Oh guys, long time its ago since this thread was started.

But now I am finally able to post the premiere graph of balanced selftetration, i.e. x[4]x where [4] is the balanced tetration.

This was possible by a mixture of recurrent and power series formula.

And this is the result:

blue: x[2]x = x*x = x^2

green: x[3]x = x^x

red: x[4]x

Note that 2[n]2 = 4 in balanced hyperoperations of arbitrary rank n.

and here with aspect ratio 1 and the identity in black as comparison, including 0:

But now I am finally able to post the premiere graph of balanced selftetration, i.e. x[4]x where [4] is the balanced tetration.

This was possible by a mixture of recurrent and power series formula.

And this is the result:

blue: x[2]x = x*x = x^2

green: x[3]x = x^x

red: x[4]x

Note that 2[n]2 = 4 in balanced hyperoperations of arbitrary rank n.

and here with aspect ratio 1 and the identity in black as comparison, including 0: