What are fractals?

Have a look at these pictures:
L to R, row 1: living human brain, neurons in brain, dark matter distribution in universe, city from space — row 2: river, galaxy, cyclone, mandelbrot-set — row 3: human heart, eye, sunflower, romanesco — row 4: moon, fern, lightning, snowflake
All of these objects show typical fractal patterns:
  • The branching of rivers, veins and neurons
  • The spirals of galaxies and cyclones
  • The self-similarity in romanesco broccoli and moon craters

You are looking at living mathematics. One could say that fractals are the opposite to the euclidean mathematics you learned at school, with its straight lines, perfect spheres, curves, squares and exact shapes.

Fractals are the mathematics of nature

the geometry of the cosmos.

The fascinating thing is, that although they look very complicated and incomputable – all those infinite details and variations are based on the most simple formulas.
Like this one:   z→z²+c  (known as the Mandelbrot-Set) The one BIG difference is the → instead of  =
It means you’re not calculating the formula just once, but take the result and feed it back into the formula, calculate again and feed the result back in, calulate again and feed it back in, calulate again and feed it back in…

The result of the recursive calculation of this simple formula is pictures like this:

Infinite detail & organic forms - from nothing but z->z²+c
Infinite detail & organic shapes – from nothing but z->z²+c

If you haven’t already, watch our short introduction on fractals here:https://www.youtube.com/watch?v=tN_eNQFcv5E

Why is it that nature is full of fractal patterns?

Research shows that fractals are the most efficient way of storing and using information in nature. All you need to generate infinite complexity is a very simple rule and repeat it over and over again.

Why should we care for fractals?

Understanding fractals helps us to know many things we couldn’t know otherwise.
We don’t actually need to understand every thing in order to understand everything.
A beautiful example for this is how knowing the fractal structure of just one single tree in a forest helps us to calculate the CO2 intake of the whole forest.

Where to go next?

Fractal guided tour showing you more fascinating facts about fractals ->

Latest news about fractals used in cutting-edge technology or new discovies in nature ->

Participate in research and help us advance – discover uncharted territory ->

Tutorials and programs to generate fractal images and videos ->

Fractal encyclopedia ->

Who we are ->