Fish number 6

Fish number 6 (F6) is a number defined by Japanese googologist Fish in 2007.Fish, Googology in Japan - exploring large numbers (2013) It is largest of the computable Fish numbers.
Fish function 6 uses m(m,n) map.
Definition and growth rate of Fish function 6, \(F_6(x)\), is
\begin{eqnarray*}
F_6(x) &:=& m(x,2)m(x,1)(x) \\
F_6(x) &\approx& f_{\zeta_0}(x)
\end{eqnarray*}
Then Fish number 6 is defined as:
\[F_6 := F_6^{63}(3)\]
Therefore, Fish number 6 is greater than Fish number 5 and is approximately \(f_{\zeta_0+1}(63)\).
== Approximations ==
Fish number 6 is comparable to grangol-carta-tethracross \(\approx f_{\zeta_0+1}(100)\).
Notation 	Approximation
BEAF (intended) 	\(\{63,63,2 (X \uparrow\uparrow X \uparrow 2) 2\}\)Using particular notation \(\{a,b (X \uparrow\uparrow X \uparrow 2) 2\}\) for \(X \uparrow\uparrow X \uparrow 2 \&\ a\)
Bird's array notation 	\(\{63,63,2 [1 \backslash 1 \backslash 2] 2\}\)
Bashicu matrix system version 4 	(0,0)(1,1)(2,1)(1,0)[8]
Extended Cascading-E notation 	E63#^^##63#63
Fast-growing hierarchy 	\(f_{\zeta_0+1}(63)\)
Hardy hierarchy 	\(H_{\zeta_0 \omega}(63)\)
Slow-growing hierarchy (using Buchholz's function)	\(g_{\psi_0(\Omega_2^2 + \psi_1(\Omega_2^2))}(63)\)
==Computer programs==
There are computer programs for calculating Fish number 6 and its variant by Okkuu:
*Okkuu, C++ program for calculating Fish number 6
*Okkuu, C++ program for calculating a version of Fish number 6
== Sources==
==See also==
ja:ふぃっしゅ数バージョン6
Category:Numbers
Category:Googology in Asia
Category:Binary phi level
Category:Fish number
Category:Numbers by Fish
Category:Eponymous numbers