Fractal Complexity and Symmetry in Lava Flow Emplacement

Abstract

This study presents a cohesive physical model that predicts lava flow morphology by establishing a quantitative link between a lava’s yield strength and its geometric complexity, measured by a prefractal dimension. The model is founded on the principle of symmetry, where the potential for fracturing and complexity peaks at an intermediate yield strength. This peak in complexity, observed with a predicted prefractal dimension (Dpf) of 1.15 for terrestrial ‘a’a-like lava, arises from a critical state where a balance between gravitational ¯ driving forces and internal resistance allows for the formation of intricate margins. The model demonstrates that as lavas deviate from this optimal strength, becoming either too fluid (pahoehoe, D ¯ pf = 1.05) or too rigid (rhyolite, Dpf = 1.07), their morphology becomes progressively simpler, representing a symmetrical decline in complexity. Our approach also incorporates the overriding influence of topographic confinement and the temporal evolution of complexity as the lava cools. Validated against terrestrial lavas and successfully applied to lower-gravity environments, the model predicts a reduction in complexity for similar flows on Mars (Dpf = 1.13) and the Moon (Dpf = 1.09), providing a tool for interpreting volcanic processes grounded in the fundamental principles of symmetry and complexity.