Superellipses and Superformula can be considered as a generalization of circles and ellipses, two of the classical conic sections. In fact, all conic sections (circle, ellipse, parabola and hyperbola) are special cases of Equation 1 . One can then also consider the same procedure applied to the classic parabola (𝑦 = 𝑥 ! ), the results of which are shown in Figure (left) for integer values of 𝑛. The log-log plot of the superparabola is known as a power law (Figure , right). Using absolute values (𝑦 = |𝑥 ! |) creates shapes that are 'open' above, and 'closed' below. For 𝑛 → ∞, the shape can be be considered a confining 'box', or infinite well. Table One below details the range of ground state energies, determined numerically, for an electron confined to a shape described by Equation where 𝐴 = 𝐵 = 1 for a variety of values of 𝑛 . The energies are reported as a function of mesh spacing (Δ), where the mesh spacing refers to the fineness of the grid used to determine the numeric solutions. Analytic solutions exist for 𝑛 = 1 (diamond), 𝑛 = 2 (square), and 𝑛 = ∞ (circle) and serve as useful validation of the approximate solutions.