Mandelbrot Set

History

    Mandelbrot fractals are the most well-known fractal there is. They are also known as the most beautiful and the most complex. In 1975, Benoit Mandelbrot created the Mandelbrot set. This set is created from extended ideas of the Julia set. The discovery of this set had a huge impact on so many items and concepts in the world today. It changed the idea that computer graphics had to look artificial. It also raised the possibility of simulating the natural world. Some examples that the simulation of the natural world is the collision of abstraction and naturalism. This was done when fractals were first used to generate landscapes. There are also huge similarities with natural forms. The Mandelbrot set also has many applications in physics and other science fields, including mathematics. Along with that the Mandelbrot set was used in art and many other applications. Some of these applications are being able to create sample coast lines and other landscapes. This is helpful because they can figure out where to build bridges, roads, and other structures.

Exploration of Mathematics

    The Mandelbrot set was first introduced by Mandelbrot as \[z^2+C\] where z is a complex function and C is a complex parameter. As more research and discovery has been done on the Mandelbrot set it can be demonstrated for cubic, quadratic, and higher degree polynomials. When dealing with the higher degree polynomials the form \[z^n+C\] where n≥2 is used. As n becomes larger the Mandelbrot set becomes circular. This means that it turns into a circle because of how many straight lines there are. Along with the Mandelbrot set being circular it is also bounded.