You may have seen the classic Heighway (or Jurrasic Park) dragon curve before. This app lets you build your own similar fractal curve. Define a pattern by drawing a line with at least two segments. Then the app will recursively replace each segment with the pattern itself, flipping the orientaton each time. I was introduced to it in one of the excellent Numberphile's videos.
Browse the top user-created patterns below, or search for one.