So, try this:

If you take your clock value and multiply it by sqrt(2), then the black will
reach all the way into the corner of each square, and will give you a fully
black texture.

- BE




#version 3.7;
global_settings{ assumed_gamma 1.0 }
#default {finish {ambient 0 diffuse 1} }


camera {
 //orthographic
 location <0,0,-50>     // position & direction of view
 look_at  <0,0,0>
 right    x*image_width/image_height
}

sky_sphere {pigment {rgb 1}}
light_source {<0, 0, -100> rgb 1}

#declare Dots = function {sqrt ( (mod(abs(x),2)-1) * (mod(abs(x),2)-1) +
(mod(abs(y),2)-1) *
(mod(abs(y),2)-1) )}


#declare Radius = sqrt(2);

plane {z, 0 pigment {function {select (Dots (x, y, z) - Radius, 0, 1)} } }

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