Hmm, now that's odd. I tried walking a base around \( \eta \) and monitoring the sickel to see what happened to it. I walked it from \( e \) up to \( e + 0.5i \), left to \( 1.3 + 0.5i \), down to \( 1.3 - 0.5i \) and finally right to \( 2.25 - 0.5i \), crossing the STR boundary twice. I noticed nothing weird at the second boundary crossing...
EDIT: I've continued it further, to \( e - 0.5i \) and then back up to \( e \), and noticed nothing "singularitylike". However, I did find that on returning to \( e \), I was once again at a sickel between the two principal fixed points, only now they had been swapped. Wtf? Does this mean there's a merged tetrational using the two fixed points in opposite order? That'd be very bizarre. Or, perhaps, this in fact indicates that there is a failure somewhere (probably at the STR boundary) and the continuation is in fact not possible.
EDIT: I've continued it further, to \( e - 0.5i \) and then back up to \( e \), and noticed nothing "singularitylike". However, I did find that on returning to \( e \), I was once again at a sickel between the two principal fixed points, only now they had been swapped. Wtf? Does this mean there's a merged tetrational using the two fixed points in opposite order? That'd be very bizarre. Or, perhaps, this in fact indicates that there is a failure somewhere (probably at the STR boundary) and the continuation is in fact not possible.
