  We consider the use of space-filling curves (SFC) in scanning control
parameters for quantum chemical systems. First we show that a formally exact
SFC must be singular in the control parameters, but a finite discrete
generalization can be used with no problem. We then make general observations
about the relevance of SFCs in preference to linear scans of the parameters.
Finally we present a simple magnetic field example relevant in NMR and show
from the calculated autocorrelations that a SFC Peano-Hilbert curve gives a
smoother sequence than a linear scan.
