  General substitution rules for non-periodic rhomb tilings are derived. From
the requirement that all substitution tiles consist of a discrete number of
prototiles, it follows that a substitution tile with angle s*pi/n must be built
out of pairs of prototiles with angles (s+t)*pi/n and (s-t)*pi/n, except if
t=0. In addition, we require that a discrete number of prototile edges must fit
between the beginning and endpoint of the substitution tile edge. By comparing
the total area of the discrete number of prototiles constituting the
substitution tile and the total area derived from the assumed edge shape, a set
of substitution rules is derived. The generalization involves the introduction
of prototiles with a negative area or subtraction tiles.
