The set of lines perpendicular to a curve are tangent to a second curve called the evolute.
The lines perpendicular to the ellipse below are tangent to the curve inside called an astroid.
If we replace the ellipse with an egg, we get a similar shape, but less symmetric.
The equation for the egg is described here with parameters a = 3, b = 2, and k = 0.
The ellipse above has the same a and b but k = 0.
I made the lines slightly transparent, setting alpha = 0.
4, so the graph would be darker where many lines cross.
Related post: Envelopes of epicycloids.