History of Fractals
Fractals have existed for a very long time in nature, but the first person who put a name to this concept was Benoît Mandelbrot in 1975. He named the fractal from the latin word fractus which means broken or fractured. He said that as a geometric shape is divided into parts, the parts will be replicas of the same shape but smaller within it. Benoît is considered the father of all fractals because of his fractal discoveries.
Mandelbrot first began researching fractals in nature by asking himself “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension”, and he has a fractal named after him called the Mandelbrot Set.
Mandelbrot first began researching fractals in nature by asking himself “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension”, and he has a fractal named after him called the Mandelbrot Set.
Benoît mandelbrot: The father of all fractals
Benoît Mandelbrot was introduced to mathematics by his uncle Szolem Mandelbrojt when he and his family moved to France from Poland to escape Hitler’s rule, since they were Jewish. Mandelbrot’s uncle introduced Mandelbrot to Julia’s work. Mandelbrot liked to see math problems visually instead of in equations from an early age which is believed to have lead him to the study fractals.
After graduating from École Polytechnique, Mandelbrot came to New York where he worked for an IBM research center. While working here in 1967, Mandelbrot published his essay 'How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension', where he argued that coastlines were "statistically self-similar".
After graduating from École Polytechnique, Mandelbrot came to New York where he worked for an IBM research center. While working here in 1967, Mandelbrot published his essay 'How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension', where he argued that coastlines were "statistically self-similar".
Then, Mandelbrot studied the work of Gaston Julia and Pierre Fatou, two french mathematicians who studied iterative functions and found what attractors (points which bring points toward it) and reactors (points which push others away) were. Mandelbrot used these ideas to created the Mandelbrot Set. Also, Julia and Paul Lévy were Mandelbrot’s mentors when he studied at École Polytechnique, and he used his teachers theories to help him discover more fractals and their properties.
Who influenced mandelbrot's work?
In 1972, Karl Weierstrass published a paper that showed if a is a positive number and 0 < b < 1, then
is not differentiable but is still analytical. While Weierstrass never published a proof on this topic, it was used by Mandelbrot to graphically represent his results.
Mandelbrot got the term self-similarity from Cesàro who defined self similarity in 1905 while he analyzed a paper by Helge von Koch, the creator of the von Koch snowflake.
Mandelbrot was also influenced by his mentors from his university, Gaston Julia and Paul Lévy, and the work on iterative functions by Fatou and Julia. He used their theories to help him learn more about fractals.
Mandelbrot got the term self-similarity from Cesàro who defined self similarity in 1905 while he analyzed a paper by Helge von Koch, the creator of the von Koch snowflake.
Mandelbrot was also influenced by his mentors from his university, Gaston Julia and Paul Lévy, and the work on iterative functions by Fatou and Julia. He used their theories to help him learn more about fractals.