MC Escher “Concentric Rinds” in 3D

I recently saw the M.C. Escher exhibit at the NC Museum of Art, and one piece that stuck with me was Concentric Rinds:

MC Escher - Concentric Rinds, 1953

The geometry bugged me for a while until I finally figured it out and sketched it up in OpenSCAD:

mc escher - concentric rinds - document


mc escher - concentric rinds - anim - transparent

Here’s a cleaned up version of the OpenSCAD script to generate it – it’s surprisingly simple:

module torus_strip(r, width, thickness) {
    rotate_extrude(convexity = 10)
        translate([r, 0, 0])
        square([thickness,width], center=true);

module the_ring(r) {
    torus_strip(r, 2, 0.5);

$fn = 256;

for (r=[50,40,30,20]) color([1-r/50+0.5,1-r/50+0.1,r/50+0.1]) {

    rotate([ 0, 0, 0]) the_ring(r);
    rotate([90, 0, 0]) the_ring(r);
    rotate([ 0,90, 0]) the_ring(r);

    for (tt=[-60,-120]) rotate([0, tt, 0]) 
        for (t=[0:45:360-1]) rotate([ t, 0, 0]) 

It took a while to figure out the geometry, but I finally got it when I saw there were three rings that were simply orthogonal, plus two arrays of 8 rings that intersected at the octagons. That’s how I modeled it above.

I also played with the animation stuff and got this:

mc escher - concentric rinds - xformer - anim2

Which I think is also neat.

That’s all.