Tile the plane with this modified circle
POV-Ray, 199 163
Old version
camera{location -9*z}light_source{-9*z}#declare L=union{#for(X,-9,9,2)#for(Y,-9,9,2)cylinder{X*x+x+Y*y,&lt;.001*pow(-1,(X+Y)/2),0,.1&gt;+X*x+x+Y*y,1}#end#end}object{L pigment{color x}}object{L rotate z*90}

Same output, but golfed down further by using default light/camera, so I dont even need to specify them
#declare L=union{#for(X,-9,9,2)#for(Y,-9,9,2)cylinder{&lt;X+1,Y,9&gt;,&lt;.001*pow(-1,(X+Y)/2),0,.1&gt;+&lt;X+1,Y,9&gt;,1}#end#end}object{L pigment{color rgb x}rotate z*90}object{L}


I am using as many default parameters for camera and lightsource as possible, thats why it is a little dark. Lets ungolf it first
camera{location 9*z look_at 0}
light_source{9*z color 1} 
#declare L=union{
    #for(X,-9,9,2)
        #for(Y,-9,9,2)
            cylinder{&lt;1+X,Y,0&gt;,                                 //central axis, start
                     &lt;1+X,Y,0&gt; + &lt;.001*pow(-1,(X+Y)/2), 0, .1&gt;, //central axis, end
                      1}                                        //radius
        #end         
    #end
}                         
object{L pigment{color x}} // x is the &lt;1,0,0&gt; vector, here interpreted as RGB
object{L rotate&lt;0,0,90&gt;}

It is obvious what is happening once we increase the offset of the cylinder axis and change the perspective