FANDOM


R Function created by Hyp cos

\(\{0\}\) has growth rate \(\omega\)

\(n\{0\}\) has growth rate \(\omega + n\)

\(\{0\}\{0\}\) has growth rate \(\omega 2\)

\(\underbrace{\{0\}...\{0\}}_{n}\) has growth rate \(\omega n\)

\(\{1\}\) has growth rate \(\omega^2\)

\(\{n\}\) has growth rate \(\omega^{n-1}\)

\(\{\{0\}\}\) has growth rate \(\omega^\omega\)

\(\{n\{0\}\}\) has growth rate \(\omega^{\omega + n}\)

\(\{\underbrace{\{0\}...\{0\}}_{n}\}\) has growth rate \(\omega^{\omega n}\)

\(\{\{n\}\}\) has growth rate \(\omega^{\omega^{n-1}}\)

\(\{\{\{0\}\}\}\) has growth rate \(\omega^\omega\)

\(\underbrace{\{...\{0\}...\}}_{n}\) has growth rate \(^n\omega\)

\(\{0,1\}\) has growth rate \(\varepsilon_0\)

\(n\{0,1\}\) has growth rate \(\varepsilon_0+n\)

\(\underbrace{\{0\}...\{0\}}_{n}\{0,1\}\) has growth rate \(\varepsilon_0+\omega n\)

\(\{n\}\{0,1\}\) has growth rate \(\varepsilon_0+\omega^{n+1}\)

\(\underbrace{\{...\{0\}...\}}_{n}\{0,1\}\) has growth rate \(\varepsilon_0+^n\omega\)

\(\{\{0,1\}\}\{0,1\}\) has growth rate \(\varepsilon_0 2\)

\(\{1\{0,1\}\}\{0,1\}\) has growth rate \(\varepsilon_0 \omega\)

\(\{\{\{0,1\}\}\{0,1\}\}\{0,1\}\) has growth rate \(\varepsilon_0^2\)

\(\{\{\{\{0,1\}\}\{0,1\}\}\{0,1\}\}\{0,1\}\) has growth rate \(\varepsilon_0^{\varepsilon_0}\)

\(\{0,1\}\{0,1\}\) has growth rate \(\varepsilon_1\)

\(\{\{0,1\}\}\{0,1\}\{0,1\}\) has growth rate \(\varepsilon_1+\varepsilon_0\)

\(\{\{0,1\}\{0,1\}\}\{0,1\}\{0,1\}\) has growth rate \(\varepsilon_1 2\)

\(\{\{\{0,1\}\{0,1\}\}\{0,1\}\{0,1\}\}\{0,1\}\{0,1\}\) has growth rate \(\varepsilon_1^2\)

\(\{\{\{\{0,1\}\{0,1\}\}\{0,1\}\{0,1\}\}\{0,1\}\{0,1\}\}\{0,1\}\{0,1\}\) has growth rate \(\varepsilon_1^{\varepsilon_1}\)

\(\{0,1\}\{0,1\}\{0,1\}\) has growth rate \(\varepsilon_2\)

\(\underbrace{\{0,1\}...\{0,1\}}_{n}\) has growth rate \(\varepsilon_{n-1}\)

\(\{1,1\}\) has growth rate \(\varepsilon_\omega\)

\(\{n,1\}\) has growth rate \(\varepsilon_{\omega^n}\)

\(\{\{0\},1\}\) has growth rate \(\varepsilon_{\omega^\omega}\)

\(\{\{\{0,1\}\},1\}\) has growth rate \(\varepsilon_{\varepsilon_0}\)

\(\{\{0,1\},1\}\) has growth rate \(\zeta_0\)

\(\{0,1\}\{\{0,1\},1\}\) has growth rate \(\varepsilon_{\zeta_0 + 1}\)

\(\{1,1\}\{\{0,1\},1\}\) has growth rate \(\varepsilon_{\zeta_0 + \omega}\)

\(\{\{\{\{0,1\},1\}\},1\}\{\{0,1\},1\}\) has growth rate \(\varepsilon_{\zeta_0 2}\)

\(\{1\{\{\{0,1\},1\}\},1\}\{\{0,1\},1\}\) has growth rate \(\varepsilon_{\zeta_0 \omega}\)

