Basic Examples 
(2)
 

This shows how the points are ordered in the simplest case:
In[21]:=
[◼]
SquareZigzagPoints
@2
Out[21]=
{{1,1},{1,2},{2,1},{2,2}}
In[22]:=
With{n=2},​​Graphics​​Arrowheads[Large],LightGray,MapArrow,Transpose[{Most@#,Rest@#}]&@
[◼]
SquareZigzagPoints
@n,​​Red,PointSize[.03],Point[Join@@Table[{x,y},{x,n},{y,n}]]​​,AxesTrue,AxesOrigin{0,0}​​
Out[22]=
———
A larger example:
In[23]:=
Graphics​​Arrowheads[Medium],MapArrow,Transpose[{Most@#,Rest@#}]&@
[◼]
SquareZigzagPoints
@11​​
Out[23]=

Scope 
(2)
 
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