  We prove that every topologically transitive shift of finite type in one
dimension is topologically conjugate to a subshift arising from a primitive
random substitution on a finite alphabet. As a result, we show that the set of
values of topological entropy which can be attained by random substitution
subshifts contains all Perron numbers and so is dense in the positive real
numbers. We also provide an independent proof of this density statement using
elementary methods.
