  The Lattice String Approximation algorithm (or LSA algorithm) of M. L.
Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex
dimensions of a nonlattice self-similar fractal string by the complex
dimensions of a lattice self-similar fractal string. The implication of this
procedure is that the set of complex dimensions of a nonlattice string has a
quasiperiodic pattern. Using the LSA algorithm, together with the
multiprecision polynomial solver MPSolve which is due to D. A. Bini, G.
Fiorentino and L. Robol, we give a new and significantly more powerful
presentation of the quasiperiodic patterns of the sets of complex dimensions of
nonlattice self-similar fractal strings. The implementation of this algorithm
requires a practical method for generating simultaneous Diophantine
approximations, which in some cases we can accomplish by the continued fraction
process. Otherwise, as was suggested by Lapidus and van Frankenhuijsen, we use
the LLL algorithm of A. K. Lenstra, H. W. Lenstra, and L. Lov\'asz.
