hi all, have gotten a sizeable spike in hits over the last week on collatz related blog posts! it seems to be traceable to an old reddit page on collatz from jun 2015 by `level1807`

talking about using a new feature in Mathematica to graph the collatz conjecture. profiled that finding/ graph myself here in this blog around that time. not sure how people are finding that page again, but googling around, it looks like this graph is now immortalized in a mathematical coloring book which was announced in a recent March 28th numberphile video getting just a few thousand short of ~200K hits at the time of writing this (maybe a few ten thousand in a few days!), and profiled the same day by a popular mechanics blogger weiner under the title of the Sea Monster. so, essentially viral, but putting the bar a little lower for mathematics! and as for the “elephant in the room” much to my amusement/ chagrin the video never once uses the word **fractal** (bipolar moods again attesting to a longterm love-hate relationship, not to mention the other (mal?)lingering facet of mania-depression!).

and this coincides very nicely with my announcement of the following. have been making some big hints lately and think finally have a Big Picture/ Big Idea from the most recent experiments. (yeah, no hesitation in the open Big Reveal on a *mere blog* after years of a similar routine…)

what is looking very plausible at this point is a formula in the form of a **matrix difference equation/ matrix recurrence relation**. the devil is of course in the details, but heres a rough sketch. prior experiments have some “indicator metrics” that are based mainly on binary density of iterates, and other “surface-like” aspects such as 0/1 run lengths etc… and its now shown that these are strong enough to predict future iterate sizes (10 for now) with some significant degree of accuracy.