Any series of strings in continuous increasing length starting from some center point and spiraled around in ascending length order will produce arms.
Why? Because they increase in same length, so for any element X(i) its length is length of X(i-1) * someConstant, so eventually their starting points on the circle's perimeter will get aligned, depending on how far from the center you position it.

This happens for any rational and non-rational number that exists, except for phi (5*sqrt(2)/2) and its family. That one is the single possible ratio that always wraps in full uniform distribution and is seen all over in nature.