  A spline wavelets construction of class C^n(R) supported by sequences of
aperiodic discretizations of R is presented. The construction is based on
multiresolution analysis recently elaborated by G. Bernuau. At a given scale,
we consider discretizations that are sets of left-hand ends of tiles in a
self-similar tiling of the real line with finite local complexity.
Corresponding tilings are determined by two-letter Sturmian substitution
sequences. We illustrate the construction with examples having quadratic
Pisot-Vijayaraghavan units (like tau = (1 + sqrt{5})/2 or tau^2 = (3 +
sqrt{5})/2) as scaling factor. In particular, we present a comprehensive
analysis of the Fibonacci chain and give the analytic form of related scaling
functions and wavelets as splines of second order. We also give some hints for
the construction of multidimensional spline wavelets based on stone-inflation
tilings in arbitrary dimension.
