Mandelbrot Set- the ultimate shape of math and nature

Can science be beautiful? The attached photo shows that it can. The picture shows so-called Mandelbrot fractals. The most interesting thing is that what you see is not a work of art created by an artist. It's a mathematical simulation.

What are fractals and the so-called Mandelbrot Set (the black shape on the picture above) ?

Imagine you have a magical drawing tool that can create amazing pictures on your computer screen. The Mandelbrot set is like a secret pattern hidden in the numbers of this magical tool.

The Mandelbrot Set is a special shape made up of lots and lots of little dots. These dots are like stars in the night sky. But instead of being random stars, they follow a special rule. This rule is like a game that the dots play.

Here's how the game works: Each dot on the screen represents a number. When we start, all the dots are colored black. Now, we do the trick: For each dot, we do some math with its number, and then we get a new number. We use this new number to move the dot.

If the new number is really close to zero, the dot stays black. But if the new number is far away from zero, the dot changes its color! It can be any color of the rainbow. And we repeat this game again and again for each dot.

As we keep playing the game, something magical happens! The dots start forming a beautiful shape on the screen- this is the black shape on the picture illustrating this text. And that shape is the Mandelbrot set!

The Mandelbrot set looks like a fancy, swirly, and spikey design. And the most amazing part is that no matter how close we look or how much we zoom in, we always see more and more details, like a never-ending adventure!

It's like exploring a hidden world full of patterns and surprises, all created by the magic of numbers. Mathematicians and artists love the Mandelbrot set because it's like a secret code that reveals the beauty of math and nature.

The Mandelbrot Set was discovered by mathematician Benoit B. Mandelbrot in 1980. Born as Benedykt Mandelbrot in my city of Warsaw in 1924 and later moved to France. He became fascinated by complex mathematical patterns and studied them throughout his career.

In the 1970s, Mandelbrot began exploring a specific mathematical formula involving complex numbers, which he called the "Mandelbrot iteration." Using early computers, he calculated and visualized the results of this iteration for different complex numbers. To his surprise, he found that certain points stayed close to the origin, while others moved far away. He marked the points that stayed near the origin as black and the others with various colors, creating a striking visual pattern.

In 1980, Mandelbrot published his findings and introduced the world to the Mandelbrot Set. This groundbreaking discovery revolutionized the study of fractals and chaos theory, revealing a previously unknown world of infinitely complex and beautiful mathematical structures. The Mandelbrot Set has since become one of the most famous and recognizable images in mathematics, captivating both mathematicians and the general public with its mesmerizing and intricate patterns.

Some call the Mandelbrot set as „God’s thumb print”. And there is quite some about it to call it so. It repeats so many times in nature..

But the Mandelbrot Set is not abstract. It is a real thing. There is a connection between the Mandelbrot set and how the nature operates.

Fractals allow us to describe natural phenomena, like mountains, for example.Fractal geometer can explain a cloud like an architect explains a house.

Fractal geometry can be applied in practice already. You can drive fractal through your data and see patterns you haven’t seen before- a very useful tool for financial markets.

Some are of the opinion that it’s fractal geometry that can finally help us to understand how our brain works and perhaps emulate it.

The very mystery about fractal geometry is the fact that Indian mandalas or objects of Islamic art very much resemble it and have been known for centuries.

So a „thumb print of God”?

The Incredible Life of Benoit Mandelbrot:

Videos: