  We present high-precision photometry on 107 variable low-mass stars and brown
dwarfs in the ~3 Myr Sigma Orionis open cluster. We have carried out I-band
photometric monitoring within two fields, encompassing 153 confirmed or
candidate members of the low-mass cluster population, from 0.02 to 0.5 M_\odot.
We are sensitive to brightness changes on time scales from 10 minutes to two
weeks with amplitudes as low as 0.004 magnitudes, and find variability on these
time scales in nearly 70% of cluster members. We identify both periodic and
aperiodic modes of variability, as well as semi-periodic rapid fading events
that are not accounted for by the standard explanations of rotational
modulation of surface features or accretion. We have incorporated both optical
and infrared color data to uncover trends in variability with mass and
circumstellar disks. While the data confirm that the lowest-mass objects
(M<0.2M_\odot) rotate more rapidly than the 0.2-0.5 M_\odot members, they do
not support a direct connection between rotation rate and the presence of a
disk. Finally, we speculate on the origin of irregular variability in cluster
members with no evidence for disks or accretion.
