This simulation plots the (x,z) projection of the angular part of the hydrogenic wave function Y_l^m(θ,0) to show the spatial orientation of the electron's orbital around the nucleus.

The hydrogenic wave function is a solution to the Schrödinger equation for an idealized hydrogen atom. It describes the probability amplitude of finding an electron in a particular state defined by quantum numbers
  n, l, and m. The complete wave function ψ_nlm(r,θ,ϕ)=
  R_nl(r)Y_l
  ^m(θ,ϕ) is expressed in spherical polar coordinates as a product of radial and angular components, where the radial part R
  _nl(r) is expressed using Laguerre polynomials and the angular part Y_l
  ^m(θ,ϕ) is given by the spherical harmonics, which are expressed in terms of associated Legendre polynomials P_l^m(cos θ).