  We describe a numerical technique to compute the equilibrium measure, in
logarithmic potential theory, living on the attractor of Iterated Function
Systems composed of one-dimensional affine maps. This measure is obtained as
the limit of a sequence of equilibrium measures on finite unions of intervals.
Although these latter are known analytically, their computation requires the
evaluation of a number of integrals and the solution of a non-linear set of
equations. We unveil the potential numerical dangers hiding in these problems
and we propose detailed solutions to all of them. Convergence of the procedure
is illustrated in specific examples and is gauged by computing the
electrostatic potential.
