We have conducted a preliminary investigation of the fractal nature of the plan‐view shapes of lava flows in Hawaii (based on field measurements and aerial photographs) as well as in Idaho and the Galapagos Islands (using aerial photographs only). Our results indicate that the shapes of lava flow margins are fractals. In other words, lava flow shape is scale‐invariant (at least within the range of scale measured, 0.5m to 2.4km). This observation has important implications for understanding the fluid dynamics of lava flows. It suggests that nonlinear forces are operating in them because nonlinear systems frequently produce fractals. Furthermore, a'a and pahoehoe flows can be distinguished by their fractal dimensions (D). The majority of the a'a flows we measured have D between 1.05 and 1.09, whereas the pahoehoe flows generally have higher D (1.14 – 1.23). We have extended our analysis to other planetary bodies by measuring flows from orbital images of Venus, Mars and the Moon. All are fractal, and have D consistent with the range of terrestrial a'a and pahoehoe values. Combining the terrestrial and extraterrestrial data, the fractal nature of lava flow outlines holds for over five orders of magnitude in scale (0.5m to 60km).