I wrote a program to cast some points out to a shape defined by lines and then connect any point to a certain amount of points down the shape with a line, and it looks like this is producing shapes on the inside of it that are very similar to $$ |x|^t + |y|^t = |r|^t $$ shapes you might graph.
Can anyone explain what is going on here?
--In more detail, the program takes a set of lines for an input, in this case creating a square rotated 45 degrees, and then it casts a number of points from the origin of the area outwards, and they are saved once they hit any of the lines,
The program then draws lines from each of these points to points a certain distance down the shape.
Hint: $$|x|^t+|y|^t=|r|^t,$$ represents a square when $t=1$, it represents a curved star like bounded figure if $0<t<1$. For $t=2$, it represents a circle. For $t>1$, it is a bounded region. For $t>>1$ it is like a square with rounded corners. For $r-1$ and $t=1/2,1,2,8$ see the figures below: