Some more Voronoi tessellations. These use non-random generating points (such as spirals, nested circles, and other curves), plus some good ol' Perlin noise in some cases.
While Voronoi tessellations look really cool, they are not the most visually intriguing patterns I've come across. My fascination with them lies more in the nature of what the patterns represent. They describe a kind of Utopian equilibrium among any group of points in space. Those points in space can be a generalization of real systems such as people in a crowd or cells in an organism.