There are many fractals. There is a classification that distinguishes geometric (constructive), algebraic (dynamic) and stochastic fractals.

In this project, we need to draw such fractals as the Mandelbrot set and the Julius set, which are algebraic fractals.

But in order to get a better understanding of the concept of fractals, let's first consider the simplest of them - geometric.

Geometric fractals

The theory of fractals began with fractals of this type in the 19th century. Since it is in geometric fractals that the properties of self-similarity are most evident.

The most famous geometric fractals are the Cantor set, the Sierpinski triangle, and the Koch snowflake.

The process of constructing them is iterative, that is, it consists in repeating the same actions many times.

Let us consider this using the example of the Cantor set.

Initially, we have a straight line segment of a certain length.

The first iteration is to remove the middle third of the segment.

At the next and all other iterations, we throw out the middle third of all segments of the current level.

As a result, you get the following picture:

The accuracy of the fractal depends on the number of iterations performed. The more there are, the more accurate the fractal.

Algebraic fractals

From the point of view of mathematics, the most interesting are algebraic fractals. The most famous of these are the Mandelbrot set and the Julia set.

These fractals are set on the complex plane.