Expandotetration refers to the binary function \(a \{\{4\}\} b = \{a,b,4,2\} = \underbrace{a \{\{3\}\} a \{\{3\}\} \ldots \{\{3\}\} a \{\{3\}\} a}_{b \text{ a's}}\), using BEAF.[1]
In the fast-growing hierarchy, \(f_{\omega+4}(n)\) corresponds to expandotetrational growth rate.
Examples[]
- \(\{10,100,4,2\} = \{10,\{10,99,4,2\},3,2\}\) (Kil-Tetoogol, Cookiefonster called the number terporal)
Pseudocode[]
Below is an example of pseudocode for expandotetration.
function expandotetration(a, b):
return hyperexpansion(a, b, 4)
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...