Powerexpansion

A very powerful expansion.

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.

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

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

See also

Hyper operators

Main article: hyper operator

Hyper-operators: successor · addition · multiplication · exponentiation · tetration · pentation · hexation · heptation · octation · enneation · decation (un/doe/tre) · vigintation (doe) · trigintation · centation (tri) · docentation · myriation · circulation
Bowers' extensions: expansion · multiexpansion · powerexpansion · expandotetration · explosion (multi/power/tetra) · detonation · pentonation
Saibian's extensions: hexonation · heptonation · octonation · ennonation · deconation
Tiaokhiao's extensions: megotion (multi/power/tetra) · megoexpansion (multi/power/tetra) · megoexplosion · megodetonation · gigotion (expand/explod/deto) · terotion · more...