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Using McMullen's Hausdorff dimension algorithm, we study numerically thedimension of the limit set of groups generated by reflections along threegeodesics on the hyperbolic plane. Varying these geodesics, we found fourminima in the two-dimensional parameter space, leading to a rigorous result whythis must be so. Extending the algorithm to compute the limit measure and itsmoments, we study orthogonal polynomials on the unit circle associated withthis measure. Several numerical observations on certain coefficients related tothese moments and on the zeros of the polynomials are discussed.

Some spectral applications of McMullen's Hausdorff dimension algorithm