[amavect]

I thought the same, so I programmed the examples into Desmos 3D (click the show/hide buttons on the left).

https://www.desmos.com/3d/3divdux6jh

Dropping the absolute value makes a better visualization. The 3D graph for Example 4 Shadow Line has an established name, a hyperbolic paraboloid. The color graph for Example 5 Phi Equation doesn't capture the odd symmetry F(x,y)=-F(-x,y). The color graph for Example 6 Underwater Islands looks far inferior to the 3D surface.

[calebm]

Interesting. I didn't know you could plot like this in Desmos. Thanks for doing the work to plug them in.

[amavect]

No problem. While fuzzy graphing has existed for a long time as contour plots, I'd still like to encourage you to experiment more. The colors look pretty. :)

I have a suggestion. Calculate z=left-right without absolute value, and try mapping [negative limit, 0, positive limit] to [black, red, white], or possibly [negative limit, 0, positive limit, outside of limits] to [red, white, blue, black]. And of course, do variations and have fun!

[calebm]

I'm not sure I've tried that - might good idea. I've actually been playing with all kind so of visualizations - I've done most of my art as stand-alone Python scripts. Here's an open-source starting point for doing this kind of math art in Python: https://github.com/calebmadrigal/truthygraph.py. You might want to try your idea yourself :)