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!

https://www.desmos.com/3d/rrm5jvz7jr

Hello,

I'm really struggling to make this work. If someone knows how to solve this, please post a solution. It would really be useful for my next big project.
Thanks.

https://www.desmos.com/calculator/qnd6q4ax3o

https://www.desmos.com/3d/dfrppk1cuh

Fast Gamma and Riemann Zeta function implementations for complex arguments.

Gamma(z) should work for all complex z within the limits of double precision arithmetic.

zeta(s) works for |Im(s)| < 50, and if s is along the critical line Re(s) = 1/2, the algorithm works for quite large |Im(s)|, but the precision is lower.

https://www.desmos.com/calculator/aisvq1hpaa

Hi,

I've implemented the prime counting function in Desmos.

The computation up to x = 104 743 is fast, because I've precomputed the first 10000 primes.

When x > 104 743, Desmos won't be able to plot the function, because the algorithm is too slow to plot in a reasonable amount of time.

Normally, you will be able to compute only pi(10^7), because of the: Lists may not have more than 10,000 elements error.

But with the Desmos Godmode script, I was able to compute pi(10^9) in like 10 seconds!

That might not seem impressive in comparison with other implementations in other languages, but these other algorithms (Meissel-Lehmer, Deleglise-Rivat, ...) require array assignment, cached recursion and advanced data structures, features that cannot be used in Desmos.

If y'all have any ideas on how to improve this, let me know!