Flourish is a visual toy app that draws harmonographs, sinuous curves simulating a multi-pendulum trace:

Each harmonograph is determined by a few dozen parameter values, which are chosen randomly. The number of parameters depends on the number of pendulums, which defaults to 3.

Click a thumbnail to see a larger version. The large-image pages have thumbnails of “adjacent” images. For each of the few dozen parameters, four nearby values are substituted, giving four thumbnails for each parameter. Clicking an adjacent thumbnail continues your exploration of the parameter space:

The settings dialog lets you adjust the number of pendulums (which determines the number of parameters) and the kinds of symmetry you are interested in.

I started this because I wanted to understand how the parameters affected the outcome, but I was also interested to give it a purely visual design. As an engineer, it was tempting to present the values of the parameters quantitatively, but I like the simplicity of just clicking curves you like.

I repeated a trick I’ve used in other mathy visual toys: when you download a PNG file of an image, the parameter values are stored in a data island in the file. You can re-upload the image, and Flourish will extract the parameters and put you back into the parameter-space exploration at that point.

This is one of those side projects that let me use different sorts of things than I usually do: numpy, SVG, sass, Docker, and so on. I had more ideas for things to add (there is color in the code but not the UI). Maybe someday I will build them.

BTW, I am happy that my first post of 2021 is called “Flourish.” I hope it is a harbinger of things to come.