One way to describe a geometric figure is in terms of the path generated by a moving point. Instead of defining a square, for example, as a four-sided polygon with equal sides and angles, you can call it the path generated by the following rule: Go straight for a distance s, turn 90 degrees right, and repeat until the path returns to its starting point.
Using the computer language LOGO, children can produce a list of commands to govern the motion of a “turtle” and trace out a geometric track on the computer screen. Indeed, such a turtle can be programmed to generate an endless variety of patterns. Mathematicians can use similar algorithms to generate fractals and other forms.