“Iterated Maps” is a sort of scary name for a fun idea. We choose some point on the graph, and use its coordinates to calculate coordinates of a string of other points that we’ll plot.
How do we calculate the coordinates for those other points? We follow some rule. In the map shown below, we calculate the coordinates for the second point by adding 1 to the x coordinate of the point we chose, and 2 to the y coordinate of the point we chose.
To calculate the coordinates for the third point, we add 1 to the x coordinate of the second point, and 2 t the y coordinate of the second point. We follow that same rule to calculate the fourth point’s coordinates from the third point’s coordinates, and the fifth point’s from the fourth point’s, etc. We keep doing that for as many points as we wish.
You might want to try this rule by yourself, on a sheet of graph paper, before you use the computer. Start with any point you want, and see what shape the following points make.