User blog:GamesFan2000/Hyper Tower Notation, Pt. 2

'''It’s now time for the second part of Hyper Tower Notation. I’ll be defining how multi-symbol separators will decompose. Last time, we left off at n#nn, and found a growth limit of w^w. The behaviour of the expressions won’t be fundamentally changed by having multiple symbols in a separator, so I’ll just get into each case:'''


 * 1) #k+1#m#p...→#k#m#p...
 * 2) ##...##→#n#n…#n
 * 3) ##...##k+1#m#p...→#n#n…#n#k#m#p...

Let’s see how those work in practice:

3##3=3#33#33^(3##2)=3#33#33^(3#33#33^(3#33#33))

3#2#3=3##3##3^(3#2#2)=3##3##3^(3##3##3^(3##3##3))

3##2#3=3#3##3#3##3^(3#3##3#3##3^(3#3##3#3##3))

I’ll now compare the notation to the FGH:

n##n~w^w

n##n#n~w^w+1

n##n#2n~w^w+w

n##n#3n~w^w+w^2

n##n##n~w^w*2

n##n##n##n~w^w*3

n#2#n~w^(w+1)

n#3#n~w^(w+2)

n##2n~w^(w*2)

n##3n~w^(w*3)

n###n~w^w^2

n####n~w^w^3

n##...##n~w^w^w