This is a fractal I now know is called the Dragon Curve (and one of my favourites). I started drawing it years ago on a piece of graph paper after reading Jurassic Park, seeing the weird patterns at the beginning of each chapter, and just for kicks, trying to figure out the pattern. At first, I got thrown off by the labelings of "first iteration," etc, etc. Now, I've figured out that the reason I was confused is because the iterations were wrong in Jurassic Park.

The biggest challenge in drawing this thing by hand and working out everything on paper is that the amount of stuff you have to do increases faster and faster at a very rapid pace. And if you mess up on a single part, the mistake will change the fractal in an increasingly large way in each iteration (which means you'll have to backtrack through an increasingly large amount of lines to find where the error was... which is a major pain).

For a long time, I'd just add a single line a day. I stopped for a while when I lost the piece of paper I was doing this on. Unfortunately, now I've lost the piece of paper I kept everything I needed to work out the next iteration (and finish the current one). So... until I get myself to rework everything from scratch, this'll probably stay "incomplete." Then again, with fractals, once you've seen a little part... you've seen it all.

I may end up cheating and using a program to zip my way through to catch up to wherever I was. I'd just feel guilty after all this time of doing it all on paper...