Googology Wiki
Register
Advertisement
Googology Wiki

View full site to see MathJax equation

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[]

Advertisement