A New Fractal Construction

Several weeks ago, I saw an online post from Matt Henderson describing a fractal construction that was new to me. Here is how to generate it: Start with a hexagon and a random point A inside it. Pick a side of the hexagon at random (for example, side GH below) and construct ∆AGH. Continue by constructing point C, the centroid of the triangle. Now start again, picking a side of the hexagon at random and use its two endpoints and point C to construct a new triangle and its centroid. By repeating this process, marking the location of all the centroids, you’ll create a fractal. To watch as the fractal is generated, download this Geometer’s Sketchpad file (You can download Mac or Windows Sketchpad for free here.) When you open the file, tap Hide Construction and then tap Animate to see the fractal emerge onscreen.

If you’re interested to learn how to build this construction from scratch, I’ve posted a YouTube video here. And here is another sketch showing other fractal constructions built with Sketchpad.