This app allows you to create a large number of alternative patterns based on nested (rotated and scaled) regular polygons. The resulting patterns are concentric and some almost seem three-dimensional. If the app is running locally, you can use the SNAPSHOT button to output the pattern to a vector-based PDF file.
This is a fully parametrised Fibonacci Phyllotaxis Pattern Generator. Try the different sliders to get different shapes. You can stop the rotation or reverse its direction using the rotation slider.