Not sure if anybody has tried this...

Two methods that may yield a pattern or clue:

Starting with the outside circle.
Connect the two points with a line.
Draw a line perpendicular to the center of the new line reaching to the adjacent circle.

For example, draw a line between the 22nd ring points. Draw the perpendicular line til you reach the 21st ring.

Two options from here:

Shift/Turn all the inner rings as one til the point on the 21st ring intersects the perpendicular line.

or

Shift/Turn just the 21st ring til the point intersects the perpendicular line.

Repeat til at center.

If this doesn't make sense let me know and I'll try to explain it in a different way. I have not been able to test this method out yet but if someone with better image software can that would be great.

Originally posted by swintersVT
If this doesn't make sense let me know and I'll try to explain it in a different way. I have not been able to test this method out yet but if someone with better image software can that would be great.

i've got photoshop, as well as others.

i really dont have a clue as to what your trying to say here. do you have a scanner? maybe you can just quickly sketch by hand what you are trying to explain... as they say, a picture is worth a thousand words....

Alright.

Looking at the picture I have drawn a line connecting the two points on the 22nd ring. Then I drew a line perpendicular through the center of the 1st line which connects to the 21st ring. The red dot indicates where to shift the rings according to the two methods.

If you choose the 2nd method I listed earlier than you would just move the black dot on the 21st ring to the red dot on the 21st ring. The yellow lines are just a guide for that paticular turn. Now remove the yellow lines and draw a new line between the two points on the 20th ring....and so forth as before til you go through all the pairs.

The 1st method is a little harder to describe. Instead of just moving the black dot to the red dot and leaving all the other points, shift all the points on the inner rings at the same time til the black dot on the 21st is on the red dot on the 21st ring. Now repeat for the 20th ring...and so forth through all the pairs.

only problem...do you draw the point on both sides of the line, or how do you decide which side to draw the perpendicular from?

---pineapple

For now I was just thinking draw the perpendicular line on the same side the point you are going to move is on. If nothing shows up try opposite hemisphere, or alternating sides.