Fun fact – vegetation on Brave was a procedural geometry generator that ran at render time. The seed for the generator was @iquilezles' phone number with the comment:
Not an an SDF sadly. @henryseg, do you have an implicit definition f(w,x,y,z)=0 around that is equivalent to your parametric version? I can try making A(t) a function of z, see how far I can go. But you've probably been there already.