Powerexpansion

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Powerexpansion refers to the binary function \(a\ \{\{3\}\}\ b = \{a,b,3,2\} = \underbrace{a \{\{2\}\} a \{\{2\}\} \ldots \{\{2\}\} a \{\{2\}\} a}_{\text{b a's}}\), using BEAF.^[1]

In the fast-growing hierarchy, \(f_{\omega+3}(n)\) corresponds to powerexpandal growth rate.

Examples[]

\(\{10,100,3,2\} = \{10,\{10,99,3,2\},2,2\}\) (Kil-Toogol, Cookiefonster called the number powporal)

Pseudocode[]

Below is an example of pseudocode for powerexpansion.

function powerexpansion(a, b):
    return hyperexpansion(a, b, 3)

function hyperexpansion(a, b, n):
    result := a
    repeat b - 1 times:
        if n = 1:
            result := hyper(a,a,result+2)
        else:
            result := hyperexpansion(a, result, n - 1)
    return result

function hyper(a, b, n):
    if n = 1:
        return a + b
    result := a
    repeat b - 1 times:
        result := hyper(a, result, n - 1)
    return result