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A glowing lattice of points shaped by real spherical harmonics, morphing from one orbital to the next around a hot nucleus. The lobes of the p, d, f and g orbitals, not an illustration.
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Quantum Orbitals draws the shapes of electron orbitals as clouds of glowing dots on black. Three nested copies of one shape, teal outside, pale blue in the middle and white-pink inside, close in on a magenta nucleus while the camera circles them once every 70 seconds.
It tours twelve orbitals, from the two-lobed p_z to the eight-lobed g_xy(x²−y²), holding each for 7 seconds and melting into the next over 3.5 seconds, so one full tour takes a little over two minutes.
The vertex shader places every dot itself: for the two orbitals being blended it runs the associated Legendre recurrence on the graphics card and mixes the two radii, so the morph costs the processor nothing.
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The angles are real: each shape follows |Y_lm(θ, φ)|, the real spherical harmonic for that orbital, so the lobes and the gaps between them sit where a textbook puts them. Two liberties are taken: the radius is raised to the power 0.75 to fatten thin lobes, and every orbital is scaled to the same size.
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Twelve, in a fixed loop: d_xz, f_xyz, d_z², g_z⁴, f_xz², d_xy, f_z³, g_z²xy, p_z, g_xy(x²−y²), f_x(x²−3y²) and d_x²−y². That covers p, d, f and g shapes. Music kicks can hurry the loop along.
Each orbital has its own field-line strength. At f_xyz the 144 dipole loops and the two pole glows are at full strength; at d_z² and f_z³ they fade almost away. During each morph the strength blends between the two orbitals, so the lines rise and fade gradually rather than switching.
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