is an interesting and important function, so what we get if we do the same with tetration: ?

I put i.x in the polynomials obtained by minimizing the error , and drawed the imaginary vs real part:

These functions probably are periodical, but my polynomials only converge on -1≤x≤1, so, be careful about looking at values outside of that range.

For example, this chart is only valid in the range 0..4, for real and -4..3 for the imaginary axis.

This is base

This is base

This is a zoom in the curl transition

base e, or something close, seems to delimit the transition towards the negative axis:

Many of these seem to be described by something like

I put i.x in the polynomials obtained by minimizing the error , and drawed the imaginary vs real part:

These functions probably are periodical, but my polynomials only converge on -1≤x≤1, so, be careful about looking at values outside of that range.

For example, this chart is only valid in the range 0..4, for real and -4..3 for the imaginary axis.

This is base

This is base

This is a zoom in the curl transition

base e, or something close, seems to delimit the transition towards the negative axis:

Many of these seem to be described by something like