It played with it for a little while quickly lost interest, despite how much I tweaked the randomization algorithm. (I tried stuff like truly random points, random jumps, slow movement, etc. etc.)

I figured out that she played much longer when I did it by hand. I realized that when I did it manually, I'd wait for her to catch the dot and then move immediately, so I thought about making something that tracked where the cat was, too, but never got around to it.