This is FGH version of Dollar Function.

## Bracket Notation

1 has growth rate 0 (equal!)

[0] has growth rate 1 (equal!), because n$[0]# = n$n#

[1] has growth rate 2 (equal!), because [@+1] = [@]...[@].

[n] has growth rate n+1 (equal!)

[[0]] has growth rate w, because it nested.

[1[0]] has growth rate w+1, because [@+1 #] = [@ #]...[@ #].

[n[0]] has growth rate w+n

[[0][0]] has growth rate w*2, because [[0] #] = [w #]

[[0]...[0]] (n [0]'s) has growth rate w*n

[[1]] has growth rate w^2

[[1]...[1]] (n [1]'s) has growth rate w^2*n

[[1]] has growth rate w^3

[[n]] has growth rate w^{n+1}

[[[0]]] has growth rate w^w

[[[1]]] has growth rate w^w^2

[[[n]]] has growth rate w^w^{n+1}

[[[[0]]]] has growth rate w^w^w

[...[0]...] (n nested) has growth rate w^^{n-1}

## Extended Bracket Notation

[[0]_{2}] has growth rate e(0), because f([0]_{2}) = f([...f([0])...]).

[n[0]_{2}] has growth rate e(0)+n

[[0][0]_{2}] has growth rate e(0)+w

[[[0]][0]_{2}] has growth rate e(0)+w^w

[[...[0]...][0]_{2}] (n nested) has growth rate e(0)+w^^n

[[[0]_{2}][0]_{2}] has growth rate e(0)*2

[[[0][0]_{2}][0]_{2}] has growth rate e(0)*w

[[[[0]_{2}][0]_{2}][0]_{2}] has growth rate e(0)^2

[[[[[0]_{2}][0]_{2}][0]_{2}][0]_{2}] has growth rate e(0)^e(0)

[[...[[0]_{2}]...][0]_{2}] (n*2 nested) has growth rate e(0)^^n

[[...[[0]_{2}]...][0]_{2}] (n*2+1 nested) has growth rate e(0)^...^e(0)^2 (n e(0)'s)

[[0]_{2}[0]_{2}] has growth rate e(1)

[[0]_{2}...[0]_{2}] (n [0]_{2}'s) has growth rate e(n-1)

[[1]_{2}] has growth rate e(w), because [@+1 #]_{@} = [@ #]_{@}...[@ #]_{@}.

[[0]_{2}...[0]_{2}[1]_{2}] (n [0]_{2}'s) has growth rate e(w+n)

[[1]_{2}[1]_{2}] has growth rate e(w*2)

[[1]_{2}...[1]_{2}] (n [1]_{2}'s) has growth rate e(w*n)

[[2]_{2}] has growth rate e(w^2)

[[n]_{2}] has growth rate e(w^n)

[[[0]]_{2}] has growth rate e(w^w)

[[...[0]...]_{2}] (n nested) has growth rate e(w^^n)

[[[[0]_{2}]]_{2}] has growth rate e(e(0))

[[[[[[0]_{2}]]_{2}]_{2}] has growth rate e(e(e(0)))

[[[...[0]_{2}]...]_{2}] (n 2's) has growth rate e(...(e(0)...) (n nested)

[[[0]_{2}]_{2}] has growth rate z(0)

[[0]_{2}[[0]_{2}]_{2}] has growth rate e(z(0)+1)

[[1]_{2}[[0]_{2}]_{2}] has growth rate e(z(0)+w)

[[[[0]_{2}]]_{2}[[0]_{2}]_{2}] has growth rate e(z(0)+e(0))

[[[[[0]_{2}]_{2}]]_{2}[[0]_{2}]_{2}] has growth rate e(z(0)*2)

[[[0]_{2}]_{2}[[0]_{2}]_{2}] has growth rate z(1)

[[1[0]_{2}]_{2}] has growth rate z(w)

[[[[0]_{2}][0]_{2}]_{2}] has growth rate z(e(0))

