FRACTALS

Fractals are geometric patterns that repeat at different scales. They are often characterized by their self-similarity, meaning that smaller parts of the fractal look similar to larger parts.

This concept was first introduced by the mathematician Benoit Mandelbrot. He was interested in the irregular shapes that are found in nature. He coined the term "fractal" to describe these shapes, and the study of fractals has since become an important branch of mathematics.

Fractals have also been used to model the behavior of chaotic systems, such as weather patterns and the stock market, computer graphics and animation, study the structure of the human body and from the branching patterns of blood vessels to the structure of the lungs.

Overall, fractals are a fascinating area of mathematics that have wide-ranging applications in science, technology, and the arts. They offer a unique way of looking at the natural world, and they have helped to uncover some of the underlying patterns that govern our universe.

MANDELBROT SET

The Mandelbrot set is defined as the set of all complex numbers "c" for which the iterative equation "z = z^2 + c" does not diverge to infinity when iterated infinitely many times, starting with "z=0".

In simpler terms, for any given complex number "c", the Mandelbrot set is the set of all points in the complex plane that,when used as the value of "c" in the iterative equation above, do not result in the sequence of values "z, z^2 + c, (z^2 + c)^2 + c, .." diverging to infinity

The Mandelbrot set is a beautiful and intricate fractal shape, with self-similar patterns repeating at different scales. It has captured the imagination of many mathematicians, artists, and enthusiasts, and has been the subject of numerous mathematical and artistic explorations.