  Streamer discharges are thin plasma channels that precede lightning and
sparks. They usually evolve in bundles as stochastic tree-like structures and
are inherently difficult to model due to their multiscale nature. In this
paper, we perform a computer investigation of positive streamer discharges in
air using contemporary photoionization models. We report on three-dimensional
computer simulations under conditions that are available in laboratory
spark-gap experiments. The solutions demonstrate a multiscale morphology
consisting of streamer fluctuations, branching, and the formation of a
discharge tree. Some branches are comparatively thick and noisy, while others
are thin, smooth, and carry electric fields exceeding $250\,\textrm{kV/cm}$ at
their tips. Our results are consistent with past experiments and clarify the
puzzling branching dynamics and stochastic morphology of positive streamer
discharges.