[[[[[0]_{2}]_{2}][0]_{2}]_{2}] has growth rate z(z(0))

[[[0]_{2}[0]_{2}]_{2}] has growth rate eta(0)

[[[1]_{2}]_{2}] has growth rate phi(w,0)

[[[[[0]_{2}]]_{2}]_{2}] has growth rate phi(e(0),0)

[[[[0]_{2}]_{2}]_{2}] has growth rate gamma(0)

[[[[0]_{2}[0]_{2}]_{2}]_{2}] has growth rate phi(1,0,0,0)

[[[[0]_{2}...[0]_{2}]_{2}]_{2}] (n [0]_{2}'s) has growth rate theta(W^n)

[[[[1]_{2}]_{2}]_{2}] has growth rate SVO

[[[[n]_{2}]_{2}]_{2}] has growth rate theta(W^w^n)

[[[[[0]]_{2}]_{2}]_{2}] has growth rate theta(W^w^w)

[[[[[[0]_{2}]]_{2}]_{2}]_{2}] has growth rate theta(W^e(0))

[[[[[[[0]_{2}]_{2}]]_{2}]_{2}]_{2}] has growth rate theta(W^gamma(0))

[[[[[[[[0]_{2}]_{2}]_{2}]]_{2}]_{2}]_{2}] has growth rate theta(W^SVO)

[[[[[0]_{2}]_{2}]_{2}]_{2}] has growth rate LVO

[[[[[1]_{2}]_{2}]_{2}]_{2}] has growth rate theta(W^W^w)

[[[[[[0]_{2}]_{2}]_{2}]_{2}]_{2}] has growth rate theta(W^W^W)

[[...[0]_{2}]...]_{2}] (n nested) has growth rate theta(W^^(n-2))

[[0]_{3}] has growth rate BHO, because f([0]_{@+1}) = f([...f([0]_{@})...]_{@}).

[[0]_{3}[0]_{3}] has growth rate theta(e(W+1),1)

[[1]_{3}] has growth rate theta(e(W+1),w)

[[[[0]_{2}]]_{3}] has growth rate theta(e(W+1),w)

[[[[0]_{3}]]_{3}] has growth rate theta(e(W+1),BHO)

[[[0]_{2}]_{3}] has growth rate theta(e(W+1)+1)

[[[[0]_{2}]_{2}]_{3}] has growth rate theta(e(W+1)+W)

[[[[[0]_{2}]_{2}]_{2}]_{3}] has growth rate theta(e(W+1)+W^W)

[[[[0]_{3}]_{2}]_{3}] has growth rate theta(e(W+1)*2)

[[[0]_{3}]_{3}] has growth rate theta(z(W+1))

[[[1]_{3}]_{3}] has growth rate theta(phi(w,W+1))

[[[[0]_{2}]_{3}]_{3}] has growth rate theta(phi(W,1))

[[[[0]_{3}]_{3}]_{3}] has growth rate theta(W_2)

[[[[[0]_{3}]_{3}]_{3}]_{3}] has growth rate theta(W_2^W_2)

[[0]_{4}] has growth rate theta(e(W_2+1))

[[[0]_{4}]_{4}] has growth rate theta(z(W_2+1))

[[[[0]_{4}]_{4}]_{4}] has growth rate theta(W_3)

[[0]_{n}] has growth rate theta(e(W_{n-2}+1))

[[0]_{[0]}] has growth rate theta(W_w)

[[0]_{1[0]}] has growth rate TBF

[[0]_{n[0]}] has growth rate theta(e(W_{w+n-1}+1))

[[0]_{[0][0]}] has growth rate theta(W_{w*2})

[[0]_{[0]...[0]}] (n [0]'s) has growth rate theta(W_{w*n})

[[0]_{[1]}] has growth rate theta(W_w^2)

[[0]_{[n]}] has growth rate theta(W_w^{n+1})

[[0]_{[[0]]}] has growth rate theta(W_w^w)

