Percolation

A coffee percolator is well-named because the Latin colare means to flow and per means through.
Transforming this kitchen appliance into an abstract problem, in physics percolation is the process of finding an unbroken path across a lattice of randomly filled cells.
Here are the basic construction and some examples.
Origins of the study of percolation.
Spanning clusters are one type of fractal generated by percolation.
Percolation clutsers exhibit scaling relations.
Other associated fractals are the backbone and hull.