Folium Of Descartes f(x,y) = 0
and other level lines of f(x,y) = x^3 + y^3 - 3x*y
Modify the curve
Select level Nr. 0 ... 13:
The level curves of the function
f(x,y) = x^3 + y^3 -3*x*y
can be computed from the ODE:
c'(t) = Rot90(grad f)(c(t))
where grad f vanishes at the origin [x,y] = [0,0],
where the Folium Of Descartes
has a double point singularity and grad f vanishes at
[x,y] = [1,1], where f has a local minimum.
The level curves of the folium polynomial are individually computed as
solutions of an ODE.
Therefore they can be treated as parametrized curves.