When graphed however, a double spiral appeared, which gave proof to a new type of order, chaos. Edward Lorenz could not have made his discovery without the aid of computers. French mathematician, Gaston Julia, established part of the foundation of chaos theory and fractals, creating many sets of numbers, which, when drawn on a graph, create pictures like the infinite snowman, dragons, and bunny ears. Benoit Mandelbrot expanded and redeveloped Julia's groundwork. This gave birth to the set of all Julia sets, more commonly known as the Mandelbrot set, and a new branch of mathematics called fractal geometry.
Function iteration is one of the basic concepts of chaos theory.
He gives the example . With that, . Then, x is set equal to four. As this continues to the next iteration, x is set equal to 16. William Woo adds insight to this statement with the example of a pile of sand.