The above animation was created inside turtleSpaces, and then exported as a webm video file using the savewebm primitive. I then used Final Cut Pro to add the audio and the titles.

The Logo code used to create the animation is fairly straightforward. The turtle moves in an arc outwards from the center, creating arcs around it and generating the pattern. The location and sizes of the arcs depends on the current loop iterations. Graphics rendering is suspended while each ‘frame’ is created, after which the code renders the frame and pauses to ensure the user sees it, then continues on.

It runs much faster via the desktop application than in the web version, so you may need to adjust it to slow it down. Tinker with it! Play around. It’s the best way to learn.