If you're looking for something to do with this program that has very little to do with binary trees, you can try some of these ideas...
I like to doodle with the nodes (you can move them around with the mouse). When you get the screen especially tangled, Keep Tidy can give you a show, especially for large trees.
If you like moving pictures, you can put in a big alphabetical tree, make the window small, and choose Find Word. Watch the scroll bars... the little elevators move, too.
You may get a surprise if you fill up memory till it bursts. You can probably type in a hundred words into an alphabetical tree without filling memory, but parsing fills it sooner: since the recursive procedures for parsing need lots of memory, parsing an expression like 4-4-4-4-4-... that takes up 4 lines will probably crash the Mac. Whether you get fireworks or a simple "serious system error" depends mostly on chance. This little game is strictly for horror film buffs, since occasionally you get some pretty hairy results when the Mac crashes. Be forewarned that there is also a small risk that when the Mac crashes it will damage the information on the disk in the drive.