Math graphs but they get increasingly more beautiful

Hello everyone! In this video, I'm creating a compilation of beautiful math graphs using a lesser-known function called the "sign function." I hope you enjoy it!
Here is the link to the graphs so you can play with them yourself: www.desmos.com...
Music info:
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Chill Retro Synthwave - Endless Night
• Chill Retro Synthwave ...
All music are provided by Karl Casey at White Bat Audio @WhiteBatAudio
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[@cyclopropinon5143]

Truly beatiful! also thanks for sharing!

[@nots4ltii]

title wasnt lying, these sure are beautiful

[@notsus8537]

5:24 I think you had just summon the one Australian painter...

[@Spiderp-p1l]

Those last ones on high v speed can cure depression❤

[@rainbowimpostor951]

I found some interesting 3D graphs in desmos and named them by their appearance...
All of the equations are using operators, which are theoretically canceling each other out.
For example squaring inside of squareroots.
Maybe this could be a video idea...
Here are the equations and their names:
Octahedron:
( x^2 )^½+ ( y^2 )^½ + ( z^2 )^½ = 2
MORE octahedron:
arcos( cos( x ) ) + arcos( cos( y ) ) + arcos( cos( z ) ) = 2
octahedron star:
( x^2 y^2 )^½ + ( x^2 z^2 )^½ + ( z^2 y^2 )^½ = 2
for the following graphs make sure to use v as a slider to animate the graphs...
diagonal waves:
z= sin ( x + y + v )
just a quarter of it:
z=sin( exp( ln( x ) ) + exp( ln( y ) ) + v )
squared waves:
z= sin ( ( x^2 )^½ + ( y^2 )^½ + v )
squared waves as pattern:
z= sin ( arcsin( sin( x ) ) + arcsin ( sin( y ) ) + v )

[@scribbllllll]

G R A P H

[@amiahooman]

What is the lowercase L in the later polar graphs

[@hayn10]

droiy

[@habarvaz3142]

Can you teach us how do you make them tho? I mean do you just guess combinations and relations of different functions and see what looks pretty and go from there or is there some more efficient way?

[@the-mathwizard]

At its core, it's a trial-and-error process, but it's not just purely guessing. Whenever you find an interesting graph, try to identify a particular structure or combination of functions. Save these graphs in a separate file so that whenever you want to make a graph look more interesting, you have some ready functions at your disposal to combine with the existing graph. Over time, you will develop a sense of which combinations of functions look good and which don't. For example, to make graphs more dynamic (with lots of moving parts), try to add variables in more places throughout the equation. That's just one of many patterns I've discovered while making these graphs. Hope that helps!