We simulate directional solidification using a phase-field model solved with adaptive mesh refinement. For small surface tension anisotropy directed at 45 degrees relative to the pulling direction we observe a crossover from a seaweed to a dendritic morphology as the thermal gradient is lowered, consistent with recent experimental findings. We show that the morphology of crystal structures can be unambiguously characterized through the local interface velocity distribution. We derive semiempirically an estimate for the crossover from seaweed to dendrite as a function of thermal gradient and pulling speed.