From Infinite Sets to Market Cycles: The Fascinating Journey of Fractals in Mathematics and Finance

Fractals have revolutionized our understanding of complexity in both mathematics and finance, revealing patterns that repeat across different scales. From Georg Cantor’s exploration of infinite sets to Benoit Mandelbrot’s formalization of fractal geometry, these concepts have challenged traditional theories and introduced new ways to analyze market behaviors. This article delves into the evolution of fractals, and their impact on finance today.

The image has been taken from https://theconversation.com/

Georg Cantor (1845 — 1918) was deeply interested in the concept of infinity, which often arose in mathematical problems, especially in calculus, where certain series and functions seemed to approach infinity, and he wanted to address these issues by defining a rigorous approach to infinite sets and numbers.

The history of fractals more specifically starts by exploring sets that had counterintuitive properties (like being uncountable yet containing no intervals). Cantor’s construction of the Cantor Set, a set that removes portions of itself recursively, was one of the first instances of a mathematically defined structure with fractal-like properties.

Benoit Mandelbrot

Benoit Mandelbrot (1924–2010) was a Polish-born French-American mathematician. He…