Note: If performance is slow/sluggish inside a web browser, consider downloading to a computer and running in GeoGebra standalone app, This is one of those constructions where I had one thing in mind at the start but then veered off in many different directions over the subsequent hours. The final construction is a metaphor for the whole process, but I still had a good time seeing it evolve. Switch between "auto" mode in which the caterpillar chases the point to somewhat-random locations along the perimeter of the polygon, or "manual" mode in which you drag the point to any locations within the polygon. Settings are as follows:
  • speed: speed of point & pursuing caterpillar (auto mode only)
  • delay: how long point delays between moves (auto mode only)
  • numlinks: number of links in caterpillar body
  • ripple: size of ripple through caterpillar body
  • (each time slider n updates, each point closes distance between itself and the preceding point by percentage 1-ripple)
  • numsides: number of polygon sides
  • link: length of each link, & radius of each circle