At 1st I mistake the programming. I'd forgotten to program the rotation of Gear with pen holes. It's like the moon stand still from us on the Earth. But it rotate 1 round / a day.
So the rings has no gears and slipping each other.
Normal Type = with 2 Gears has 2 way to draw both slipping type and real gear type.
3 gears type has only slipping, because slipping type is not so different from real type and I cannot understand how many rounds to draw-up a 3 gears spirograph. Only case I found was G(ear)1>G2>G3, and G2 is inside of G1, and G3 is inside og G2.
How to calculate the rounds to draw-up a Spirograph.
Make simplizing ratio G1:G2 and G1:G3 and G2:G3.
These are G1a:G2a and G1b:G3b and G2c:G3c.
Next lowest common multiple of G2a and G3b and G3c.
It's the answer of the rounds to draw-up a Spirograph. But it's not always true.
And I found real 3 Gears and slipping type are not so different to draw-up design. So I programmed only slipping type.
How many rounds drawing-up a spirograph needs?
Make simplizing ratio G1:G2 and G1:G3.
These are G1a:G2a and G1b:G3b.
Next searching is the lowest common multiple of G2a and G3b.
It's the answer of the rounds to draw-up a Spirograph.