Open and closed random walks with fixed edgelengths
by Jason Cantarella, Kyle Chapman, Philipp Reiter, and Clayton Shonkwiler
In this paper, we show that a random walk is (with overwhelming probability) surprisingly close to a closed loop with the same step sizes, and that closing up has very little impact on local features.
In particular, this suggests that local knots should occur at essentially the same rate in loops as in open chains.
Omnes Pro Uno
Yet more Mercator projections of level sets of sums of dot products, now with the vertices of a triangular bipyramid.
Source code and explanation: xhttp://community.wolfram.com/groups/-/m/t/1350667
Start with a bunch of points on loxodromes. Now rotate in space, then stereographically project to the plane. Finally, form the Voronoi cells of the resulting point set.
The aggressive video compression does this one no favors; see a better version along with source code at http://community.wolfram.com/groups/-/m/t/1291902 https://mathstodon.xyz/media/OsWh_UoCkHrl6fm7nkg