[[0]_{[[0]2]}] has growth rate theta(W_e(0))

[[0]_{[[0]3]}] has growth rate theta(W_BHO)

[[0]_{[[0]n]}] has growth rate theta(W_theta(e(W_{n-2}+1)))

[[0]_{[[0][0]]}] has growth rate theta(W_theta(W_w))

[[0]_{[...[0][0]...]}] (n subscripts) has growth rate theta(W_...theta(W_w)...) (n W's)

[[0]_{[0]2}] has growth rate theta(W_W)

[[0]_{[0]2...[0]2}] (n [0]_{2}'s) has growth rate theta(W_{W*n})

[[0]_{[1]2}] has growth rate theta(W_{W*w})

[[0]_{[[0]2]2}] has growth rate theta(W_W^2)

[[0]_{[0]3}] has growth rate theta(W_e(W+1))

[[0]_{[0][0]}] has growth rate theta(W_W_w)

[[0]_{...[0]}] (n [0]'s) has growth rate theta(W_..._w) (n-1 W's)

## Linear Array Notation

[[[0],1]] has growth rate psi(psi_I(0))

[[[0]...[0],1]] (n [0]'s) has growth rate psi(psi_I(n-1))

[[[1],1]] has growth rate psi(psi_I(w))

[[[0]_{2},1]] has growth rate psi(psi_I(W))

[[[0]_{3},1]] has growth rate psi(psi_I(e(W+1)))

[[[0]_{[0]},1]] has growth rate psi(psi_I(W_w))

[[[0]_{[0][0]},1]] has growth rate psi(psi_I(W_W_w))

[[[[0],1],1]] has growth rate psi(psi_I(psi_I(0)))

[[[0,1]_{2},1]] has growth rate psi(psi_I(I))

[[[[0],1][0,1]_{2},1]] has growth rate psi(psi_I(I+psi_I(0)))

[[[0,1]_{2}[0,1]_{2},1]] has growth rate psi(psi_I(I*2))

[[[0,1]_{2}...[0,1]_{2},1]] (n [0,1]_{2}'s) has growth rate psi(psi_I(I*n))

[[[1,1]_{2},1]] has growth rate psi(psi_I(I*w))

[[[[0]_{2},1]_{2},1]] has growth rate psi(psi_I(I*W))

[[[[0]_{[0]},1]_{2},1]] has growth rate psi(psi_I(I*W_w))

[[[[0],1],1]_{2},1]] has growth rate psi(psi_I(I*psi_I(0)))

[[[0,1]_{2},1]_{2},1]] has growth rate psi(psi_I(I^2))

[[[[0,1]_{2},1]_{2},1]_{2},1]] has growth rate psi(psi_I(I^I))

[[[0,1]_{3},1]] has growth rate psi(psi_I(e(I+1)))

[[[0,1]_{2}[0,1]_{3},1]] has growth rate psi(psi_I(e(I+1)+I))

[[[[0,1]_{3},1]_{2}[0,1]_{3},1]] has growth rate psi(psi_I(e(I+1)*2))

[[[0,1]_{3}[0,1]_{3},1]] has growth rate psi(psi_I(e(I+2)))

[[[1,1]_{3},1]] has growth rate psi(psi_I(e(I+w)))

[[[[0]_{2},1]_{3},1]] has growth rate psi(psi_I(e(I+W)))

[[[[0,1]_{2},1]_{3},1]] has growth rate psi(psi_I(e(I*2)))

[[[[[0]_{2},1]_{2},1]_{3},1]] has growth rate psi(psi_I(e(I*W)))

[[[[[0,1]_{2},1]_{2},1]_{3},1]] has growth rate psi(psi_I(e(I^2)))

[[[[[0,1]_{3},1]_{2},1]_{3},1]] has growth rate psi(psi_I(e(e(I+1))))

[[[[0,1]_{3},1]_{3},1]] has growth rate psi(psi_I(z(I+1))) or psi(psi_I(theta_{I+1}(2)))

