La curva de Weierstrass y el análisis técnico de las criptomonedas

Almost 150 years ago, the German mathematician Karl Weierstrass discovered a very strange and very interesting "curve".

Working with "soft" curves, endowed with high roughness, he conceived a curve that was only composed of "points". From this, the super thorny curves were christened the "Weierstrass function". The interesting thing from the mathematical point of view is that these curves have neither tangent nor derivative. This discovery caused a stir in the mathematical circles of the time, in love with the mathematical calculation of Newton and Leibniz, developed in the seventeenth century, and these curves were considered as "mathematical pathologies" difficult to fit into a general theory.

The general scientific opinion was that these curves were of academic and theoretical interest, but they did little to explain nature. However, by 1970, adverse opinions about these curves began to change. Of course, the great change was brought about by the advent of computing, and, according to my criterion, by finding us in this matter close to a phase of fractal transition. Probably, if the computer had been invented before or after, things would not have changed much.

Computation revolutionized the power of numerical calculation and allowed us to work with previously inaccessible problems, such as irregular mathematical objects of great complexity, such as the Weierstrass function. Mandelbrot showed that nature does not seem to be displeased with "roughness", but quite the opposite. In 1975 he baptized these forms with the name of "fractals", a term that comes from the Latin "fractus" which means "fractured". The Weierstrass function became one of the first mathematical fractals.

All the processes of a company, of a market, of an industry and in general, of a business, respond to a fractured function whose nature can be studied with fractal mathematics.

Fractal models have yet to be developed to explain the behavior of cryptocurrencies. Still it is followed with the traditional analysis of Fibonacci or the tendencies of diagonals with limits. It's the same thing that happened with poor Wierstrass a few years ago...