A finite area inside and infinite skin! You can paint the interior
of this fractal with a small tin of paint but you could never get
enough paint to paint the edge.
Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.
This article gives a proof of the uncountability of the Cantor set.