Following a MIT lecture surveying collective phenomena in everything from Atomic nuclei to stellar inteiors, Hans Bethe once remarked that there was no real difference between the crystallization of neutrons under the strong force in degenerate stellar cores, and the assembly of floating silica micro-spheres by electrostatic repulsion into what become the colorful flashes of optical Bragg diffraction we see in opals.
Couls Saturn 's symmetrical polar feature fit somewhere in the middle of Bethe's grand tour of order arising from competing physical forces? 120 degree intersections are dictated by least energy considerations in a wide spectrum of systems. Discrete-particle molecular dynamics simulations generate six sided patterns when used to model three-dimensional Rayleigh-Bénard convection- a phenomenon often clearly visible in a quietly heated soup pot !
A model reported by Rappaport in a 2006 Physical Review paper (Hexagonal convection patterns in atomistic simulated fluids D. C. Rapaport 14 February 2006) produces an almost perfect array of hexagonally shaped convection rolls over a broad ranger of inputs, and under a narrower range of conditions , the model forms a set of linear rolls. The nature of the flow within the convection cells , and quantitative development of the hexagonal pattern arises from realistic algorithims of automated polygon subdivision . Despite the microscopic scale of the modeled interactions , the six sided patterns persist in relatively large simulations with several million particles over a broad scale of integration time steps
The big difference between this model microcosm and a big planet like Saturn is the enormous density and temperature contrast from the visible surface down into the gas giants interior- it makes the Earths crust-mantle core arrangement look very simple indeed , as there ate may different phases with differing ranges of liquidity and viscosity , and several horizons corresponding to the critical points of the various components. Some, like hydrogen, only condense at great pressures. others , like ammonia and methane, may exhibit chemical interactions of mineralogical complexity- continent sized rafts of slushy mixed solids afloat in Saturn's nether regions could greatly alter the simple picture of hexagonal convection cells in an earthly stock-pot. Saturn's supercritical gas atmosphere supports gradients of density as great as pressures are high, and particles and aerosols may be vertically sorted, each different phase , liquid or solid , sinking to the altitude at which it is neutrally buoyant-- most frozen gases are dense than ice. Molecular weight may accordingly play a major role in how solids stack up in gas giant atmospheres in motion.
The matter is further complicated by the wild electrical storm activity near Saturn's poles - the planet's strong magnetic field rives rise to circumpolar bombardment of charged solar wind particles in a manner akin to the Aurora Borealis ,and electrostatic charging effects on cloud particle may give rise via Debye screening to coulomb repulsion, size and charge segregation, and Saturnine natural history could even have a place for electrostatic crystalization of suspended particles into opal-like domains.