Another category of fractals represents the so-called chaotic, non-linear fractals. This fractal type is connected with the theory of chaos, and its elements are obtained by a simple mathematical equation .For visualizing them, each point on the paper or screen is related to a certain number - e.g. in the case of the “Mandelbrot set” this is a complex number. This number is then iterated, that means it is used in a formula and the new number resulting from that is then again used in the same formula, which leads to the next iteration. This sequence of operations is "similar" to the work of the "copy-machine" of linear fractals - with regard to insertion.
The insertion is repeated until the numerical values approach infinity, converge or fluctuate between several numbers. Depending on the result, the original point may be colored differently.