I made a comment elsewhere on this thread that explains that symbols themselves being compact isn't so important, but that the set of descriptions of the symbols must be compact. For example, if the description of the symbol is not the symbol itself as a set, but a map f:[0,1]^2 -> [0,1] that describes the "intensity" of ink at each point, then the natural conclusion is that the description of a symbol must be upper semicontinuous, which makes the set of descriptions compact.