Benoit Mandelbrot used a wool-skein to show the changing of mathematical constancy - the changing of the "effective" dimensions. For a viewer who is far enough away from the wool-skein, which may have a diameter of 10 centimeters and consists of a 1-millimeter yarn, it looks like a point, a zero-dimensional object. In a 10 centimeter resolution the skein is a three-dimensional object, in a 10 millimeter resolution it turns out to be a confusion of one-dimensional twines, at a 0.1 millimeter resolution each twine is experienced as a three-dimensional column and at a 0.01 millimeter resolution each column turns again into one-dimensional fibers. If we zoom in deeper on the resolution of an atom, the wool-skein is presented as an object of finite numbers of atom-like points and therefore it is again zero-dimensional - remember the Cantor Set. So the wool-skein shows a sequence of different effective dimensions. Some badly defined change-over between zones of well defined dimensions are interpreted as fractal zones where the fractal dimension is higher than the topological one.
Benoit Mandelbrot also wrote about the surface of timber being spongy but nevertheless the beam is said to be even. This is because of the scale, in a certain ratio of size the regular and continual aspect can describe an object in a correct way. He compared this scale with a tinfoil that is put over a sponge, which follows the surface but does not show the many little complex details, see picture 26.