I learned this from President Obama...

A: For small arrays. I would add: particularly if you need a stable sort algorithm, which is either complex (Block Sort) or uses O(n) space (Merge Sort).

  if you apply quicksort to 2^20 random integers, at some point you're sorting 2^17 8-integer subpartitions

why not use an 8 wide optimal sort network for those 8 integers?

Well, I used Bubblesort to sort the results of lottery draws because it was very easy to implement.

Related to this is Timsort which combines merge sort and insertion sort https://en.wikipedia.org/wiki/Timsort

Can confirm, have used bubble sort for incrementally sorting particles in a particle system and plants in a terrain renderer.

The only use I've seen is incrementally sorting large arrays during brute-force search of said arrays, since that is approximately free and brute-force search is pretty efficient and fast on modern CPUs. Set a "sorted" flag if/when the array is eventually sorted.

The idea was that the vast majority of arrays in a large set are not searched often enough to justify the cost of sorting them and sorting is an expensive operation if you are computing on a deadline. You also don't always know which ones will be heavily searched ahead of time. Using bubblesort, only the heavily accessed arrays end up sorted but as a side-effect of search rather than having separate heuristics to decide when/what to sort.

to compare other sort algos against it

I used bubblesort on purpose in a game project. Specifically, to sort sprites in an NES game back to front, lazily, spending as few CPU cycles as possible. Bubblesort on the very small list (a dozen objects max), and early exit after the first swap. It eventually completes, and that was just fine. It's tiny, incredibly simple, and somewhat resilient to the list changing from frame to frame as objects spawn and despawn. Each partial sort makes some progress no matter what.

A few other algorithms would have fit the bill just as well, but bubblesort is perfectly adequate, so that's what will likely ship. More complex algorithms end up losing out due to greater initial overhead or larger ROM size.

I’ve used it when I didn’t want the hassle of another dependency

I've used bubblesort when simulating LEO satellite constellations, calculating which satellite is closest to a location. I used one single backwards pass of bubblesort, so O(n) every k timesteps to bring the closest to the head of the array, then every timestep just do one backwards bubblesort pass over the first few in the array. Given satellites move smoothly, if you initialize right (a few full passes at the start to get the closest few at the front) and get the constants right so a satellite outside the front few in the array can't have moved far enough to become closest without being promoted to the front few by a periodic full pass, then you always maintain the closest at the front of the array very cheaply. And this has the advantage of also being very simple to code.

If you need a stable sort, can't be bothered finding a massive oversize library to link to, and only need to sort a relatively small number of objects on a system that's resource-constrained, I'm guessing?

For small sets, or small-ish sets when you are coding quick, don't have a convenient standard library sort to hand, and are prioritising correctness over absolute performance.

Though in reality almost never: you almost always have a convenient built-in sort that is as quick & easy to use (likely quicker & easier), and in circumstances where the set is small enough for bubblesort to be just fine, the speed, memory use, or other properties of what-ever other sort your standard library uses aren't going to be a problem either.

As others have pointed out, sometimes it is useful for partial sorts due to the “always no less sorted than before at any point in the process (assuming no changes due to external influence)” property.

wrt:

> If you make each frame of the animation one pass of bubblesort, the particles will all move smoothly into the right positions. I couldn't find any examples in the wild,

There are hundreds of sort demos out there, both live running and on publicly hosted videos, that show the final positions by hue, getting this effect. Seems odd that they couldn't find a single one.

EDIT: actually, I can't find any of the rainbow based sort demos I was thinking of, a lot of promising links seem dead. I take back my little moan!