We discuss the asymptotic behavior of Fourier transforms of Cantor
measures and wavelets, and related functions that might be called
multiperiodic because they satisfy a simple recursion relation
involving a blend of additive and multiplicative structures.
¶ Our numerical experiments motivated conjectures about this asymptotic
behavior, some of which we can prove. We describe the experiments,
the proofs, and several remaining conjectures and open problems. We
also contribute to the evolving iconography of fractal mathematics by
presenting the numerical evidence in graphical form.