Fractal

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A fractal is defined as a figure that does not become simpler under any level of magnification.

Mandelbrot set

Probably the most well-known example of a fractal, the Mandelbrot set is the set of all points $c$ in the complex plane for which the sequence $z_0=0, z_{n+1}=z_n^2+c$ is bounded.

This fractal is NOT self-similar. However, it is almost self-similar.

If one were to plot all points in the Mandelbrot set using the complex plane, it would look like this.