The specification of cell identities during development is orchestrated by signaling molecules named morphogens that establish spatial patterns of gene expression within a field of cells. In the classical view, the interpretation of morphogen gradients depends on the equilibrium morphogen concentrations, but the dynamics of gradient formation are generally ignored. The problem of whether or not morphogen gradient dynamics contribute to developmental patterning has not been explored in detail, in part, because genetic experiments that selectively affect signaling dynamics while maintaining unchanged the steady-state morphogen profile are difficult to design and interpret. Here, I present a mathematical approach to identify genetic mutations in developmental patterning that may affect the transient, but leave invariant the steady-state signalling gradient. As a case study, I illustrate how these tools can be used to explore the dynamic properties of Hedgehog signalling in the developing wing of the fruit fly, Drosophila melanogaster. This analysis provides insights into how different properties of the Hedgehog gradient dynamics, such as the duration of exposure to the signal or the width of the gradient prior to reaching the equilibrium, can be genetically perturbed without affecting the local steady-state distribution of the gradient. I propose that this method can be generally applicable as a tool to design experiments to probe the role of transient morphogen gradients in developmental patterning and discuss potential applications of these ideas in other problems.