Abstract: Circle packings, introduced by Bill Thurston, are configurations of circles with prescribed patterns of tangencies. Viewed another way, circles can impose geometry on abstract combinatorial patterns. It turns out that that geometry is profoundly "conformal" in nature --- so much so that circle packing is the basis for a comprehensive theory of discrete conformal geometry. This talk, however, will focus on geometrically random triangulations and experimental evidence suggesting that conformality becomes an emergent phenomenon when we let circles do the work. With some adjustments, quasiconformality may also be brought into the picture. The talk will be image-driven and so should be accessible with little background.