User blog:Cookiefonster/Left-arrow notation?

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:


 * 1) is anything, can be nothing

a<--b = a^b


 * 1) <--1 = #


 * 1) <--1<--a = #


 * 1) <--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.