Dendrites are typical growth morphologies in alloy solidification. However, the ways in which dendrites grow and form solidification microstructures remain poorly understood. Here we show unexpected findings that reveal the survival of unfavorably oriented dendrites and highly complicated dendrite-dendrite interactions in three-dimensional space during the directional solidification of a binary alloy. These results are observed for the first time through very-large-scale phase-field computations performed by a graphics processing unit (GPU) supercomputer and a high-performance algorithm developed for parallel computing. (c) 2013 Elsevier B.V. All rights reserved.