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GLB3D Fractals and What You Can Do With Them
0Article by Yuri Ilyin
From alien stations through Lovecraftian horrors and all the way to the visualization of the Halls of Reason, 3D fractals enable vast possibilities, but it will take time to get a grip on them.
Explained With Mathematics
There is an absolutely arcane world - by all means - as awesome as it is hard to access. The band Marillion (bitterly) sang, "Wise man once said // that everything can be explained // with mathematics." Fractals, especially 3D fractals, seem like good evidence corroborating this statement.
Everything here - both visual and audio data - is squeezed into a tiny 4096-byte (!) executable file. The video became the winner of Assembly 2012's 4k demo competition.
Check YouTube for other 4k and/or 64k demoscene competition videos, and you'll find a large number of similar masterpieces. The majority of them utilize fractals to a certain - usually very high - degree.
Yes, it's about hardcore coding and mathematics, as every fractal is, essentially, a formula.
What Are Fractals?
A geometric shape that possesses self-similarity trait, also known as expanding symmetry or unfolding symmetry, is called fractal. A self-similar object as a whole looks more or less similar - but not necessarily identical - to any of its parts.
Many natural phenomena exhibit some form of self-similarity, which means that they can be modeled by fractals, or fractal surfaces.
The very term 'fractal' is relatively recent, for mathematics, at least: it was coined by venerable mathematician Benoit Mandelbrot by the mid-1970s, preceded by his 1967 paper on self-similarity ('How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension') in which he brought forward a notion of 'fractional dimension'.
Reference: Benoit Mandelbrot
It started with a 'coastline paradox', the counterintuitive observation that the coastline of a landmass does not have a well defined length: it has features at all scales, from hundreds of kilometers in size to tiny fractions of a millimeter and below. So there is no obvious size of the smallest feature that should be taken into consideration when measuring, and hence no single well-defined perimeter to the landmass.
In simpler terms it means that the shorter segments, or measurement sticks, used to represent (approximate) the whole coastline, the more fractured its approximation is, the larger values its measuring yields.
All in all, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern.
Mandelbrot's term 'fractal' has been derived from Latin 'fractus', i.e. 'broken'. Eventually Mandelbrot developed a new branch of mathematics called fractal geometry.
To comprehend fractals, a lot of reading and learning is required. Even the Wikipedia articles on the topic like this one, is written in a rather complex language; fractally complex in fact: the more in-depth knowledge is desired, the deeper it is necessary to go into numerous links and references.
Take a look at this video too:
It is an even earlier example: the winner of the 2009 Breakpoint 4k demoscene competition. As one can see, it's pretty much a flight over rather realistic landscapes - generated, again, with fractals..
Natural Looks
Landscape generation is one of the best-known practical uses of fractals, dating back as far as 1982 with Star Trek II: The Wrath of Khan, where the creation of alien landscapes was visualized using fractals.
In the early 2000s, a number of software suites emerged that used fractal formulae to visualize natural landscapes with varying levels of realism. Among them were Mojo World, Bryce 3D, and Terragen.
The latter has a decent, if limited, free version called Terragen Classic, which allows for creating photorealistic landscapes that could occasionally be mistaken for real photography. However, it had a somewhat shallow learning curve and often required a lot of tinkering to achieve the desired results.
Reference: Terragen Classic Render by mattiascibien
Terragen is still in active development and has been used in major Hollywood productions more than once. Naturally, its current version is much more complex than the one from the early 2000s.
Reference: Terragen 4 official gallery image by Ulco Glimmerveen
MojoWorld Generator had been originally created by none other than Ken Musgrave (whom Benoit himself called the first true fractal artists).
A distinct feature of this software, aside from the beauty of its visuals, was its ability to create an entire procedural planet, not just a specific area, and render views from a virtual camera positioned anywhere: from distant space or right at the surface.
Reference: A MojoWorld-rendered scene by MoodyBlue
MojoWorld was also used in Hollywood blockbusters - the best-known example being The Day After Tomorrow, where it was used for matte backgrounds.
The final release of the software dates back to 2005. Reportedly, there are communities that try to keep this last version alive, though they are not affiliated with the original developers.
Ken Musgrave passed away in 2018.
Bryce (Bryce3D) was another similar software, and Musgrave contributed to it as well. Over time, it evolved into a fully-fledged 3D modeling, rendering, and animation suite, still specializing in fractal landscapes, but no longer limited to them.
Daz3D acquired the software in 2004 and continued developing it until 2018, although the last stable release, version 7.1.0.109, dates back to 2010.
E-on Vue, yet another "world generator," was in active development until 2023. It was used in a number of feature-length films. Its final owner, Bentley Software, now offers it for free.
Formulaic Explorations
Much more complex and technical are 3D fractal explorers like the freeware Mandelbulber or Mandelbulb 3D.
The Mandelbulb itself is a three-dimensional fractal developed in 2009 by Daniel White and Paul Nylander. It uses spherical coordinates to produce a volumetric visualization of the classic 2D Mandelbrot Set.
Reference: Mandelbrot set by Wolfgang Beyer
Just like the Mandelbrot Set, the Mandelbulb has a very distinct look - a highly complex object that resembles a cross between a sphere, a rose, and a cauliflower or broccoli.
You can't mistake it for anything else.
Reference: Mandelbulber 2 with Mandelbulb object preview
Mandelbulb 3D and Mandelbulber 2 are both free software still in active development. Each allows users to generate a 3D fractal object and then move freely around and inside it. Sounds easy, right? Well, that doesn't mean it's easy to master. In fact, the best course of action is to study their lengthy manuals first.
Mandelbulb 3D has a more user-friendly interface than Mandelbulber and includes a wide array of ready-to-use formulas. However, compared to Mandelbulber 2, it has one major drawback: no support for GPU-assisted rendering as of yet.
Rendering on CPU, meanwhile, is relatively slow - the following image was rendered in over a minute on a Core i7 processor (an older model) using one of the preset formulas:
And if you look closely, you'll notice quite a few visible artifacts.
All in all, 3D fractals are a powerful and highly addictive tool for graphic design, especially for abstract and surreal visuals. Unsurprisingly, they're often used to depict alien or sci-fi themes like space stations, insectoid alien lairs, or Lovecraftian cosmic horrors. Even a basic effort can yield visually stunning results, but achieving precise outcomes requires deep exploration and practice.
Reference: A quick render using Mandelbulb 3D presets with minor tweaks
It's also possible to use fractals created in Mandelbulb 3D as a base for 3D environments: objects can be exported as point clouds and then converted into solid meshes. Unfortunately, more straightforward workflows haven't been implemented yet.
On the other hand, some 3D suites offer their own fractal capabilities - either natively or through third-party add-ons. Blender, for instance, enables extensive fractal experimentation using Geometry Nodes. Additionally, there's a paid add-on called Fractal Machine ($39), which combines the imposing aesthetics of fractal geometry with the material and lighting power of a traditional 3D suite.
Fractals are difficult to handle: they're hardboiled mathematics in visual form. But when used skillfully, they can produce incredibly rewarding results.
