Ackermann function over the real numbers?

Question

I was thinking about the Ackermann function, and whether or not it is possible to extend this function over the positive real numbers in Python.

def naive_ackermann(m, n):
    calls = 0
    calls += 1
    if m == 0:
        return n + 1
    elif n == 0:
        return naive_ackermann(m - 1, 1)
    else:
        return naive_ackermann(m - 1, naive_ackermann(m, n - 1))

 print(naive_ackermann(3,4))

I found somebody asked about this concept here on Math Overflow. Can somebody write a continuous Ackermann function that goes over the real numbers? I want to do this so I can see a function that goes between exponentation and tetration.