  Araneiforms are radially converging systems of branching troughs exhibiting
fractal properties. They are found exclusively in the Southern polar regions of
Mars and believed to be result of multiple repetitions of cold CO2 gas jets
eruptions. Araneiform troughs get carved by the overpressurized gas rushing
underneath a seasonal ice layer towards a newly created opening. Current work
is an attempt to quantitatively analyze araneiforms patterns and model their
formation mechanism. The dendritic quality of most araneiforms are suggestive
that they can be described in terms commonly applied to terrestrial rivers. We
have adapted and for the first time applied to Martian araneiforms qualitative
morphological analysis typically used for terrestrial rivers. We have shown
that the large and well-developed araneiforms (with tributary orders larger
than 4) closely follow Horton's law of tributary orders and have bifurcation
ratio that falls well inside the range of terrestrial rivers. We have
implemented a two-dimensional Diffusion-Limited Aggregation (DLA) model that
describes formation of dendrite shapes by mathematical probabilistic means. We
compared modeled dendrite shapes to the araneiform shapes observed in the
Martian polar regions and evaluated their similarity using the morphological
analysis of araneiforms. We showed that DLA model can successfully recreate 2D
shapes of different observed araneiforms. Modeling the creation of araneiform
patterns with DLA leads to better understanding of seasonal processes that
create them.
