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Explosion refers to the binary function $$a\ \{\{\{1\}\}\}\ b = \{a,b,1,3\}$$, using BEAF.[1]

Intuitively, explosion can be defined like so:

$a\ \{\{\{1\}\}\}\ b = a\ \{\{a\ \{\{a \ldots \{\{a\}\} \ldots a\}\}\ a\}\}\ a$

with $$b$$ copies of $$a$$ from the center out.

In the fast-growing hierarchy, $$f_{\omega2 +1}(n)$$ approximately corresponds to explodal growth rate.

## Examples

• $$\{10,2,1,3\} = \{10,10,10,2\}$$ (grand tridecal)
• $$\{10,100,1,3\} = \{10,10,\{10,99,1,3\},2\}$$ (Dukil-Googol, Cookiefonster called the number corplodal)

## Pseudocode

Below is an example of pseudocode for explosion.

function explosion(a, b):
result := a
repeat b - 1 times:
result := hyperexpansion(a,a,result)
return result

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