Power towers

Let's define the tower function. (denoted as tow(n) )

tow(n）= n↑(n↑(n↑...(n)...n)n)n

Power tower （p-tow(n)(m))

p-tow(1)(n) = tow(tow(n))

p-tow(n)(m) = ptow(n-1)(...(n)...p-tow(n-1)(p-tow(n-1)(m)))

Θ(n) = p-tow(n)(n)

it grows kinda fast.