Cantor set
Mandelbrot's construction by "curdling"

In The Fractal Geometry of Nature, mathematician Benoit Mandelbrot provides a whimsical thought experiment to assist non-mathematical readers in imagining the construction of C {\displaystyle {\mathcal {C}}}. His narrative begins with imagining a bar, perhaps of lightweight metal, in which the bar's matter "curdles" by iteratively shifting towards its extremities. As the bar's segments become smaller, they become thin, dense slugs that eventually grow too small and faint to see.

CURDLING: The construction of the Cantor bar results from the process I call curdling. It begins with a round bar. It is best to think of it as having a very low density. Then matter "curdles" out of this bar's middle third into the end thirds, so that the positions of the latter remain unchanged. Next matter curdles out of the middle third of each end third into its end thirds, and so on ad infinitum until one is left with an infinitely large number of infinitely thin slugs of infinitely high density. These slugs are spaced along the line in the very specific fashion induced by the generating process. In this illustration, curdling (which eventually requires hammering!) stops when both the printer's press and our eye cease to follow; the last line is indistinguishable from the last but one: each of its ultimate parts is seen as a gray slug rather than two parallel black slugs.
startend:quotation, detectable_content:postscript