Fractals
The name of Benoît Mandelbrot is forever linked to fractal geometry.
In 1951, he invented the word "fractal", by using the Latin words frangere / fractus (break, fragment) and, in 1977, published his book "The fractal geometry of Nature" .
In order to show the characteristics of complex mathematical systems, Mandelbrot used the “up-to-date” devices at his disposal : graphs and printing or computer developments.
Auto-similarity : So typical of the fractals, the auto-similarity can be observed by “zooming” onto the observed object and this closer and closer, to the infinity.
Note : Producing fractals is not predictable. This means there is no algorithm that would tell if a given point, a number, an object is part or not of the whole. The only way to know it is to go through the iteration, the starting algorithm ..
"Nature gave us a big challenge : the study of the shapes of clouds, mountains and sea shores.."
Benoît Mandelbrot - 1977
Ref : Partial extracts from the book : "Histoire des mathématiques" by Richard Mankiewicz (Seuil).