Iterating at eta minor

[JmsNxn]

So, I cut the rendering of my graph, because I was lazy, and it's been about 30 hours, but here's the result of the beta super function for base \(b = e^{i/e^i}\) and period \(2 \pi i\). The black and white areas, are again, the chaos. The small line of them, is where the essential singularities inherited from \(\beta\) appear. The bigger black and white areas are the actual chaos inherited from \(b^z\). And the nice orange areas are where we are holomorphic and unproblematic. We, again, are holomorphic almost everywhere (under an area measure); but there is a lot of chaos/branching such that it's difficult to compute and graph perfectly.

   

This is about \(0 \le \Re(z) \le 15\) and contains a full periodic strip (a strip of width \(2 \pi\)).