$\frac{\max(1,xy)}{y} = x$: Did I just create a fractal? https://www.desmos.com/calculator/6hfyqc6ks9
Did I just create a fractal? Again, the function is $\frac{\max(1,xy)}{y} = x$.


Even uncannier version, from the alternative form with "sgn" that Wolfram provided: https://www.desmos.com/calculator/rikex4bvld
 A: You have definitely created a strange fractal-like behavior, but not in the equation itself -- rather in Desmos's plotting software :)
The problem with this equation is that it is true not for a one-dimensional curve of points, but rather for the two-dimensional space of points $(x,y)$ where $xy \ge 1$. Algebraically:
$$
\frac{\max(1, xy)}{y} = x
\iff \max(1, xy) = xy \iff xy \ge 1.
$$
The true plot of this is as follows:

Graphing software -- including Desmos -- is usually optimized for the case of plotting a curve, rather than a 2-dimensional space of points. It is likely that is the reason for the weird behavior.
FWIW, Desmos does warn us that something might be up with this plot, as shown by the following warning in your screenshot:

A: I have identified the regions as being delimited by powers of $2$ and graphs of $y=2^k/x$. The issue is with the implementation of their max function. If you change it to $\max(0,xy)/y=x$, you can extend the pattern all the way down to the origin:
Desmos link

The clean lines make up the true "fractal". But I think this is the end of the line for me, because I have no idea why max would have an issue understanding that if $a\approx 2,b\approx 2$ then clearly, $\max(ab,0)=ab$.
