  We present an analysis of the $BVRI$ photometry of the blazar BL Lacertae on
diverse timescales from mid-July to mid-September 2020. We have used 11
different optical telescopes around the world and have collected data over 84
observational nights. The observations cover the onset of a new activity phase
of BL Lacertae started in August 2020 (termed as the August 2020 flare by us),
and the analysis is focused on the intra-night variability. On short-term
timescales, (i) flux varied with ~2.2\,mag in $R$ band, (ii) the spectral index
was found to be weakly dependent on the flux (i.e., the variations could be
considered mildly chromatic) and (iii) no periodicity was detected. On
intra-night timescales, BL Lacertae was found to show bluer-when-brighter
chromatism predominantly. We also found two cases of significant inter-band
time lags of the order of a few minutes. The duty cycle of the blazar during
the August 2020 flare was estimated to be quite high (~90\% or higher). We
decomposed the intra-night light curves into individual flares and determined
their characteristics. On the basis of our analysis and assuming the turbulent
jet model, we determined some characteristics of the emitting regions: Doppler
factor, magnetic field strength, electron Lorentz factor, and radius. The radii
determined were discussed in the framework of the Kolmogorov theory of
turbulence. We also estimated the weighted mean structure function slope on
intra-night timescales, related it to the slope of the power spectral density,
and discussed it with regard to the origin of intra-night variability.
