Wednesday, March 11
Visitors from infinity, reprise
When I posted my Visitors from infinity on New Year's day, I had been working with a database of two-and-a-half billion (10^9) numerical correspondences. On February 6, I completed a computation taking the Yellowstone permutation to five billion — but only as another two-and-a-half-billion-term file, because I cannot (with only 64 GB RAM) store all five billion terms into Mathematica at the same time.
The limitation of that shortcoming is that when I map n into A098550(n) or A098550(n) into n, any time the mapping crosses over into the other-file regime I have to reboot Mathematica with that other file. Just the reading of it takes about nine hours and working the 302 currently unknown-outcome trajectories (with minima < 10^4) backwards (towards the left in the graph) might take another day or two on each reading. But I finally completed the task yesterday! The picture shows all 302 orbits with their minima synced (although many of the more-or-less random-hued paths are obscured by others).
One can see in the graph that my backward reach is limited to five billion, while moving forward (to the right) always ends in a point beyond (sometimes well beyond) that. If you are interested in the raw data, it is still here — and I have placed individual graphs for all 302 chains here.