Although composed of lines, orbits on this beast do not flow continuously, but hop from one location to another. When drawn, the attractor seems to materialize out of nothing. It is also chaotic. All seed values that converge to the attractor do so in a different manner. Distinct points that are initially separated by even the most minuscule gap will eventually diverge and evolve separately.
Successive magnifications show an ever increasing degree of detail.
What look like lines turn out to be sets of lines on closer inspection. When these lines are magnified they also turn out to be sets of lines. And so on. 1X 8X 64X 512X Similar bizarre creatures can also be generated using complex numbers . Think back to the time when you first learned about square roots.