User blog comment:Wythagoras/Dollar function part 2/@comment-5529393-20130616054606/@comment-5529393-20130616073721

My first quibble with yor comparisons is here:

a$[0,[0,1]_2] ≈ f_phi(1,1,0)(a)

a$[0,1[0,1]_2] ≈ f_phi(1,1,1)(a)

a$[0,0,1]_2 ≈ f_phi(1,2,0)(a)

a$[0,[0,1]_2] ≈ f_phi(2,0,0)(a)

a$[0,[[0,1]_2]] ≈ f_phi(1,0,0,0)(a)

a$[0,[[[0,1]_2]]] ≈ f_phi(1,0,0,0,0)(a)

a$[0,[1,1]_2] ≈ f_theta(Omega^omega)(a)

Previously, surrounding a single entry with a pair of brackets applied the function x -> omega^x. So I would expect something similar to happen here. How did you get each pair of brackets leading to a higher variable in phi?