Bubble sort beats quicksort... when you start thinking about parallelism, locality, and communication cost.

(See figures on p10 and p11, as well the last section on p13.  This article is from Scientific American, Sept 1977.)

This is one of the things that the toy at the top of your bubble sort essay exemplifies so well through play -- by sweeping the mouse over the bars, you can make them do their jumps in parallel.  Bubble sort is only "slow" on a sequential processor, and it has a bad reputation only because we're all still using overgrown ENIACs.  Your toy is not a sequential processor -- it simulates a parallel processing environment, where the efficiency of bubble sort can actually shine.