mountain ranges and coastlines all have in common?

They all contain never ending patterns known as fractals.

A classic example of a fractal in nature is broccoli -

in that the whole stalk is a similar version of one of its branches.

So cut off one piece

and you're left with a smaller version of the entire broccoli.

Snowflakes are another example.

It's often said that no two snowflakes are ever the same

and fractals offer a fascinating explanation

as to why nature works in this way -

why nature continuously creates new, self-replicating

yet unique structures and how the smallest things in existence

are necessary components of the greater whole.

The term fractal was coined by Benoit Mandelbrot

who was working at computer giant IBM in 1980.

Mandlebrot had been fascinated by discoveries of mathematicians

from the early 19th Century

who were attempting to define their understanding of what a curve is.

Experiments such as Georg Cantor's discovery

that a single line could be divided forever

and Helge von Koch's triangle -

a shape that has an infinite perimeter but a finite area -

resulted in the term 'monsters'.

Mandelbrot used the modern computing powers developed by IBM

to run these monster equations millions of times over.

This process led him to a breakthrough equation

combining the patterns found in previous monsters

resulting in his own set of numbers.

This would become known as the Mandelbrot set -

an infinite geometrical visualisation of a fractal.

One of the most amazing things about the Mandelbrot set

is that theoretically, if left by itself,

would continue to create infinitely new patterns

from the original structure

proving that something could be magnified forever.

Fractal geometry is currently applied in many fields.

For example, research into climate change

and the trajectory of dangerous meteorites,

helping with cancer research

by helping to identify the growth of mutated cells.

It's even believed by some that the universe itself may be a fractal

and as you zoomed in

you would discover it's made up of billions of galaxies.

Inside of those galaxies, you would find trillions of stars

and billions of solar systems and planets.

And on one of those planets you would find Earth.

On Earth you would find continents, cities and a human.

And inside of that human you would find a brain

made of millions of cells

in which you would find trillions of synapses firing away.

And inside of those you would find DNA

Inside DNA you would find atoms, electrons, protons, neutrons.

Deeper still you would find quarks, neutrinos and so on

and then, just maybe, continuously deeper into infinity.

Some believe that, due to their highly complex and mysterious nature,

the greatest use of fractals is yet to be discovered.

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