With a fractal object, like a coastline, the smaller you make your ruler, the longer the coastline gets. This is because smaller and smaller rulers measure smaller and smaller jigs and jags in the coastline and fractals objects have jigs and jags on all scales. They do not start to look smooth as you magnify them. In other words, a fractal is a mathematical object that is self-similar and chaotic. Most fractals are generated by a relatively simple equation where the results are fed back into the equation until it grows larger than a certain boundary.
Most fractals are just a graph of an equation using complex numbers.
The real line is the X-axis. The imaginary number line is the Y-axis. The point is fed into the equation such as the one for the Mandelbrot set.