Basic Examples 
(4)
 

Here are the points on the first four sides of the spiral:
In[29]:=
[◼]
SquareSpiralPoints
[4]
Out[29]=
{{0,0},{0,1},{-1,1},{-1,0},{-1,-1},{0,-1},{1,-1}}
———
This shows the sequence of points in order on the first six sides:
In[30]:=
Withs=
[◼]
SquareSpiralPoints
[6],Graphics[{{Pink,PointSize[.03],Point[s]},Arrow@Partition[s,2,1]}]
Out[30]=
———
Forty black sides with 20 red sides overlaid:
In[31]:=
GraphicsLine@
[◼]
SquareSpiralPoints
[40],Red,Line@
[◼]
SquareSpiralPoints
[20]
Out[31]=
———
The number of points in n sides:
In[32]:=
Length@
[◼]
SquareSpiralPoints
@#&/@Range[0,10]
Out[32]=
{1,2,3,5,7,10,13,17,21,26,31}
In[33]:=
Table[Floor[(n+1)^2/4]+1,{n,0,10}]
Out[33]=
{1,2,3,5,7,10,13,17,21,26,31}

Neat Examples 
(2)
 
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