One of my earliest experiences of computer programming was when my school acquired a computer lab, and we did some Turtle Graphics programming, probably in Logo. The school even had a robotic turtle which was used to draw lines on paper on the floor. I think one project we did was to draw the letters of the alphabet which made up the name of the school, or some other message. In any case I remember making the turtle go round drawing lines.
Earlier this year I read Mindstorms by Seymour Papert, which describes how computers can be used by children to learn about Mathematics and programming, and how the Turtle Graphics system is a better system for exploratory learning than the Math is conventionally taught. One of the reasons for this is that the child is able to identify with the turtle, and solve problems by walking out the path of the turtle, and performing the instructions of the program. There is a fascinating description of how younger children were actually better at figuring out how to get the turtle to draw a circle by going forward a bit and turning a bit repeatedly, than were older children who had already learned more objective facts about circles, such as that they have a radius and a center. Even older children who had learned the algebraic formula for a circle were actually incapable of solving the problem.
Here is a screenshoot of the application.. click on it to open it up, and start exploring ;)
All the code is available at the GitHub project.