and other level lines of f(x,y) = y^3 + y^2 − x^4

The level curves of the function f(x,y) = y^3 + y^2 - x^4

can be computed from the ODE: c'(t) = Rot90(grad f)(c(t))

grad f vanishes only at [x,y] = [0,0]. The Tactonal Quartic

has been studied because of its singularity at the origin.

The singularity looks like two curves touching each other.

can be computed from the ODE: c'(t) = Rot90(grad f)(c(t))

grad f vanishes only at [x,y] = [0,0]. The Tactonal Quartic

has been studied because of its singularity at the origin.

The singularity looks like two curves touching each other.

Our ODE solver for the level curves can deal with the singularity,

it computes the 0-level of the function f as two curves (Nr.3 & 4)

But the curvature computation fails at the sigularity.