To explore the pattern formed by rivers as they crisscross the land, we developed a way to measure how these patterns vary, from straight to complex, winding paths. We discovered that a river's degree of complexity depends on how the river slope changes downstream. Although this is strange (i.e., why would changes in slope affect twists of a river in map view?), we show that this dependency is almost inevitable and that the complexity could signify how arid the climate is or used to be.