User blog:Ynought/LS function

You take an infinite square.At every unit at the bottom most horizontal line there is a vertical line that is also infinite and goes upwards and at every unit at the left most vertical line there is a horizontal line that is also infinite that goes to the right.

Now apply the following rules:

1.color a single line segment in one of \(n\) colors(the line segment is as long as you want and it has to touch the bottom left point)

2.color another line segment of chosen lenght in one of \(n\) colors(it has to touch one the already existing lines

3.remove 1 line segment entirely (just the color)

4.repeat rules 1-3 until you have a graph that is homeomorphically embeddable in some previus graph

You are not allowed to do moves that are capable of being repeated infinetly (with a continous shift)

then the LS function is the longest game playeable with \(n\) colors given the game desribed above   (just in case anyone cares LS standes for Limetles square)