I so enjoyed sitting back and watching the animated graphing that I thought: hmm, it would be cool to easily adjust the settings for the program via a simple GUI.
So I put my RAD (Rapid Application Development) hat on, grabbed an empty TiddlyWiki instance, and quickly put together the "Auto Biaxial Symmetry Graphing Personalizer".
This TiddlyWiki lets you run the program, see how it looks, and adjust various settings to get various results from what is really a fairly simple drawing algorithm.
If and when you like what you see, you can export the personalized program to a small HTML file that has everything needed to run your version of the program without ever needing to write/edit any of the BASIC code. Store that HTML file wherever you like for access via your online web browser, or wherever you like for your offline web browser.
A few sample images:
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