The word 'fractal' originated in French around the year 1970 from Latin 'fract' meaning 'broken'. Corresponding to Latin verb frangere means "to break" to create irregular fragments. In wider term 'fractal' is a geometrical shape or pattern made up of identical parts, which are in turn identical to the overall pattern. The basic unit of the Koch snowflake, first constructed by a Swedish mathematician Niels Fabian Helge von Koch(1870–1924). In his 1904 paper entitled "Sur une courbe continue sans tangente, obtenue par une construction géométrique  élémentaire" he used a mathematical techniques to show that it is possible to have figures that are continuous everywhere but differentiable nowhere. The equilatorial triangle which can be built up into a much larger but still similar pattern. Any part of the snowflake is equally crinkly, whatever scale it is viewed at.

Some of the most remarkable fractals are the Julia sets, devised by the French mathematician Gaston Julia (1893–1978). He was a French fractal mathematician who devised the formula for the "Julia Set", fractal shapes defined on the complex number plane.
Born on February 3, 1893, in Sidi Bel Abbes, Algeria, which was under French rule, Julia was interested in mathematics and music from early on. When he was 20 years old, his studies were interrupted when he was called to serve in the army in World War I. He was severely wounded, losing his nose. Several operations were unsuccessful, and for the rest of his life Julia was forced to wear a leather strap over the area where his nose had been.

During those hard times, Julia continued his researches in mathematics, and after the war, he became a distinguished mathematician. In 1918, at the age of 25, he published a 199-page article in the Journal de Mathematic Pure et Appliqué (pp. 47-245), titled "Mémoire sur l'itération des fonctions rationnelles". In it, he discussed the iteration of a rational function, a topic that was also studied by another contemporary Frenchman, Pierre Joseph Louis Fatou—1878-1929—at the same time and in a similar way, but from a different perspective. In that said article, Julia precisely described the set J(f) of those z in C for which the nth iterate fn(z) stays bounded as n tends to infinity. This work was so important that he received the Grand Prix de l'Académie des Sciences (The Great Prize of the French Academy of Sciences—France) and made him famous throughout most of the mathematics centers of his days (the Académie also recognized Fatou's contribution with a secondary award). Gaston Maurice Julia died in Paris the 19th day of March 1978 at the age of 85.

One of the world's most influential mathematicians, Mandelbrot is recognized as the mathematician principally responsible for originating fractal geometry and applying it to science and engineering research. Examples of fractals range from natural objects with self-similar patterns, such as clouds and plants, to unique computer-generated graphical art forms created using mathematical formulas. The best known of these is called the Mandelbrot Set. Researchers use fractals to model and measure irregular patterns and structures, such as the rough coastline that cannot be represented by classical geometry.
Benoit Mandelbrot was largely responsible for the present interest in Fractal Geometry. He showed how Fractals can occur in many different places in both Mathematics and elsewhere in Nature.