User:Wythagoras/Rado's sigma function/BB(6,4)

\(\Sigma(6,4) > 2\uparrow\uparrow2047\) 0 _ 3 l 1 0 1 3 l 0 0 2 3 l 0 0 3 1 r 0 1 _ 3 r 1 1 1 2 l 1 1 2 2 l 3 1 3 3 r 0 2 _ 3 r 2 2 3 _ l 2 2 1 3 l 3 2 2 1 r 4 3 3 3 l 3 3 _ 3 l 2 4 _ _ r halt 4 2 2 l 5 5 3 1 l 5 5 1 1 l 5 5 _ 1 l 2

Explanation
The first part is the machine for \(\Sigma(2,4)\). It outputs: 3222...2223 (2046 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.

There are many unused colours in state 3, 4 and 5. There is clearly some room for improvement!