which sorting algorithm keeps up with constant random updates best? at every second in this animation, a random item is taken (blue), and its value is changed

Stop it you’re hurting them 😭

How do I know if it's working without sound?

Rather than using a sorting algorithm, which will have to move on average N/2 elements to accommodate a changed value, isn’t it better just to use either a heap or a self-balancing binary tree? These are data structures specifically designed for this task

stumbled on this pretty cool gif of bubble sort

Well, that's one way to make merge and quicksort misearable.

this is inhumane

Bubble sort would come out much better if you did alternating sweeps in opposite directions.

Knowing the obsession with randomness in the complexity community, I'm sure there are many un-readable papers on this.

Special requirements may warrant special algorithms. How about an alternating bubble sort that switches between walking upwards and downwards the array?