User:Wythagoras/Rado's sigma function/BB(7,4)

\(\Sigma(7,4) > 2\uparrow\uparrow(2.4\cdot10^{26})\) 0 _ 2 l 1 0 2 2 r 0 0 1 2 r 1 0 3 2 l 0 1 _ _ r 0 1 2 1 l 1 1 1 1 r 2 1 3 2 l 3 2 _ 3 l 1 2 2 1 r 1 2 1 2 l 2 2 3 _ l 2 3 3 3 l 3 3 2 2 l 3 3 _ 3 l 6 4 _ 1 r halt 4 2 2 l 5 5 3 1 l 5 5 1 1 l 5 5 _ 1 l 6 6 _ 3 r 6 6 3 _ l 6 6 1 3 l 3 6 2 1 r 4

Explanation
This combines an machine with 3 states and 4 colors, which outputs: 222...222 (~2.4*10^26 2's) Then for each 1 the number of ones will be duplicated, and for each 2 all the 3s will be changed into ones, giving a function comparable to \(2^n\). It uses LittlePeng9's duplication machine.