Each orbital is an electron wavefunction of hydrogen, labeled by the quantum numbers n, ℓ, m.
n (1–6) sets the energy and overall size — higher n, bigger orbital. ℓ (0 … n−1) sets the shape: 0 = s (sphere), 1 = p (dumbbell), 2 = d (cloverleaf), then f, g, h. m (0 … ℓ) is the angular momentum about the vertical axis — it controls how the shape wraps around that axis.
Brightness follows the probability of finding the electron there. Blue marks regions where the wavefunction is positive, red where it is negative. Dark gaps are nodes — surfaces where the electron is never found: n−ℓ−1 spherical shells plus ℓ angular planes or cones.
Some structure hides inside the cloud — the Slice and Cutaway displays expose it, and lowering the brightness thins the cloud.
Rotating states are the true angular-momentum eigenstates: the electron circulates about the vertical axis with definite momentum m, so orbitals with m > 0 appear as symmetric rings around it (the phase rotates; the magnitude shown here does not).
Standing states combine the +m and −m rotations into standing waves — the lobed textbook shapes chemists draw (px, dxy, …). Same physics, different choice of basis.