How does one achieve a square spiral like the the Ulam spiral in Netlogo?

Question

I spent the morning trying to find an easy function (x,y) -> n that would number the patches like this

I was not successful. Do any of Y'all have any experience or suggestions?

Answer 1

Here is my take on it:

patches-own [ n ]

to setup
  clear-all
  resize-world -4 4 -4 4 ; so it looks better, but use any size you like...
  create-turtles 1 [
    set heading 180
    foreach n-values count patches [ ? + 1 ] [
      set n ?
      if [ n = 0 ] of patch-left-and-ahead 90 1 [ left 90 ]
      fd 1
    ]
    die
  ]
  ask patches [ set plabel n ]
end