My snake

We can see what this requires.  Along the axis 1,1,1 to x,y,z the x counter must lay out a ring of marks on some surface around that axis but perpendicular to the x axis.  So these deviation counters spiral outside and long that centroid.  But they drop every two thirds measurement because of cross over.

So I am counting some deviations axis, say t from 111 to xyz, all combinations. t will have bounded error in that  can always get the current t by flooring. My spirals are at a relative tilt.

My snake will close and maintain bounded deviations.

A colored snake connected in a loop defines a constant curvature.

So crossing my rope once make even odd, crossing twice gets me the tripod. And we have lots of cross overs when deviation count is minimized. My snake goes in and out of each partition.

My snake makes a centroid in any partition.

I sample each counter at Nyquist but dump every third counter. Total sample rate is 3/2.

Dropping a hole, (skipping one mark on the circle), Means the fast counter will fill it immediately.  These are combined paths making, and constant light steps can maintain deviation count.

Take my three colored snake, lay it straight. Rotate the middle counter a notch and tthe snake will curve. You can bias curvature with that little trick Rotate the  larger counter notches in the counter direction and the snake curves the other direction. Rotate the small counter and the he snake will count from the other end.

I bet my snake counts out the atomic orbitals.