I have a chain of discrete segments, of equal sizes, built by the following rules:
1)every next segment rotates around it's Y axis by 7 degrees,
2)then it pivots at the join with the previous segment by 4 degrees.
Regardless of the angles used, the resulting pattern is always a kind of helix, it spirals forwards into space indefinitely.
In 2d, such a ruleset would always form a spirograph rotating around a point.
Why does the rule set make helix shapes and never 3d spirographs?
I suspect that this explanation be a bit too imprecise, but I think it can be made to work. (In what follows, it may help to consider the image of a triangular helix joint shown here.)
Take two consecutive segments of your helix, and consider the isosceles triangle with them as its legs. Draw the line in 3D which bisects the joint angle, and repeat this construction for the next joint. Note that the two triangles formed this way do not lie in the same plane due to the rotations; consequently the two bisectors will not intersect and are skew. Consequently they are both perpendicular to some common axis.
If we repeat this again, we receive another bisector; however, it stands in the same geometric relation to the second bisector as that did to the first bisector. Thus we will get a sequence of bisectors which are all displaced from each other by the same amount and lie along a common axis: this provides the skeleton of which our segmented curve is built. But that requires the curve so formed to be a segmented helix.