the last installment ended with some idea of possible “traps” in certain metrics. this idea occurred to me quite awhile ago and didnt work out under some examination previously but theres some new ways of looking at this. in the past, it is clear that eg there is no strict density trap in the sense of one iterates density bounding the next ones eg wrt to the density core. but the last experiments led to a different idea. what if a metric is bounded over some count of iterations, does that limit future glide potential? its a simple variation, seems to be quite related, but is maybe the key twist that looks more plausible as a measurable/ consistent property.
this new experiment simplifies the code a lot and bounds distance-from-core labelled ‘dc’ and a entropy metric. the entropy is counting total # of 0-to-1 and 1-to-0 transitions in the binary form, scaled by the bit width. the (scaled) inverse entropy formula (aka “order”) ends up as one minus sum of count of 0/ 1 runs/ groups divided by iterate bit width, labelled ‘e’. this upper bound on the inverse entropy is equivalent to a lower bound on the entropy (because as mentioned entropy increases as glides progresses, and the potential trap is at the end; also note a “low upper bound (on order)” is a “high lower bound (on entropy)”). it finds a sharp transition point ‘e’ ≈ 0.40. (as mentioned, suspect that both low and high entropy may be tending to bound glide length, therefore maybe glide bounding wrt density-distance-from-core is inversely related to entropy-distance-from-core?)