From our perspective, Fractals are beatiful incommensurable structures where Maths, Art and Nature converge.
Here are some interesting quotes about fractals.
“Why is geometry often described as ‘cold’ and ‘dry?’ One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”
(Benoît B. Mandelbrot, The Fractal Geometry of Nature)
“Beyond their amazing aesthetics and their hypnotic repetition effect, fractals are especially interesting because they seem to show that you can have an infinite number of levels, or scales, or iterations, within a limited structure. In other words: anything which is finite and fractal may contain the infinite within itself.”
“Fractals are exquisite structures produced by nature, hiding in plain sight all around us. They are tricky to define precisely, though most are linked by a set of four common fractal features: infinite intricacy, zoom symmetry, complexity from simplicity and fractional dimensions.”
If you are so amazed about the beauty of fractals as we are, and want to dig into fractal art and 3D fractals for VFX, this is for you.
What Are 3D Fractals?
In 2009, Daniel White and Paul Nylander found a way to project the Mandelbrot set and similar equations into 3D space. The Mandelbulb is a three dimensional manifestation of the Mandelbrot set. It is an infinitely complex, naturally occurring fractal object.
Beyond these shape exist a wild variety of endlessly detailed 3D fractals. They are formed using different projections of the Mandelbrot set, projections of other equations, folding and symmetry-making transformations, and hybridizations that mix the Mandelbrot set with other equations. As fractal-generating/imaging software evolves, the range of 3D fractal objects is growing.
Mandelbulb (rendered in Arnold for Maya)
3D fractals are a range of chaotic equation-based objects – most often derived from, or related to, the Mandelbrot set. These are also called “Mandelmorphs.” The term “Mandelmorphic art” is used to describe art made with with these kinds of forms. Most Mandelmorphic art is image and video based – but the Mandelbulb was even 3D printed shortly after its discovery.
The following images were taken from Mandelbulb.com and are property of their respective authors (Hal Tenny, John Vega, Jorge Abalo and Matthew Haggett). They were created with Mandelbulb 3D software (MB3D)
“Hypertube” by Hal Tenny
“Cognitive Dissonance” by John Vega
unnamed by Jorge Abalo
unnamed by Matthew Haggett
“With its expansive resolution, lighting and shadow, various textural qualities, and color depth, the complex beauty of the Mandelbulb becomes a thing to behold.”
“…a string of increasingly mesmerizing and poetic takes on the natural world. Caves, planets, and even a fractal universe…”
(The Creators Project)
Fractals in movies: VFX & fantasy landscapes
Inspired by the astonishing VFX of movies like Tron Legacy (2010), Inception (2010) or Limitless (2011), film directors have been increasingly using CGI fractals for creating mesmerizing fantasy landscapes, futuristic architecture and alien cities, spatiotemporal travels through fractal nebulas, and amazing visual effects in general.
For the making of Lucy (2014), Doctor Strange (2016), Suicide Squad (2016) and Guardians of the Galaxy Vol. 2 (2017), VFX studios have directly incorporated a custom CG fractal creation tool to their VFX pipeline, and directors had to deal with the unattainable nature of fractals.
The following are 3 nice articles about the use of 3D fractals for VFX in recent films.
- Examples of Graphics, Animation and Fractals in Film
- Suicide Squad, vortical flows and fractal machines
- The fractal nature of Guardians of the Galaxy Vol. 2
Mandelbulb 3D Tutorials, by Don Whitaker
How to Render a Mandelbulb – Arnold for Maya Tutorial