Black and white graphics with Polygon​
​by Oliver Seipel
The aim is to construct a large polygon and let Wolfram Language do the hard work behind the scenes rendering it.
Where you see white, there is actually no color, it’s the background color shining through.
In[]:=
GraphicsPolygonJoinJoin@@Table[N[r]{Cos[φ],Sin[φ]},{r,1,7},{φ,0,2π,π/64}],NTable
φ
2π
{Cos[φ],Sin[φ]},{φ,0,7×2π,π/64}
Out[]=
And color inverse:
In[]:=
GraphicsPolygonJoinJoin@@Table[N[r]{Cos[φ],Sin[φ]},{r,1,7},{φ,0,2π,π/64}],TableN
φ
2π
{Cos[φ],Sin[φ]},{φ,0,7×2π,π/64},Table[7.01{Cos[φ],Sin[φ]},{φ,0,2π,π/64}]
Out[]=
Ying and Yang spiral:
In[]:=
With{n=5,k=1},GraphicsPolygonJoinTableN
k
Log[1+φ]
Log[1+2nπ]
{Cos[φ],Sin[φ]},{φ,0,n2π,π/60},TableN
k
Log[1+φ]
Log[1+2nπ]
{Cos[φ+π],Sin[φ+π]},{φ,0,n2π,π/60},{{-1,1},{1,1},{1,0}},FrameTrue,FrameStyle->Directive[Black,Medium],FrameTicks->False,PlotRange1
Out[]=
And color inverse:
In[]:=
With{n=5,k=1},GraphicsPolygonJoinTableN
k
Log[1+φ]
Log[1+2nπ]
{Cos[φ],Sin[φ]},{φ,0,n2π,π/60},TableN
k
Log[1+φ]
Log[1+2nπ]
{Cos[φ+π],Sin[φ+π]},{φ,0,n2π,π/60},{{-1,-1},{1,-1},{1,0}},FrameTrue,FrameStyle->Directive[Black,Medium],FrameTicks->False,PlotRange1
Out[]=
Checkerboard-Flower:
In[]:=
With{n=17},GraphicsCircle[{0,0},1],​​PolygonJoin@@TableMapRotationMatrixi2
π
n
.#&,JoinTableN
φ
π/2
{Cos[φ],Sin[φ]},{φ,0,π/2,π/64},TableN
φ
π/2
{-Cos[φ],Sin[φ]},{φ,π/2,0,-π/64},{i,0,n-1}
Out[]=
And color inverse:
In[]:=
With{n=17},GraphicsCircle[{0,0},1],​​PolygonJoinJoin@@TableMapRotationMatrixi2
π
n
.#&,JoinTableN
φ
π/2
{Cos[φ],Sin[φ]},{φ,0,π/2,π/64},TableN
φ
π/2
{-Cos[φ],Sin[φ]},{φ,π/2,0,-π/64},{i,0,n-1},Table[N[{Cos[φ],Sin[φ]}],{φ,0,2π,π/64}]
Out[]=
Triangular-Flower:
And color inverse:
Checkerboard-Spiral:
And color inverse:
Flower-Spiral:
And color inverse:
Circular Interference:
Rectangular area:
Color inverse:
Restricted to circular area:
And color inverse: