  Paper I of this series introduced a nonlinear version of quantum mechanics
that blocks cats, and paper II postulated a random part of the wavefunction to
explain outcomes in experiments such as Stern-Gerlach or EPRB. However, an ad
hoc extra parameter was assumed for the randomness. Here I provide some
analytic and simulation evidence that the nonlinear theory exhibits sensitive
dependence on initial conditions in measurement scenarios, perhaps implying
that the magnitude of randomness required is determined by structural features
of the model, and does not require a free parameter.
