  We analyse the spatial statistics of the 2D gas-phase oxygen abundance
distributions in a sample of 219 local galaxies. We introduce a new adaptive
binning technique to enhance the signal-to-noise ratio of weak lines, which we
use to produce well-filled metallicity maps for these galaxies. We show that
the two-point correlation functions computed from the metallicity distributions
after removing radial gradients are in most cases well described by a simple
injection-diffusion model. Fitting the data to this model yields the
correlation length $l_{\rm corr}$, which describes the characteristic
interstellar medium mixing length scale. We find typical correlation lengths
$l_{\rm corr} \sim 1$ kpc, with a strong correlation between $l_{\rm corr}$ and
stellar mass, star formation rate, and effective radius, a weak correlation
with Hubble type, and significantly elevated values of $l_{\rm corr}$ in
interacting or merging galaxies. We show that the trend with star formation
rate can be reproduced by a simple transport+feedback model of interstellar
medium turbulence at high star formation rate, and plausibly also at low star
formation rate if dwarf galaxy winds have large mass-loading factors. We also
report the first measurements of the injection width that describes the initial
radii over which supernova remnants deposit metals. Inside this radius the
metallicity correlation function is not purely the product of a competition
between injection and diffusion. We show that this size scale is generally
smaller than 60 pc.
