We report the laser-induced solid-state transformation between a periodic "approximant" and quasicrystal in the Al-Cr system during rapid quenching. Dynamic transmission electron microscopy allows us to capture in situ the dendritic growth of the metastable quasicrystals. The formation of dendrites during solid-state transformation is a rare phenomenon, which we attribute to the structural similarity between the two intermetallics. Through ab initio molecular dynamics simulations, we identify the dominant structural motif to be a 13-atom icosahedral cluster transcending the phases of matter.