  Clouds in observations are fractals: they show self-similarity across scales
ranging from one to 1000 km. This includes individual storms and large-scale
cloud structures typical of organised convection. It is not known whether
global storm-resolving models reproduce the observed fractal scaling laws for
clouds and organised convection. We compute the fractal dimension of clouds
using Himawari satellite data and compare this to global storm-resolving model
simulations completed as part of the DYAMOND intercomparison project. We find
cloud fields in these simulations are indeed fractal, and reproduce the
observed fractal dimension to within 10\%. We find the fractal dimension is
sensitive to the choice of boundary layer parametrisation scheme used in each
model simulation, and not to the convection parametrisation as might have been
expected. The fractal dimension is independent of cloud area distributions,
providing a complementary metric to assess the multi-scale structure of
convection and convective organisation in model simulations.
