I guess you have heard about fractals. Sets like Julia Set and Mandelbrot Set are totally connected to complex fractals. It is a fascinating piece of art first discovered by mathematician Benoit Mandelbrot.
Mandelbrot set is a specialised set of complex numbers c, where the image is formed bascically by breaking a small part of argand plane into infinitisimally small parts. And the mandelbrot set condition which is a recursive set of solution z(n+1)=z(n)+c with base case z(0)=0 Mandelbrot set is the combination of all julia sets which are itself complex fractals.
A curve or geometrical figure, each part of which has the same statistical character as the whole. They are useful in modelling structures (such as snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth and galaxy formation.