Expandotetration

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.Array Notation by Jonathan Bowers
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 ==
ja:膨張テトレーション
Category:Functions
Category:Binary operators
Category:BEAF
Category:Jonathan Bowers
Category:Extended hyper operators