Saturday, August 25, 2012

Star From Circles: How Does a Circle Get Pointy?

I am enchanted by this design I created while playing in TurtleArt. This turtle draws circles. I wanted this turtle to draw 1000 circles. I also wanted the turtle to wander a little so these 1000 circles were not drawn in the same place. That would make the turtle look like it only drew 1 circle!

When the program first runs the turtle draws a circle with a radius of 500. It tells itself that the next time it runs it subtracts 10 from this original radius. The turtle moves a little to the right and a little forward. The procedure also changes the color and shade of the turtle's pen. The indefatigable turtle repeats this procedure 1000 times.

Use the help button in TurtleArt to clarify any of these commands, colors, or shades and to see an example piece of code that you can adapt and use in your project.

Here is an example of this program. The colors change every time this program runs.

As the program runs the radius of the circle moves into negative numbers. How does that change how the circle is drawn? As the program repeats points develop from overlapping circles. I am fascinated by the simple math that creates stars from circles.