And now, finally, the picture of regular tetration!
The red lines are \( {^{0.5} x} \), \( {^{1.5} x} \), \( {^{2.5} x} \), \( {^{3.5} x} \).
The blue lines are \( x, x^x, x^{x^x}, x^{x^{x^x}} \)
And the green line is the limit \( \lim_{n\to\infty} ({^n x}) \).
In the range \( 0<x<e^{1/e} \).
I computed the graphs with the powerseries development with 20 summands and 500 bits precision.
The same picture with x and y equally scaled:
The red lines are \( {^{0.5} x} \), \( {^{1.5} x} \), \( {^{2.5} x} \), \( {^{3.5} x} \).
The blue lines are \( x, x^x, x^{x^x}, x^{x^{x^x}} \)
And the green line is the limit \( \lim_{n\to\infty} ({^n x}) \).
In the range \( 0<x<e^{1/e} \).
I computed the graphs with the powerseries development with 20 summands and 500 bits precision.
The same picture with x and y equally scaled:
