Related ideas

A project log for PEAC Pisano with End-Around Carry algorithm

Add X to Y and Y to X, says the song. And carry on.

Yann Guidon / YGDESYann Guidon / YGDES 07/02/2022 at 10:540 Comments

Veritasium just uploaded a new video.

And apart from the funny subject in itself, it contains a few related and pertinent ideas.

First : it calculates the probability for any permutation to create a "loop", or "orbit", of length one half (or more) of the total number of items. So this is a first hint to find the distribution of "maximal" or "perfect" orbits, except that generalised PEAC are not random.

Second : adding an offset to the items' coordinates changes the topology of the loops/orbits. And this is exactly what the carry does in PEAC.