  The geometric characteristics of dust clouds provide important information on
the physical processes that structure such clouds. One of such characteristics
is the $2D$ fractal dimension $D$ of a cloud projected onto the sky plane. In
previous studies, which were mostly based on infrared (IR) data, the fractal
dimension of individual clouds was found to be in a range from 1.1 to 1.7 with
a preferred value of 1.2--1.4. In the present work, we use data from Stripe82
of the Sloan Digital Sky Survey to measure the fractal dimension of the cirrus
clouds. This is done here for the first time for optical data with
significantly better resolution as compared to IR data. To determine the
fractal dimension, the perimeter-area method is employed. We also consider IR
(IRAS and Herschel) counterparts of the corresponding optical fields to compare
the results between the optical and IR. We find that the averaged fractal
dimension across all clouds in the optical is $\langle D \rangle
=1.69^{+0.05}_{-0.05}$ which is significantly larger then the fractal dimension
of its IR counterparts $\langle D\rangle=1.38^{+0.07}_{-0.06}$. We examine
several reasons for this discrepancy (choice of masking and minimal contour
level, image and angular resolution, etc.) and find that for approximately half
of our fields the different angular resolution (point spread function) of the
optical and IR data can explain the difference between the corresponding
fractal dimensions. For the other half of the fields, the fractal dimensions of
the IR and visual data remain inconsistent, which can be associated with
physical properties of the clouds, but further physical simulations are
required to prove it.
