrot set. We’re talking about a fractal which produces exquisite detail on all axes and zoom levels; one that doesn’t simply produce the ‘extruded’ look of the various height-mapped images, or the ‘whipped cream’ swirls of the Quaternion approach.”
It looks better in 4D. B-)
Hi,
I find that the connection between the M-Set and the Mandelbulb really becomes obvious when you “cut through” the 3d object.
http://chillheimer.deviantart.com/art/3d-Mandelbrot-Set-555199368
I don’t intend to spam, but thought you might find this picture interesting.
If not, feel free to delete this comment..
cheers,
chillheimer