\(\{\{\{\{0,1\},1\}\}\{\{\{0,1\},1\}\},1\}\{\{0,1\},1\}\) has growth rate \(\varepsilon_{\zeta_0^2}\)

\(\{\{1\{\{0,1\},1\}\},1\}\{\{0,1\},1\}\) has growth rate \(\varepsilon_{\zeta_0^\omega}\)

\(\{\{\{\{0,1\}\}\{\{0,1\},1\}\},1\}\{\{0,1\},1\}\) has growth rate \(\varepsilon_{\zeta_0^{\varepsilon_0}}\)

\(\{\{\{\{\{0,1\},1\}\}\{\{0,1\},1\}\},1\}\{\{0,1\},1\}\) has growth rate \(\varepsilon_{\zeta_0^{\zeta_0}}\)

\(\{\{\{0,1\}\{\{0,1\},1\}\},1\}\{\{0,1\},1\}\) has growth rate \(\varepsilon_{\varepsilon_{\zeta_0 + 1}}\)

\(\{\{0,1\},1\}\{\{0,1\},1\}\) has growth rate \(\zeta_1\)

\(\{1\{0,1\},1\}\) has growth rate \(\zeta_\omega\)

\(\{\{\{0,1\}\}\{0,1\},1\}\) has growth rate \(\zeta_{\varepsilon_0}\)

\(\{\{\{\{0,1\},1\}\}\{0,1\},1\}\) has growth rate \(\zeta_{\zeta_0}\)

\(\{\{0,1\}\{0,1\},1\}\) has growth rate \(\eta_0\)

\(\{\{1,1\},1\}\) has growth rate \(\varphi(\omega,0)\)

\(\{\{\{\{0,1\}\},1\},1\}\) has growth rate \(\varphi(\varepsilon_0,0)\)

\(\{\{\{\{\{0,1\},1\}\},1\}\) has growth rate \(\varphi(\zeta_0,0)\)

\(\{\{\{0,1\},1\},1\}\) has growth rate \(\Gamma_0\)

See the pattern? \(\{n,m\}\) is same at \([[n]_m]\), because growth rate is same.

\(\{0,0,1\}\) has growth rate \(\psi(\psi_I(0))\)

\(\{0,n,1\}\) has growth rate \(\psi(\psi_{I + n}(0))\)

\(\{0,0,2\}\) has growth rate \(\psi(\psi_{I_2}(0))\)

\(\{0,0,n\}\) has growth rate \(\psi(\psi_{I_n}(0))\)

\(\{0,0,\{0,0,1\}\}\) has growth rate \(\psi(\psi_{I_I}(0))\)

\(\{0,0,0,1\}\) has growth rate \(\psi(\psi_{I(1,0)}(0))\)

\(\{0,x,y,z\}\) has growth rate \(\psi(\psi_{I_{I(1,z - 1) + y} + x}(0))\)

\(\{0,0,0,0,1\}\) has growth rate \(\psi(\psi_{I(2,0)}(0))\)

\(\{0,x,y,z,w\}\) has growth rate \(\psi(\psi_{I_{I(1,I(2,w - 1) + z) + y} + x}(0))\)

\(\{0,0,0,0,0,1\}\) has growth rate \(\psi(\psi_{I(3,0)}(0))\)

\(\{0,0...0,0,1\}\) (n zeroes) has growth rate \(\psi(\psi_{I(n-2,0)}(0))\)

\(\{0\{1*\}1\}\) has growth rate \(\psi(\psi_{I(\omega,0)}(0))\)

\(\{0,1\{1*\}1\}\) has growth rate \(\psi(\psi_{I(\omega,0)+1}(0))\)

\(\{0,0...0,0,1\{1*\}1\}\) (n zeroes) has growth rate \(\psi(\psi_{I(n-2,I(\omega,0)+1)}(0))\)

\(\{0\{1*\}n\}\) has growth rate \(\psi(\psi_{I(\omega,n-1)}(0))\)

\(\{0\{1*\}0,0...0,0,1\}\) (n zeroes) has growth rate \(\psi(\psi_{I(\omega + n,0)}(0))\)

\(\{0\{1*\}0\{1*\}1\}\) has growth rate \(\psi(\psi_{I(\omega 2,0)}(0))\)

