What is a fractal and who is famous for discovering the concept?

Answer 1

A fractal is a shape which shows the same pattern at every level of magnification.

The concept of fractals emerged form the ideas of recursive functions in the 17 Century. Those ideas were put into more rigorous framework by 19th Century mathematicians like Bolzano, Reimann and Weierstrass who studied functions which were continuous but not differentiable - particularly those that were non-differentiable almost everywhere. The term, "fractal" was first used by Mandelbrot in 1975.