Extreme Mandelbox Morphing

Discover the wonders of the Mandelbox.
Soundtrack "Morituri te salutant" courtesy of zzzzra.

Explore a digital space, a space that has got different dimensions. Navigate in a universe made of numbers, formulae, and iterative calculations. This is our own universe. Thanks to fractals you can visualize the naked beauty of nature.

This video is a panorama of the Mandelbox parameter space. The Mandelbox is a 3 dimensional fractal object discovered in 2010 by Tom Lowe and named after the father of fractal geometry Benoit Mandebrot.

What we see here is actually a fixed cut in the middle of the Mandelbox, which has a cubic shape in general. We don’t travel in our usual 3D space, instead we explore another 3D space, where each dimension corresponds to one of the 3 parameters found in the Mandelbox formula.

All the morphing going on is due to the variations of these 3 parameters - see links below for a detailed explanation of the Mandelbox formula -. They are the 3 axis of the space through which we draw our trajectory, made of segments that join many interesting triplets, especially those that include round numbers, among an infinite set of combinations.

I have made my best efforts to walk you through a collection of the most interesting points and at the same time show you a wide variety of shapes and dynamics that can be found when playing with "the box".

I originally created this video because I had already realized a series of 25 unique prints based on variations on the same theme, and I wanted to take advantage of this work and materialize the journey through these 25 images.

Actually, the original request for images came from a professor in mathematics who needed mathematical illustrations for an article about 3D fractals in a scientific magazine - planned release date: April 2015. He was finding one of my 3D images particularly interesting - “The Treasure”, see link below - and at the same time wanted to give some mathematical content to his article, not to talk just about nice images. As “The Treasure” was actually a Mandelbox with a particularly simple set of parameters - yet not widely explored by the fractal community where the Mandelbox is a well know source of inspiration, I came up with the idea of this series: a systematic exploration of the box in an attempt to map its unchartered territories and expose some of its more noticeable features. I carefully traced scenic highways for the occasion to share the places I found the most aesthetically appealing in this  strange multi-dimensional world.

To make the video more enjoyable and to match the length of the tune from my friend Zzzzra - thanks! -, I extended the number of key frames from 25 to more than 80, further exploring into the parameter space, or focusing on areas exhibiting richer structures and more variety that deserved to be shown.

I generally produce animations in 3D, but the complexity of the inner structures of the Mandelbox required a specific treatment: back to 2D! In 3D the effects and the patterns are equally interesting and deserve their own way of exploration, in my opinion more by navigating in the usual 3D space and with relatively small variations of parameters in order not to dramatically blow up the landscape with extreme morphing. On the contrary, 2D lends itself much better to radical transformations. These strong variations and their intense dynamics are also a reason why I kept the whole animation in black and white, in order to maintain a level of purity – to be linked to the round values used in many key frames, my favorites – and to avoid data overload in the brain!

Thanks for watching!

Links
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The Mandelbox explained by Tom Lowe - sites.google.com/site/mandelbo…
“The treasure”, the image at the origin of this video – bib993.deviantart.com/art/The-…
My other 3D fractal videos – www.youtube.com/user/bib993
This video was made with Mandelbulb3D - www.fractalforums.com/index.ph…
3D printed fractal objects, sculptures and jewels – www.shapeways.com/shops/3Dfrac…
Livre d’art fractal - www.amazon.fr/Lart-fractal-Aux…