[[[[0,1]_{3}[0,1]_{3},1]_{3},1]] has growth rate psi(psi_I(eta(I+1))) or psi(psi_I(theta_{I+1}(3)))

[[[[1,1]_{3},1]_{3},1]] has growth rate psi(psi_I(phi(w,I+1))) or psi(psi_I(theta_{I+1}(w)))

[[[[[0]_{2},1]_{3},1]_{3},1]] has growth rate psi(psi_I(phi(W,I+1))) or psi(psi_I(theta_{I+1}(W)))

[[[[[0]_{[0]},1]_{3},1]_{3},1]] has growth rate psi(psi_I(phi(W,I+1))) or psi(psi_I(theta_{I+1}(W_w)))

[[[[[[0],1],1]_{3},1]_{3},1]] has growth rate psi(psi_I(theta_{I+1}(psi_I(0))))

[[[[[[0,1]_{2},1],1]_{3},1]_{3},1]] has growth rate psi(psi_I(theta_{I+1}(psi_I(I))))

[[[[[[0,1]_{3},1],1]_{3},1]_{3},1]] has growth rate psi(psi_I(theta_{I+1}(psi_I(e(I+1)))))

[[[[[0,1]_{2},1]_{3},1]_{3},1]] has growth rate psi(psi_I(theta_{I+1}(I)))

[[[[[[0,1]_{3},1]_{2},1]_{3},1]_{3},1]] has growth rate psi(psi_I(theta_{I+1}(e(I+1))))

[[[[[[[0,1]_{3},1]_{3},1]_{2},1]_{3},1]_{3},1]] has growth rate psi(psi_I(theta_{I+1}(e(I+1))))

[[[[[[[1,1]_{3},1]_{3},1]_{2},1]_{3},1]_{3},1]] has growth rate psi(psi_I(theta_{I+1}(theta_{I+1}(w))))

[[[[[[[[0]_{2},1]_{3},1]_{3},1]_{2},1]_{3},1]_{3},1]] has growth rate psi(psi_I(theta_{I+1}(theta_{I+1}(W))))

[[[[[[[[[0],1],1]_{3},1]_{3},1]_{2},1]_{3},1]_{3},1]] has growth rate psi(psi_I(theta_{I+1}(theta_{I+1}(psi_I(0)))))

[[[[[[[[0,1]_{2},1]_{3},1]_{3},1]_{2},1]_{3},1]_{3},1]] has growth rate psi(psi_I(theta_{I+1}(theta_{I+1}(I))))

[[[[[[[[[[[0,1]_{2},1]_{3},1]_{3},1]_{2},1]_{3},1]_{3},1]_{2},1]_{3},1]_{3},1]] has growth rate psi(psi_I(theta_{I+1}(theta_{I+1}(theta_{I+1}(I)))))

[[[[[0,1]_{3},1]_{3},1]_{3},1]] has growth rate psi(psi_I(W_{I+1}))

[[[[[[0,1]_{3},1]_{3},1]_{3},1]_{3},1]] has growth rate psi(psi_I(W_{I+1}^W_{I+1}))

[[[0,1]_{4},1]] has growth rate psi(psi_I(e(W_{I+1})))

[[[0,1]_{n},1]] has growth rate psi(psi_I(e(W_{I+n-3})))

[[[0,1]_{[0]},1]] has growth rate psi(psi_I(W_{I+w}))

[[[0,1]_{[0]2},1]] has growth rate psi(psi_I(W_{I+W}))

[[[0,1]_{[0][0]},1]] has growth rate psi(psi_I(W_{I+W_w}))

[[[0,1]_{[[0],1]},1]] has growth rate psi(psi_I(W_{I+psi_I(0)}))

[[[0,1]_{[[0,1]2,1]},1]] has growth rate psi(psi_I(W_{I+psi_I(I)}))

