The Unraveling of the Real 3D Mandelbulb (2009) | Hacker News Reader

The Unraveling of the Real 3D Mandelbulb (2009)

skytopia.com

27 pointscodewiz10 comments

While this is a neat 3D fractal I think the best use of a third dimension in the Mandelbrot set is to show how it corresponds to the logistic map.

https://commons.m.wikimedia.org/wiki/File:Logistic_Map_Bifur...

This is incredible, thanks for sharing. I found the linked veritasium vid also worth watching

https://www.youtube.com/watch?v=ovJcsL7vyrk

How have I gone so long without seeing this? I guess the fact that it's animated makes it hard to put into traditional textbooks (which I learned from because I'm old... okay, old-ish). But still!

There's a huge difference between 2D Mandelbrot renderings and 3D fractal renderings -- whether 3D slices of 4D Julia sets, or 3D Mandelbulbs.

Which is that the 2D Mandelbrot is mostly interesting in the shapes of swirls and whorls generated just outside of the set -- the rainbow spirals surrounding the black parts.

But all the 3D/4D fractal renderings I've ever seen focus on just the "black parts" turned into 3D surfaces.

What about 2D rainbow slices of the 3D/4D fractals? Does the Mandelbulb exhibit the same spirals etc.? Do 2D slices through the third dimension look qualitatively similar to the regular 2D version, or are the spirals different?

Its incredible to think the shape was only discovered in the last few years and not earlier in computing history (80s/90s or earlier). Just goes to show there is still much to be discovered.

This is what I come to hacker news for!

Heh, dunno, seems kinda obvious to me. I was fascinated by the Mandelbrot set, and had read the original description in scientific american. I wrote an implementation in turbo pascal for a CGA display. After my dad bought an EVGA I wrote the first (to my knowledge) EGA driver for turbo pascal based on the hardware description in PC tech Journal.

A few years later I was at U Pitt and rendered a Mandelbrot zoom at 300 dpi in postscript. The big lab printer that normally printed ASCII only (mostly homework assignments). A print kept the normally 100 page/minute printer busy for a minute or two. I begged the lab attendant to not reset the printer. Everyone in the room was amazed when it printed out. Printed a few dozen out for people to pin up on walls.

I wrote some hand assembly for the x87 (and managed to keep the calculations on the stack at 80bit precision). Later on I did similar in PA-risc assembly, even participated in one of the first distributed computing projects, to map the area of the Mandelbrot set. 2 mathematicians argued that the higher resolution maps would asymptotically approach some number and a higher precision area would settle that.

I was working at Pittsburgh Super Computing (PSC) in the 90s as a student. I was working under Joel Welling who was working on an implementation of the marching cubes algorithm. So I needed a 3D dataset to tinker with. I tinkered a bit with how to get different 3D slices (I forget what tweak I used for the Z axis). Submitted a job to calculate a 256^3 volume, used the marching cubes algorithm, and rendered it. The result looked pretty similar to the current mandelbulb, granted at a pretty low resolution.

More info:

https://en.wikipedia.org/wiki/Mandelbulb

And here's a pretty insane video of a power-2 Mandelbulb, that appears to end with a smooth increase in the number of powers:

https://www.youtube.com/watch?v=uAG6YmB8q_M

The movie "Annihilation" ends with a very neat and slightly scary Mandelbulb animation... Very dope Burial-esque bassy soundtrack too