Here is a Terdragon Curve formed by an L-System. It is a fractal. You can play around with the pen size, and hopefully it is aesthetically pleasing to look at. Press space to draw it again. Here's how it works. Given the L-System: ({F, −, +}, F, {F → F − F + F}) We can create the Terdragon Curve in a "turtle graphics" fashion. The first part, {F, −, +}, tells of what "symbols" we will be using. The next part, F, tells of what symbol we will be starting with. The final part, {F → F − F + F}, illustrates the rule we must follow to reach the next sequence. In our case, the rule says that every time we encounter an F, we must replace it with F, -, F, +, F. If we encounter a - or +, since it is not specified, we just leave as is. So, starting with F, we get F - F + F. From that we get (F - F + F) - (F - F + F) + (F - F + F). We can repeat this rule to get the next sequence any number of times. In this project, that happens six times. If we interpret every F as "move forward" and every - as "turn left 120" and every + as "turn right 120," then the picture to the right, the Terdragon Curve, becomes visible. I rounded the corners for effect. It is a beautiful space-filling curve.
-Wow my first unfeatured project to reach above 1000 views! Previously, I had no clue what an L-System was. I learned entirely about them through this wonderful PDF (in English): https://math.okstate.edu/people/segerman/papers/developing_fractal_curves.pdf Near the very beginning, it explains the algorithm for this curve. Next, ,I wonder if I could use the Mobius Function to do something similar!
