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[1] This study aims at quantifying the spatial distribution of cones within rootless cone groups (RCGs). Our data set consists of (1) seven Icelandic RCGs (identified through field investigations), (2) seven candidate RCGs on Mars (identified through Mars Orbiter Camera (MOC) and Thermal Emission Imaging System (THEMIS) images), and (3) four groups of impact craters on Mars (also identified through MOC and THEMIS images) to determine if they can be remotely distinguished from the RCGs purely on the basis of their spatial distribution. Several independent statistical techniques are used, including nearest neighbor analysis, analysis of variance (ANOVA), and linear alignment detection analysis. Our results indicate that the spatial distribution of each RCG is not random: Within a cone group, cones preferentially form near existing cones. The presence of at least one significant linear cone alignment in each RCG (and strong linear alignments in some groups) suggests that rootless cones form as the surface signature of preferred lava pathways. An ANOVA on mean nearest neighbor distances reveals the Martian cone groups to be statistically indistinguishable from the Icelandic RCGs, supporting existing interpretations that they represent rootless cone groups. A similar ANOVA showed that the Martian cone groups do not resemble the Martian impact crater clusters studied: The impact craters have significantly greater nearest neighbor distances and show no evidence of aggregation within a crater group.

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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).