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What is a Fractal?
A fractal is an irregular pattern that is not easily defined by classical geometry, which is based on the study of smooth, continuous curves and shapes. Fractals are irregular and complex, and are much more representative of the way the world actually is, rather than the idealized world of classical Euclidean geometry.
Although it's easy to identify when something is a fractal, it's almost impossible to come up with an easy definition of this concept. Indeed, the father of fractals, Benoit Mandelbrot, defined them in this way:

"A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension."

Luckily you don't have to understand such definitions to apply fractal analysis into financial markets!
Fractals are all around us in nature, in mountains, trees, snowflakes, rivers, clouds, and turbulence. There are even fractals in our bodies, in the system of blood vessels.

But the most important and fascinating fractals in nature occur in financial markets.