A multiplicative cascade is a randomization of any measure on the unit interval, constructed from an iid collection of random variables indexed by the dyadic intervals. Given an arbitrary initial measure I will describe a method for constructing a continuous time, measure valued process whose value at each time is a cascade of the initial one. The process also has the Markov property, namely at any given time it is a cascade of the process at any earlier time. It has the further advantage of being a martingale and, under certain extra conditions, it is also continuous. I will discuss applications of this process to models of tree polymers and one dimensional random geometry. Joint work with Ben Rifkind (University of Toronto).