A noise-driven model is developed to describe the role of fluctuations in sidebranch phenomena in growth patterns for the fluid displacement problem and for dendritic crystal growth. Simulation results are compared with recent experiments on NH₄Br dendrites. It is found that the RMS sidebranch amplitude is an exponential function of distance from the tip, with no apparent onset threshold. Moreover, the sidebranches are non-periodic (at all distances from the tip) with apparently random variations in amplitude.