\(\{0\{1*\}0...0\{1*\}0\{1*\}1\}\) (n zeroes) has growth rate \(\psi(\psi_{I(\omega n,0)}(0))\)

\(\{0\{n*\}1\}\) has growth rate \(\psi(\psi_{I(\omega^n,0)}(0))\)

\(\{0\{\{0,1\}*\}1\}\) has growth rate \(\psi(\psi_{I(\Omega,0)}(0))\)

\(\{0\{\{0,0...0,0,1\}*\}1\}\) (n zeroes) has growth rate \(\psi(\psi_{I(I(n-2,0),0)}(0))\)

\(\{0\{\{0\{1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(I(\omega,0),0)}(0))\)

\(\{0\{... \{0\{1*\}1\} ...*\}1\}\) (n nested) has growth rate \(\psi(\psi_{I(...I(\omega,0)...,0)}(0))\) (n nested)

\(\{0\{0,1*\}1\}\) has growth rate \(\psi(\psi_{I(1,0,0)}(0))\)

\(\{0\{0,1*\}0,1\}\) has growth rate \(\psi(\psi_{I(1,1,0)}(0))\)

\(\{0\{0,1*\}0\{1*\}1\}\) has growth rate \(\psi(\psi_{I(1,\omega,0)}(0))\)

\(\{0\{0,1*\}0\{0,1*\}1\}\) has growth rate \(\psi(\psi_{I(2,0,0)}(0))\)

\(\{0\{1\{0\{0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(\omega,0,0)}(0))\)

\(\{0\{\{0\{\{0\{0,1*\}1\}*\}1\}\{0\{0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(I(1,0,0),0,0)}(0))\)

\(\{0\{\{0\{0,1*\}1\}\{0\{0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(1,0,0,0)}(0))\)

\(\{0\{\{1\{0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(M^\omega,0)}(0))\)

\(\{0\{\{\{0,1\}\{0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(M^\Omega,0)}(0))\)

\(\{0\{\{\{0\{0,1*\}1\}\{0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(M^M,0)}(0))\)

\(\{0\{\{0,1\{0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(\varepsilon_{M+1},0)}(0))\)

\(\{0\{\{0,0,1\{0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(\psi_{I_{M+1}}(0),0)}(0))\)

\(\{0\{\{0\{0,1*\}2\}*\}1\}\) has growth rate \(\psi(\psi_{I(M_2,0)}(0))\)

\(\{0\{\{0\{0,1*\}0,1\}*\}1\}\) has growth rate \(\psi(\psi_{I(M(1,0),0)}(0))\)

\(\{0\{\{0\{0,1*\}0\{1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(M(\omega,0),0)}(0))\)

\(\{0\{\{0\{0,1*\}0\{0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(\Xi(3,0),0)}(0))\)

\(\{0\{\{0\{1,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(\Xi(\omega,0),0)}(0))\)

\(\{0\{\{0\{0,2*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{I(\Xi(K,0),0)}(0))\)

\(\{0\{\{0\{0,2*\}0\{0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{\Omega(1,1,0,0)}(0))\)

\(\{0\{\{0\{0,2*\}0\{0,2*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{\Omega(2,0,0,0)}(0))\)

\(\{0\{\{0\{0,3*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{\Omega(1,0,0,0,0)}(0))\)

\(\{0\{\{0\{0,n*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{\Omega(\Omega\{2\}^{n+1})}(0))\)

\(\{0\{\{0\{0,\{0\}*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{\Omega(\Omega\{2\}^\omega)}(0))\)

\(\{0\{\{0\{0,0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{\Omega(\Omega\{2\}^{\Omega\{2\}})}(0))\)

\(\{0\{\{0\{0,0,1*\}0,1\}*\}1\}\) has growth rate \(\psi(\psi_{\Omega(\Omega\{2\}(1,0))}(0))\)

\(\{0\{\{0\{0,0,1*\}0\{0,0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{\Omega(\Omega\{2\}(\Omega\{3\}^{\Omega\{3\}}))}(0))\)

\(\{0\{\{0\{1,0,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{\Omega(\Omega\{\omega\})}(0))\)

\(\{0\{\{0\{0,1,1*\}1\}*\}1\}\) has growth rate \(\psi(\psi_{\Omega(\Omega\{0\}\{1\})}(0))\)

More coming soon!

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