Rendezvous hashing is a generalisation of consistent hashing, and is a lot simpler to explain. It's also more flexible, if you want to give your node different weights: there's no need to futz around with virtual nodes and fiddle with the right trade-off between number of nodes and performance. There's just a simple formula based on probability theory.

See eg https://en.wikipedia.org/wiki/Rendezvous_hashing

If you want to make this more predictable you really ought to take advantage of the golden angle.

I mean there is a free well known way to assign successive ranges integers to near equally distanced points on a circle, so why not use it?

Claude3.5 helped me write a hashing visualization, which supports shadow nodes, adding nodes and keys, and can intuitively understand the hash ring method. By the way, there are many visualizations of common algorithms. Welcome to https://gallery.selfboot.cn to experience them.