A little while ago I did some research looking at limb reduction in terrestrial vertebrates. It turns out, nearly all modern & fossil examples are one of two types, a long tailed “grass swimming” type and a short tailed “burrowing” type. These are examples of morphologic attractors like you describe
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i've studied insect gait a little and there are multiple gaits, but it seems like the foundational one is moving in two sets of three.