  The evolution of galaxies is governed by equations with chaotic solutions:
gravity and compressible hydrodynamics. While this micro-scale chaos and
stochasticity has been well studied, it is poorly understood how it couples to
macro-scale properties examined in simulations of galaxy formation. In this
paper, we show how perturbations introduced by floating-point roundoff, random
number generators, and seemingly trivial differences in algorithmic behaviour
can produce non-trivial differences in star formation histories, circumgalactic
medium (CGM) properties, and the distribution of stellar mass. We examine the
importance of stochasticity due to discreteness noise, variations in merger
timings and how self-regulation moderates the effects of this stochasticity. We
show that chaotic variations in stellar mass can grow until halted by
feedback-driven self-regulation or gas exhaustion. We also find that galaxy
mergers are critical points from which large (as much as a factor of 2)
variations in quantities such as the galaxy stellar mass can grow. These
variations can grow and persist for more than a Gyr before regressing towards
the mean. These results show that detailed comparisons of simulations require
serious consideration of the magnitude of effects compared to run-to-run
chaotic variation, and may significantly complicate interpreting the impact of
different physical models. Understanding the results of simulations requires us
to understand that the process of simulation is not a mapping of an
infinitesimal point in configuration space to another, final infinitesimal
point. Instead, simulations map a point in a space of possible initial
conditions points to a volume of possible final states.
