Since I now work in an environment with regular longish meetings, I've rekindled my interest in the art of doodling. Mostly what I draw is fractals.
I can't remember who gave me the idea of drawing Sierpinski Triangles on paper, but I've been doing that for years, in any situation where I'm bored and have pen and paper available but no computer. The triangle is easy to do, because you just have to keep drawing upside-down triangles on any space that doesn't have one already, and you can pretty much go on forever until the triangles get too small to draw. However, I recently got sick of Sierpinskis, so I started branching out into Koch curves.
I've tried to draw Kochs in the past, but always screwed up... I would freestyle just fine for a while, but then I would always turn a line in the wrong direction and wind up with an ugly asymmetric mess.
So I've been practicing my technique, and hit on the way to fix this. Draw dots that represent the framework first, and then draw more dots closer together, until you've got the level of detail you want; then fill in the curves. The down side to this approach is that unlike a Sierpinski, you can't increase the complexity after you're finished. You have to pick a level and stick with it until you're done, and then start a new one.
By gradually increasing the size and practicing smaller and smaller lines, I've managed to create a vertical square Koch curve against the left margin of a notebook page, which fills up most of the lines on the page and goes to a depth of five iterations. It took me about four meetings to finish. I've also drawn a snowflake which goes to four iterations, but I could probably get five because I still have room on the page to make it about 50% bigger next time.
I've gotten funny looks from people who saw what I was doing, but no comments so far. I wish I could do Mandelbrots, but it seems way too math-intensive to do in real time.
A few other fun facts about my history with fractals. When I was in college, I spent two years tutoring a smart high school kid named Willy in computer programming. One year, we wrote several fractal programs in Visual C++ for a science fair project. He went to state level but didn't win.
I still have several interesting fractal programs which I translated to Java and put on my Java applet page. One of them allows you to generate your own Koch curve, and another shows how you can get a Sierpinski to emerge naturally from pseudo-random rules.
My friend Denis Loubet introduced me to a term that I love to use: "Fractally wrong." This applies to someone whose opinions are wrong in the big picture, and regardless of where you zoom in on any particular detail, it's still wrong.