Exploring a Fractal
One of a series of iterated maps created for a teacher friend whose 6th Graders learn about functions, coordinates, plotting points, and spreadsheets. Iterated maps are a fun way to combine those math skills. In this one, you can locate the inital point as you wish, the click the "Show another point" button repeatedly to follow the trajectory of points that results. At any time, you may move the initial point around to see how the trajectory changes. For an example of how to use this worksheet, please see the video https://www.youtube.com/watch?v=dceDzwbS36g.
Notice the colors of the regions in which the points along the trajectory are located. If you put the initial point on a yellow region (for example), what are the colors of the region for each succeeding point? If you put the initial point as close as possible to the center of the fractal, what happens when you click the "Show another point" button? Click the "Show another point" button about 15 times to make a string of points, then drag the initial point along the boundaries between the larger solid-color regions. (For example, between the red and yellow regions.) What happens to the string of points?