[[[0,1]_{[[0,1]n,1]},1]] has growth rate psi(psi_I(W_{I+psi_I(e(W_{I+n-3}))}))

[[[0,1]_{[[0,1][0],1]},1]] has growth rate psi(psi_I(W_{I+psi_I(W_{I+w})}))

[[[0,1]_{[[0,1][[0],1],1]},1]] has growth rate psi(psi_I(W_{I+psi_I(W_{I+psi_I(0)})}))

[[[0,1]_{[[0,1][[0,1][0],1],1]},1]] has growth rate psi(psi_I(W_{I+psi_I(W_{I+psi_I(W_{I+w})})}))

[[[0,1]_{[[0,1][[0,1][[0],1],1],1]},1]] has growth rate psi(psi_I(W_{I+psi_I(W_{I+psi_I(W_{I+psi_I(0)})})}))

[[[0,1]_{[0,1]2},1]] has growth rate psi(psi_I(W_{I*2}))

[[[0,1]_{[0,1]2...[0,1]2},1]] (n [0,1]_{2}'s) has growth rate psi(psi_I(W_{I*(n+1)}))

[[[0,1]_{[n,1]2},1]] has growth rate psi(psi_I(W_{I*w^n}))

[[[0,1]_{[[0,1]2,1]2},1]] has growth rate psi(psi_I(W_{I^2}))

[[[0,1]_{[0,1]2[[0,1]2,1]2},1]] has growth rate psi(psi_I(W_{I^2+I}))

[[[0,1]_{[[0,1]2,1]2[[0,1]2,1]2},1]] has growth rate psi(psi_I(W_{I^2*2}))

[[[0,1]_{[1[0,1]2,1]2},1]] has growth rate psi(psi_I(W_{I^2*w}))

[[[0,1]_{[[0,1]2[0,1]2,1]2},1]] has growth rate psi(psi_I(W_{I^3}))

[[[0,1]_{[[1,1]2,1]2},1]] has growth rate psi(psi_I(W_{I^w}))

[[[0,1]_{[[[0,1]2,1]2,1]2},1]] has growth rate psi(psi_I(W_{I^I}))

[[[0,1]_{[[0,1]3,1]2},1]] has growth rate psi(psi_I(W_e(I+1)))

[[[0,1]_{[[[0,1]3,1]3,1]2},1]] has growth rate psi(psi_I(W_theta_{I+1}(2)))

[[[0,1]_{[[[[0,1]2,1]3,1]3,1]2},1]] has growth rate psi(psi_I(W_theta_{I+1}(I)))

[[[0,1]_{[[[[0,1]3,1]3,1]3,1]2},1]] has growth rate psi(psi_I(W_theta_{I+1}(W_{I+1})))

[[[0,1]_{[[0,1]4,1]2},1]] has growth rate psi(psi_I(W_theta_{I+1}(e(W_{I+1}+1))))

[[[0,1]_{[[0,1][0],1]2},1]] has growth rate psi(psi_I(W_theta_{I+1}(W_{I+w})))

[[[0,1]_{[0,1]3},1]] has growth rate psi(psi_I(W_W_{I+1}))

[[[0,1]_{[0,1][0]},1]] has growth rate psi(psi_I(W_W_{I+w}))

[[[0,1]_{[0,1][[0],1]},1]] has growth rate psi(psi_I(W_W_{I+psi_I(0)}))

[[[0,1]_{[0,1][0,1]2},1]] has growth rate psi(psi_I(W_W_{I*2}))

[[[0],2]] has growth rate psi(psi_{I_2}(0))

[[[0,1]_{2},2]] has growth rate psi(psi_{I_2}(I))

[[[0,2]_{2},2]] has growth rate psi(psi_{I_2}(I_2))

[[[0,2]_{2}[0,2]_{2},2]] has growth rate psi(psi_{I_2}(I_2*2))

[[[1,2]_{2},2]] has growth rate psi(psi_{I_2}(I_2*w))

