For each point in the Mandelbrot set there is an entire Julia Set. Zooming in over and over again produces images which are similar but not identical in structure and shape. You will view pattern within pattern, detail in finer and finer scales. In essence, fractals are pictures which have similar characteristics at different magnifications. Enlarged View Zoomed View Fractal Geometry Chaos Theory is the the study of perpetually changing complex systems based on mathematical concepts of recursion .
Fractals are a geometric application of recursion .
Two fundamental fractals, the Sierpinski Triangle and the Koch Snowflake , provide the basis for more complex, elaborate fractals. Fractals and Cosmology Recent versions of the inflationary cosmos theory assert that instead of being an expanding ball of fire the universe is a huge growing fractal. It consists of many inflating balls that produce new balls, which in turn produce more balls, ad infinitum. This scenario similarly describes the universe as a self-generating fractal that sprouts other inflationary universes. This constitutes a fundamental change in how the universe is seen as being created and structured.