Click on one type of radius growth (blue buttons). Click on any shape. Then click the green flag. As the invisible radius cycles around like a clock, a drum beats sound every cycle. Notes play higher when the pen is higher. The main purpose is to compares the parabolic spiral (Archimedes spiral) to the growth spiral (logarithmic spiral) to a simple circle. This same code can create a triangle, square, hexagon, and all regular polygons (see below).
If you click either radius growth button, this modifies part of the code for drawing a circle so that the radius grows for each unit increase of angle. The code draws a simple circle if you leave the radius constant. For the two spirals, the radius grows in two different ways. The radius growth is geometric (logarithmic) for the geometric growth spiral (logarithmic spiral). The radius growth is constant for the Archimedes spiral. That is, for each angle increment, the radius increases with a fixed increase increment for Archimedes spiral, but the radius grows geometrically for the logarithmic spiral. The program creates a circle, or spiral, with small angle increments. For a constant radius, we create a polygon with many sides, approximating a circle when the angle is small. But for larger angle increments, it creates familiar polygons. A triangle results when you use an angle increment of 120 degrees. Set it to 90 degrees, you get a square. An angle of 60 degrees results in a hexagon. Find the angle to get a pentagon. As the invisible radius cycles around like a clock, drum beats sound at every cycle, a snare drum at zero degrees (3 o'clock) and a clave stick sound at 180 degrees (9 o'clock). Notes play higher when the pen is higher.