[[[[0]_{2},2]_{2},2]] has growth rate psi(psi_{I_2}(I_2*W))

[[[[0,1]_{2},2]_{2},2]] has growth rate psi(psi_{I_2}(I_2*I))

[[[[0,2]_{2},2]_{2},2]] has growth rate psi(psi_{I_2}(I_2^2))

[[[0,2]_{3},2]] has growth rate psi(psi_{I_2}(e(I_2+1)))

[[[0,2]_{[0]},2]] has growth rate psi(psi_{I_2}(W_{I_2+w}))

[[[0,2]_{[0]2},2]] has growth rate psi(psi_{I_2}(W_{I_2+W}))

[[[0,2]_{[0,1]2},2]] has growth rate psi(psi_{I_2}(W_{I_2+I}))

[[[0,2]_{[0,2]2},2]] has growth rate psi(psi_{I_2}(W_{I_2*2}))

[[[0,2]_{[0,2][0]},2]] has growth rate psi(psi_{I_2}(W_W_{I_2+w}))

[[[0,2]_{[0,2][0,1]2},2]] has growth rate psi(psi_{I_2}(W_W_{I_2+I}))

[[[0,2]_{[0,2][0,2]2},2]] has growth rate psi(psi_{I_2}(W_W_{I_2*2}))

[[[0],3]] has growth rate psi(psi_{I_3}(0))

[[[0],n]] has growth rate psi(psi_{I_n}(0))

[[[0],[0]]] has growth rate psi(psi_{I_w}(0))

[[[0],[0]_{2}]] has growth rate psi(psi_{I_W}(0))

[[[0],[0,1]_{2}]]] has growth rate psi(psi_{I_I}(0))

[[[0],[[0],[0]]]] has growth rate psi(psi_{I_I_w}(0))

[[[0],[0,1]_{2}]] has growth rate psi(psi_{I(1,0)}(0))

[[[0],[0,1]_{2}[0,1]_{2}]] has growth rate psi(psi_{I(1,0)}(1))

[[[0],[1,1]_{2}]] has growth rate psi(psi_{I(1,0)}(w))

[[[0],[[[0],1],1]_{2}]] has growth rate psi(psi_{I(1,0)}(psi_I(0)))

[[[0],[[0],[0]]_{2}]] has growth rate psi(psi_{I(1,0)}(I_w))

[[[0],[[0],[0,1]_{2}]_{2}]] has growth rate psi(psi_{I(1,0)}(I(1,0)))

I don't know of limit growth rate of linear array notation. I predict psi(psi_{Xi(w,0)}(0)).

So, can you convert Dollar Function to FGH?

## Dimensional Arrays

[[[0](1)1]] has growth rate psi(psi_{Xi(w,0)}(0))

[[[[0](1)1](1)1]] has growth rate psi(psi_{Xi(Xi(w,0),0)}(0))

[[[0(1)1]_{2}(1)1]] has growth rate psi(psi_{Xi(K,0)}(0))

[[[0(1)1]_{2}[0(1)1]_{2}(1)1]] has growth rate psi(psi_{Xi(K*2,0)}(0))

[[[0(1)1]_{3}(1)1]] has growth rate psi(psi_{Xi(e(K+1),0)}(0))

[[[0],1(1)1]] has growth rate psi(psi_{W(W{2}^3+W{2})}(0))

[[[0](1)2]] has growth rate psi(psi_{W(W{2}^3*2)}(0))

[[[0](1)0,1]] has growth rate psi(psi_{W(W{2}^4)}(0))

[[[0](1)0(1)1]] has growth rate psi(psi_{W(W{2}^w)}(0))

[[[0](2)1]] has growth rate psi(psi_{W(W{2}^W{2}^w)}(0))

[[[0]([0])1]] has growth rate psi(psi_{W(W{2}^W{2}^W{2}^w)}(0))

## Nested Array Notation

[[[0](0,1)1]] has growth rate psi(psi_{W(e(W{2}+1))}(0))