In 1992, Manuel Fernandez-Guasti introduced a smooth algebraic curve that lies between the circle and the square.
The curve has two parameters: radius r and squareness s
This is a quartic curve (i.e. degree 4) because of the x²y² term.
When s = 0, the FG-squircle is a circle with radius r.
When s = 1, the FG-squircle is a square with side length 2r.
In between, it is a shape that resembles both the circle and the square
Note: For this discussion, we are mainly interested with the curve located in the region
-r ≤ x ≤ r and -r ≤ y ≤ r
This quartic polynomial equation can have values for (x,y) outside this scope, but we can ignore those 4 extraneous regions.
for Fernandez-Guasti's original paper.
See also my paper https://arxiv.org/ftp/arxiv/papers/1604/1604.02174.pdf
for more details.