Explosion

Explosion refers to the binary function \(a\ \{\{\{1\}\}\}\ b = \{a,b,1,3\}\), using BEAF.Array Notation by Jonathan Bowers
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
== Sources ==
== See also ==
ja:爆発
Category:Functions
Category:Binary operators
Category:BEAF
Category:Jonathan Bowers
Category:Extended hyper operators