TITLE: $\frac{\max(1,xy)}{y} = x$: Did I just create a fractal?
QUESTION [7 upvotes]: 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

REPLY [5 votes]: 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, $\max(ab,0)=ab$.