I made some interesting observations today relating to functions in the plane and saw some neat things today while playing around on Desmos.
For instance, if I have some fixed function $f(x)$ ($f$ for fixed), I can distort it by adding some other function $a(x)$ which will take on the role of a new "axis" ($a$ for axis).
I noticed two main things:
If the function $f$ is periodic wrt the x-axis, $f + a$ is periodic wrt $a(x)$
The area between $f$ and the x-axis on some interval $[a, b]$ is the same as the area between $a(x) + f(x)$ and $a(x)$ on $[a, b]$.
Along with a few other things that I haven't yet fully analyzed.
I am really interested in unraveling or rectifying the function $a$ so that it looks like a proper axis, and studying the properties of the distorted $f + a$ ( phence the name). Does this make sense? Is this anything interesting? Is this worth pursuing further?