Closed Constant Curvature Autoevolutes

These curves are their own evolutes

These curves are defined by the following variation of the Serret-Frenet ODE:
T'(t) = kappa*vel(t)*N(t),
N'(t) = -kappa*vel(t)*T(t) + kappa/vel(t)*(T(t) x N(t)).
The velocity function vel(t) satisfies
vel(t+pi) = 1/vel(t). It is constructed from a function
h(t) = a1*sin(t) + a3*sin(3t) as
vel(t) = sqrt(1 + h^2(t)) - h(t).
For more freedom we scale t := fr*t. This parameter is redundant, by changing all the others one can achieve the same.