  The law of proportionate growth simply states that the time dependent change
of a quantity $x$ is proportional to $x$. Its applicability to a wide range of
dynamic phenomena is based on various assumptions for the proportionality
factor, which can be random or deterministic, constant or time dependent.
Further, the dynamics can be combined with additional additive growth terms,
which can be constants, aggregated quantities, or interaction terms. This
allows to extent the core dynamics into an agent-based modeling framework with
vast applications in social and economic systems. The paper adopts this
overarching perspective to discuss phenomena as diverse as saturated growth,
competition, stochastic growth, investments in random environments, wealth
redistribution, opinion dynamics and the wisdom of crowds, reputation dynamics,
knowledge growth, and the combination with network dynamics.
