
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.[1]
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
Sources
See also
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 · circulationBowers' 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...
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