Also, here is the run with $a=-0.2$, and 80k particles.
The cold runs with slope <-0.5 appear to exhibit the same flattening in the center as the warm runs. Qualitatively, the warm and cold appear indistinguishable. However, runs with initial slope >-0.5 do not appear to retain their original scaling, and they do not go to the attractor behavior, even when they are cold. The run with initial slope >0 appears to do something like the attractor behavior, oddly enough.
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