Ebook: Math for Everyone: Fractals

This text introduces vaguely the mathematical concept of Fractal. It is not possible to teach the theory of fractals at the upper middle level, because the contents go far beyond, however, it is possible that the student acquires a slight notion that allows intuitively, to know what this beautiful mathematical object is.

In the first two chapters the idea of fractal is introduced, first in nature and then as a geometric object, it even shows how diseases also appear. A first approximation is given using the idea of self-similarity, which refers to a geometric property of a part as the whole.

In the third chapter the idea of dimension is introduced, and the dimension of some classical fractals is calculated, allowing a second approximation to its definition. Chapter 4 is a different way of approaching fractals, using the growth of plants to understand fractal behavior.

In Chapter 5 and 6 the language of functions between complex numbers is introduced, which serves to describe two very important examples of fractals: the Julia Set and the Mandelbrot Set.

We finish the book with a gallery of fractals, so that the reader can enjoy the beauty of such mathematical objects.