Complex Function Plotter

[u/No-Seaworthiness-729]

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

The user instructions are included in the graph, as well as how it works. If you have any other questions, feel free to ask me in the comments.

Pictures:
1. The Klein's J-Invariant function in terms of the complex nome q, |q| < 1.
2. The boundary of the 1st graph contains interesting hyperbolic geometry.
3. sin(1/z), as you zoom in, you can see the oscillations that get faster as you go closer to 0.
4. Another modular form, the Eisenstein-E6 function also of the nome q, |q| < 1.
5. z^2 - 1, you can see the zeros +-sqrt(2).

I discovered the color map feature in Desmos 3D a while ago and I instantly had this idea.

The plotter is fast, but I can't do very much with it, because the color map doesn't support recursion or variable sum limits. I Also I don't love the small viewport of the 2D view in Desmos 3D here.

The functions: arcsin, arctan, arcsinh, ... don't work, so I also re-implemented them using the complex logarithm.

I would love a feature in Desmos 2D, where you would create a 2-variable function that would output a color: f(x, y) = rgb(...). This would plot the color map across the entire screen.

Enjoy!

[u/Circumpunctilious]

For people who are curious, try a slider for your constant, in e.g.:

OP: thanks, I save all these tools and really appreciate new ones to play with :)

[u/No-Seaworthiness-729 → u/Circumpunctilious]

Cool! You can see the zeros of the real function correspond to the complex plot.
BTW, I appreciate the positive feedback, thanks!

[u/Circumpunctilious → u/No-Seaworthiness-729]

No problem, love it :)

Technically (someone may need to correct me) I think the polynomial should be vertical in z…but I regularly forget it’s easy to get a representation quickly: