patterns only serve as labels for correlated wavefunctions that cannot be thought of as a simple crystal of electrons pinned at each third orbital and repelling each other via electrostatic forces.

![(Color online). Overlap between the Coulomb ground state at $\nu=1/3$ for fixed anisotropy $\alpha_0=2,\phi_0=0$ and the family of Laughlin states parametrized by varying $\alpha$, $\phi$. The system is $N_e=9$ electrons on a hexagonal torus.[]{data-label="fig_optimize"}](bulleye2.eps){width="0.85\linewidth"}

For a model wavefunction, the “gauge" freedom in $b,b^\dagger$ implies that the shape of elementary droplets changes with varying $g$, but the basic physical properties remain invariant unless the anisotropy magnitude $\alpha$ becomes too large or too small. If $\alpha$ is such that the maximum effective separation between electrons along some direction is of the order of $\ell_B$ or smaller, the FQH liquid correlations are expected to break down and CDW states might be favored (we will present some examples of this in Sec. \[sec\_ll1\]). On the other hand, a generic state involves a competition of two different metrics – the cyclotron metric, $g_m$, and the Coulomb metric $g_C$, therefore it is best approximated by the Laughlin state with an intrinsic metric $g$ that is generally different from both $g_m$ and $g_C$. Intrinsic metric $g$ 