Farsi / Persian
NetLogo Models Library:
The turtle goes forward "distance-of-travel" and returns to (start-x, start-y). The green patch is the center patch upon which there is a turtle at (start-x, start-y), and the patch "distance-of-travel" away from that center will flash as the turtle passes through it.
This is an illustration of the difference between a radius of 1 and the distance from patch to patch. Distance in NetLogo is measured in patches, and so "forward 1" for a turtle means for it to go forward exactly the length of one side of a patch. However, as illustrated by the pythagorean theorem, the distance across the diagonal of a patch is root 2 (around 1.414). As such, there are points and headings of a turtle within a patch from which going forward 1 will not result in changing the patch on which the turtle lands.
There is a searcher turtle that travels clockwise at distance-of-travel from the center (start-x,start-y). The searcher returns to the center each tick and goes forward distance-of-travel. distance-of-travel, start-x, and start-y are all sliders. The center turtle simply marks the center at (start-x, start-y).
Press setup, then press go. You can change the sliders while the model is running.
Patches are laid out in NetLogo such that they span from pxcor - 0.5 on the left to an open boundary at pxcor + 0.5. The same equation is used for pycor. That is, for patch 3 1, it's actual real range is ([-3.5,2.5), [-1.5,-0.5)). This is illustrated in the model.
Try changing start-x to 0.5 and start-y to 0.5. Where is the green patch now? Now try changing start-x to -0.5 and start-y to -0.5. When the start-x = -0.5 and start-y = -0.5, the turtle is centered on patch 0 0. When the start-x = 0.5 and start-y = 0.5, the turtle is centered on patch 1 1.
You could change the model such that there are a "halo" of turtles always distance-of-travel from the center.