This applet simulates the pouring of water into a triangular stack of buckets. When a bucket is full, it spills its excess water equally out its left and right sides. The result is something like Pascal's Triangle, but more complicated since buckets only spill once they are full. The applet was inspired by a question from my step-cousin's high school math class: how much water must be poured before the sixth row is "one-full", i.e. at least one bucket on the sixth row is full? (Computing this analytically is harder than it sounds; try it! The answer turns out to be precisely 15.4. Actually the high school question uses two-litre buckets for some reason, thus doubling the answer to 30.8.) An easier question is, how much water is required before the n'th row is completely full (answer: 2^n - 1).
The applet accepts the following keyboard inputs. (You may need to "click" on the applet first.)