I ran a test where I changed the spatial resolution of the ring oscillator system (changing the number of spatial buckets while also changing the capacitance and conductance variables accordingly) to make sure that the pattern formation is not an artifact of the integration technique. These images show a 32, 64, and 128 bucket integration in each. It is clear that the spatial resolution matters in the sense that you can see a few small changes (features look temporally sharper, not just spatially), but I don't think that the pattern formation is an artifact. As always, thanks to JHD for help in working out the right parameter transformation -- which he knows like the back of his hand because its equivilent to a transmission line / heat equation.
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