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I had an idea: 

You are all familiar with up-arrow notation, and down arrow notation, and chain arrow notation. Those can be thought of as up, down, and right arrows. But what is left-arrow notation?

I present: left-arrow notaiton, which has the rules:

# is anything, can be nothing

a<--b = a^b

#<--1 = #

#<--1<--a = #

#<--a<--b<--c = #<--(#<--a<--b-1<--c)<--a<--c-1

Example:

3<--3<--2<--2

= 3<--(3<--3<--1<--2)<--3<--1

= 3<--27<--3

=(3<--26<--3)<--3<--2

= ((3<--25<--3)<--3<--2)<--3<--2

etc

This number ~ 10^^27 w/ Hypercalc if i'm not mistaken.

idk much about the behavior, but it seems rather erratic. gonna try some more examples later.

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