How Recursion in Nature Shaped the Modern World

issue six : the shape of things to come

An exploration into natures recurring patterns and how it connects everything


Think not of what you see, but what it took to produce what you see
— Benoit Mandelbrot

By design, nature is flawless. While at first glance it may appear haphazard and erratic, when you begin playing with perspective, that is when you start to realise just how truly ordered nature is.

You may have heard about fractals as an abstract mathematical term. One of the many theories we learnt about at school but quickly discarded as irrelevant to 'real life'. I know I did. It wasn't until I started becoming aware of the connections in life and ideas that I began to understand their invaluable offering. If even only as a way to make sense of how I see the world.

I was reintroduced to fractals by my dad (who has an extraordinary ability to explain scientific notions in a way that I understand. By making it visual) and have become somewhat obsessed with seeking them out. They are everywhere in nature.


Everything is connected

The study of fractal geometry has led to a greater understanding of things that for centuries, remained a mystery. When Benoit Mandelbrot had the original idea to look at mathematics as an art form instead of the go-too analytical offering that mathematicians had used for millennia, he opened up a whole new world for all of us. From unique fashions, modern animation techniques, the detection of difficult to diagnose cancers to being able to measure how much carbon dioxide a rain forest could absorb by looking at a single tree. 

While Mandelbrot by no means observed the reoccurring patterns in nature first, he certainly did connect the dots and allowed an entire fraternity to start looking at things from a fresh perspective. That's called vuja de.

 Mandlebrot Set

Mandlebrot Set

Fractal Geometry

In the most simplistic explanation I can muster up, a fractal is merely a self repeating pattern that, in theory, could continue on for infinity.

This artwork by Rafael Ruggiero, shows a Sierpinski triangle transforming into a tree - and perfectly demonstrates the concept of how a recurring pattern can appear as a work of art, and in nature, in countless variations.

 Creative Commons:  By Rafael Ruggiero  - Own work

Creative Commons: By Rafael Ruggiero - Own work

Examples in nature

Who hasn't noticed the different and varied vein patterns of leaves? Have you ever truly studied them? This cabbage leaf is a glorious example of fractals in nature. At first glance, we see the main vein systems. As we move in closer, we can start to see smaller veins, but it's not until we zoom in even closer that you can really begin to notice that it is not simply a random pattern, but rather a replication of the main vein pattern, which simply continues to repeat itself.

Take a look at any leaf and you will see that the veins always mimic each other, and generally take the shape of the leaf itself. This pattern will continue throughout the plant. Roots, leaves and flowers.

 By Jon Sullivan [Public domain], via Wikimedia Commons

By Jon Sullivan [Public domain], via Wikimedia Commons

 Sea Snail and Bubbles, both demonstrate fractals

Sea Snail and Bubbles, both demonstrate fractals

Another glorious example is this Romanesco broccoli. At first glance, a strange sci-fi looking vegetable, but upon closer inspection, simply fractals in action.

Snow flakes are made up of fractals. While we all know that each snow flake is unique, they are only unique next to another snowflake, but not in and of itself.

 Nature's Fractals Series 1.b by Sya

Nature's Fractals Series 1.b by Sya

 Satellite view of fractals at work in Egypt, by Paul Bourke

Satellite view of fractals at work in Egypt, by Paul Bourke

I am excited to see how the further application of creative geometry such as fractals and chaos theory, could have on the shape of our future.

If you fancy geeking out on the wonders of fractals and have an hour to spare, I highly recommend this PBS Nova documentary.