  When information is spatially repeated in self-similar fractal beam patterns,
only a portion of the diffracted beam is needed to reconstruct the kernel data.
What is unique to a fractal-encoding scheme is that the image demultiplexing
process can be, to a first approximation, easily performed optically. In prior
work, we experimentally and numerically study fractal-encoded optical beams and
their mid- and far-field propagation without added turbulence. Here, we present
preliminary simulations of fractal-encoded beams with high turbulence ($C_n^2
\geq 10^{-14}$ m$^{-2/3}$) where we achieve respectable bit error rates of
$10^{-3}$. These results are impressive given that: data with low fractal
orders is shown, simple threshold-algorithms are used (i.e., no machine
learning), and only a third of the beam, off-axis, is needed. More robust
channel encoding is associated with increased fractal orders, larger collection
areas, and higher kernel singular value decomposition entropy.
