  The quark mass dependence of nucleon magnetic moments is explored over a wide
range. Quark masses currently accessible to lattice QCD, which lie beyond the
regime of chiral perturbation theory (chiPT), are accessed via the cloudy bag
model (CBM). The latter reproduces the leading nonanalytic behavior of chiPT,
while modeling the internal structure of the hadron under investigation. We
find that the predictions of the CBM are succinctly described by the simple
formula, \mu_N(m_\pi) = \mu^{(0)}_N / (1 + \alpha m_\pi + \beta m_\pi^2), which
reproduces the lattice data, as well as the leading nonanalytic behavior of
chiPT. As this form also incorporates the anticipated Dirac moment behavior in
the limit m_\pi \to \infty, it constitutes a powerful method for extrapolating
lattice results to the physical mass regime.
