Why is mandelbrot so important to us?

Answer 1

Benoit Mandelbrot was a French/American Computer Scientist and Mathematician who worked on interesting problems.

One of those problems had to do with Mathematical oddities. While an IBM Fellow, he entered some of the formulas into a computer program and printed out the results that revolutionized Chaos science and brought to the public the Mandelbrot Sets. They looked somewhat like Seahorses, yet when he printed out zoomed versions he kept seeing more Seahorses.

What he saw was a vastly complicated shape made up of smaller and smaller versions of itself, and the deeper he went, the theme changed but he found yet more smaller versions of the shape. He named the whole thing fractals.

The funny thing is all this complexity came from a single class of Mathematical formulas, called recursives. Basically, the computer program plugs some numbers into the formula, then feeds the result back into the formula, and does it again, letting the number go out and then back in, branching off into another set of calculations.

Another funny thing that people after him discovered while playing with the same type of formulas shook Science. ALL OF IT.

Fractals replicated life. The twirling of cream in a cup of coffee, the swirl of cigarette smoke. Mountains. Coastlines. The curves of a pepper. The shape of a tree. The vortex of a Tornado. The changing form of clouds. The Rings of Saturn. The majestic turbulence of Galaxies. The Mathematical Oddity was the accidental discovery of an inner working of the Universe.

We left the Newtonian view of the Universe - where everything can be eventually broken down and decoded. And we entered a wild, woolly, riotous Reality.

Mandelbrot's curious shapes expanded our ability to model the physical world, and the principles are in use in Finance, the Stock Market, the Biotech industries, Astronomy, Physics, Quantum Dynamics, Oceanography, Medical science, Populations, Genetics, Governance, Infectious Diseases. Practically every avenue of research grappling with the curiosities of the world around us employ the curious discovery of Dr. Benoit Mandelbrot.

ID0403095245 is paullwolborsky - I registered after answering.

ADDENDA

If you want to make the trip from the Euclidian universe you've lived in all of your life to the fantastical world of stubborn conundrum there is no need to find a rabbit hole. All you need is a handy coastline.

The whole investigation leading to Fractals started with a 1967 paper 'How long is the Coast of Britain'. The Coastline paradox have been a paramount paradox for a long time. It postulates if you have enough initiative to measure the coast with a Yardstick you will arrive at one number. If you still have time left in the day before Tea you could start again with a 12" ruler. When by the end of that long day you finish, you will arrive at a larger number. The paradox concludes if you measured with a 0" ruler, you could arrive at infinity assuming infinity was sufficiently cooperative.

This paper was cited by a wide variety of other papers over time in the Journal Science. You can get a sampling of papers citing this seminal document that illustrates how far and wide fractals are used at the link I've added.

Answer 2

The Mandelbrot set is important because it is a visual representation of complex mathematical concepts related to fractals, chaos theory, and iteration. It has intrigued mathematicians, scientists, and artists for its infinite complexity and beauty, and has paved the way for further research in nonlinear dynamics and computer graphics.