Fractals can be found everywhere in our universe and are used to generate the procedural game No Man's Sky.
To find out more about fractals or participate in research visit [ Ссылка ]

This film was created by a small team of independent fractal researchers trying to establish fractalogy as a distinct field of study.

Producer: Bernard Geiger
Editing & VFX: Christoph Kramer [ Ссылка ]
3d-fractals: [ Ссылка ]
Music& SFX: [ Ссылка ]
Narrator: Michael Baer

Transcript:
Could mere mathematics create an entire universe?
What does broccoli have in common with the Big Bang?
And what does it have to do with a video game like No Man's Sky or Minecraft?

One thing: All are based on simple formulas that create infinite complexity.

The more you repeat this calculation, the more complex details are being revealed. Ultimately, you could repeat this infinitely – the only limitation being the processing power of your computer.

The patterns one can find here look strangely familiar and widespread.
Mandelbrot gave them the name "fractals".
Fractal patterns seem so familiar because these shapes are omnipresent in nature.

The most important characteristic of fractals is their so-called self-similarity.
Look at a fern leaf – it is made out of smaller and smaller copies of itself.
The same is true for romanesco broccoli.
The branching patterns of trees follow this principle as well as courses of rivers. Lightning spreads into smaller and smaller branches, each sharing the same features as the main bolt.
But also man-made structures organize themselves into fractal patterns – without us actually planning them this way.
Here is a map of all the roads leading to Rome.
And a map of the internet.

It's especially fascinating that even your own body shows many fractal characteristics.
Thanks to it's fractal structure, your lungs have a surface area of over 100 square meters, enabling them to efficiently absorb oxygene.
This oxygene is then transported through your fractal bloodstream into your brain - in which the neurons are interconnected fractally.

Every thought you think – even right now at this very moment – is a cascade of electric impulses, travelling through the fractal network in your brain.

This is a simulation of dark matter in our universe – the visible section is 10 million light years across.
Even on these scales you can find the same fractal branching patterns as in the neurons of your brain, in rivers or in lightning.

All this complexity is based on simple feedback processes and on formulas like the Mandelbrot-Set.
With today's computers we can take these fractal formulas and add a third dimension. With simple maths beautiful 3D-worlds can be created.

As it turns out, the easiest way to simulate a world as realistic as possible is to use fractal formulas.
The first completely computer - generated movie scene in a feature film was the fractal animation of a planet in Star Trek 2: The Wrath of Khan.

The Lucasfilm group responsible for this was later acquired by Steve Jobs. From this he created Pixar - thus revolutionizing Hollywood.
Their animated movies look so realistic because the generated landscapes are based on the fractal principle of self-similarity.

Progress has continued and today these elaborate and costly movie scenes have evolved into realtime"walkable gameworlds" like the landscapes of Minecraft.
Their origin has not changed: Mathematical formulas that just need to be fed with variables.

The most impressive simulation of an entire universe has now been created by a small team of 15 indie developers: The game "No Man's Sky" is probably the most complex and the largest gameworld ever created – and it fits on a single DVD.

Every player starts exploring on a randomly chosen planet in the games‘ universe. The players starting coordinates are the variable that is put into the games‘ sophisticated but still simple formulas.
The result creates the whole visible gameworld in realtime.
It would be impossible to store all of the details using traditional methods. You would need entire datacenters to store the data of the roughly 18 quintillion true-to-scale planets, together with their unique ecosystems.

It doesn't matter if it is a whole planet, a space ship, a tree, a rock or a single blade of grass – every detail is the fractal result of a mathematical formula.

So: One of the most realistic and complex simulations of our cosmos emerges from nothing but mere mathematics !

And no matter where you look around in nature and our man-made reality – you encounter fractal patterns all over!

Don't you think it is time to consider the possibility that fractals are a fundamental element of our cosmos?

свернуть