The Geometry of Understanding

Introduction: Can a Structure Build Itself? Imagine having thousands of tiny square tiles laid out on a flat surface. Each tile has coloured edges that determine how it can connect to other tiles. These tiles have no knowledge of the final structure they are meant to form. They simply follow a local rule: whenever two edges with matching colours meet and their connection is strong enough, the tiles stick together. At first, small clusters of tiles form randomly. But as time p