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Dendritic crystal growth patterns have fascinated scientists for several centuries. Much of the aesthetic appeal of these patterns stems from the hierarchical structure of primary-, secondary-, and higher-order branches, which typically grow along principal crystallographic axes. Atypical growth directions have also been observed. Here, we demonstrate both computationally and experimentally that the range of possible dendrite growth directions, and hence the morphological diversity of the resulting dendritic structures, is much richer than previously anticipated. In particular, we show that primary dendrite growth directions can vary continuously between different crystallographic directions as a function of the composition-dependent anisotropy parameters. The study combines phase-field simulations of equiaxed dendritic growth and directional freezing of Al-Zn alloys. Both simulations and experiments exhibit continuous changes of direction from <100> to <110> for an underlying cubic symmetry. These results have important implications for controlling the microstructure of a wide range of cast alloys that solidify dendritically.