Fractal Geometry and Insomnia: A Heavenly Combination

The famous Mandelbrot Set

by Madeleine Kando

Falling asleep is an elaborate process for an insomniac. Your mind starts fighting with your body, like a boxing match. I have tried many things in the past: deep breathing, soothing music, dark curtains, white noise. None of it worked. But recently I have developed a routine, which shows some promise of success.

The very first thing I do, is barricade my bedroom door with a row of cotton balls dabbed with citrus, a smell that my cat hates. That way, she won’t scratch at my door the minute I close it. It’s not like she has a need for space, since the whole house has become cat territory, but she won’t even allow me to time-share my own bedroom at night.

Once I am barricaded, I make sure my head rests comfortably on my favorite pillow, the one with the flower cover. But the piece de resistance in my quest for sleep, is the psychedelic Youtube movies that I have been watching: psychedelic tunnels, mandala movies, and moved on to ‘electric sheep’,


which is a genre of computer animation that is very beautiful and totally psychedelic and finally ended up with the cream of the crop, called ‘fractals’. I was hooked. It became my nightly drug of choice.

The most fascinating part of my journey was finding out how fractals were discovered. I am not qualified to explain to you what fractals exactly are, but they are all around us in the world we live in. Mountains, flowers, rivers, they are all fractal shapes. It has to do with ‘self-similarity’ and ‘iteration’.

Fractals in Nature

Fractals are the simplest way for nature to make something grow: create a copy of what’s already there and go on from there. A tree is the perfect example of a fractal. The trunk splits into 2 or 3 branches and each branch splits into other smaller branches and so on, until the smallest branch splits again to grow leaves. Even our lungs have a fractal shape, as do the coastlines of landmasses.

The genius that made this invisible aspect of our world visible is Benoit Mandelbrot a Polish-born, French/American mathematician. In 1982 he published The Fractal Geometry of Nature, in which he shows that the complexity of shapes in nature only seems chaotic and ‘rough’. Even though nature is not made up of squares, lines and circle, if you zoom in long enough, you find an incredibly ordered system to which mathematics can be applied. This is called Fratal Geometry.

What that’s got to do with my struggle falling asleep? If anything, all this intellectual mumbo jumbo should keep one wide-awake, right? But if you key in ‘Mandelbulb 3D’ on YouTube, you find a treasure chest of mind-blowingly beautiful short movies, all created with code.

This world of computer animation based on fractal geometry is so prolific; you could feast on the genius of these digital artists until your hair turns grey. It’s all based on open source code; so one person feeds on another’s creation. Here is one example of what you find:



So you see, having trouble falling asleep has allowed me to discover an entire new world I didn't know existed. I pity the folks who fall asleep the minute they lie down. There is so much out there, that only us insomniacs are privy to.  leave comment here