When I was around six years old, my parents bought me a fractal kaleidoscope. It was my favourite toy that travelled with me everywhere. It stimulated my curiosity and helped me grow. I was looking at fractals and was getting sucked into it. It helped me recognise and develop my love for colours.
That was a long time ago, and here I am writing about fractals!
Without getting too mathematical, I will explore some interesting facts about fractals and their relationship with you.
Do you remember looking at the frosted glass as a kid and getting deeper and deeper into an exploration of snowflakes? A snowflake inside a snowflake, and there’s another one inside that.
Or maybe you remember laying on the grass under a large oak tree on a sunny Sunday afternoon. You are gazing at the branches of the tree and the blue sky in between… And when you zoom in on a branch of a tree, you find there’s another tree with mini braches and another…
Or were you being fascinated with the globe of the world that your parents got you for Christmas? You follow an outline of a continent with your small index finger, seeing it curve and form a beautiful shape.
Or being fascinated with the clouds, broccoli, flowers, blood vessels, seashells, lightning, stalagmite and stalactites?
Fractals are everywhere; they are just a part of nature.
Is the name Benoit Mandelbrot sounds familiar to you?
He was born in 1924 into a family of Lithuanian Jews, for which I am very proud as I am Lithuanian myself. Some sources say he was Polish-born, but that’s not true.
His mother Lurie was a doctor, and Karl, his father, was a haberdasher (a dealer in men’s clothing). In 1936, the whole family moved permanently to France. In Paris, Benoit fell under the influence of his uncle, who was the founder of the local club of mathematicians. Benoit exhibited outstanding mathematical abilities and had a wonderful spatial imagination at an early age.
After graduating from university in France, Benoit moved to America, where he graduated from the University of Technology in California. After returning to Paris in 1952, he received his doctorate. In 1955, Benoit married and moved to Geneva.
In 1975, Mandelbrot published a work entitled “The Length of the Coast of Great Britain” it was the first full-fledged study of fractal theory.
He defined and simplified fractal as follows: “A fractal is a shape made of parts similar to the whole in some way.” He showed how fractals could occur in many different places in both mathematics and nature.
The Romans were henchmen of order, and the Greeks, believed in formless formations that lived according to their order, having specific patterns. It is these patterns that Mandelbrot managed to find and began to look a little differently at everything that surrounds us in everyday life.
Later, fractal patterns with various degrees of self-similarity have been rendered or studied in visual, physical, and aural media and found not only in nature but also in architecture and technology.
One way of defining the Mandelbrot set is by looking at how complex functions behave under repeated iteration.
The functions in question have the form f(z)=z2+c, where c is a complex number. For each c, we seed the function by plugging in 0 as the initial value for z. Then we take whatever we get out and plug it back into the function. As we iterate (repeat) the function, one of two things can happen: either the iterates get larger and larger, moving further and further away from 0, or they stay close, possibly bouncing around the area wildly but never getting very far from 0.
If you are mathetically minded, here’s an excelent video that explains this in detail, enjoy!
Benoit died 11 years ago, on October 14, 2010 at the age of 85. He experienced serious problems with the pancreas, which probably caused his death.
He is an oustanding man who found the courage to look around and understand that fractal structures are everywhere. In fact, fractals are closely related to the so-called butterfly effect. When even the slightest events can have a considerable resonance, even the shift of a tiny grain of sand can provoke a mountain collapse. If we think about it, then from two tiny grains of sand, the effect will be the same. That is, the nonlinearity of events appears.
Stop and think about this for a minute…
The world is in chaos at the moment, fear is being instilled into our psyche and thousands of people are dying still. People are being lied to and our dignity and freedom is under attack. In times like these it can be challenging to stay positive and hope for a better future.
Whenever you feel afraid or doubt yourself, pause and remember that every time you are feeling fearful, you are spreading the frequency of fear around you and affecting others. The opposite is true; staying positive, no matter what goes on around you, working on your mind, body and soul, staying calm, has the butterfly effect and spreads faster than the frequency of fear.
Fractals are everywhere in nature and closely related to the butterfly effect.
Our lungs, our circulatory system and our brains are like trees.
We are made of energy and information.
We can take inspiration from Benoit Mandelbrot and find the courage to look around and notice fractal structures and stay true to ourselves, contributing to the positive butterfly effect in the world. A good way to start is learning how to expand your consciousness. Here’s an article I wrote about dimensions of consciousness and of the physical world that will put you on the right track.
Stay true to yourself, be healthy and stay safe.