Electron Orbitals s, p, d, f

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Just managed to fulfill an old dream of mine since my school years. First, visualised the 'd' electron orbitals of a single atom, then all of them (s, p, d, f) in OpenSCAD. Back then they were only vaguely described in the schoolbook. And I always wondered how they are really shaped. I needed this direct feeling of harmonic oscillation in them. Now found decent descriptions of the related Schrödinger equations and their solutions in the net. All boils down to spherical harmonics. Elegant and compelling at the same time, how Nature plays the harmony game all around and inside us. These forms are created by the standing waves, depending on the amount of energy captured by the electrons. The formulae which describe the orbitals are made of functions sin() and cos() combined mostly by multiplication. They are best to be handled in a polar coordinates. It was relatively easy to implement the polar-to-Carthesian coordinate shift for plotting the 3D shapes. It is done in the code by module polar(rho,theta,phi). The orbitals are shown both in an assembled, spherical form and an "exploded" form, revealing the shape of each orbital separately, displaced vertically. I also applied some colouring just to make the view more 3D'ish. Practice showed that p and f orbitals are represented in conjugated pair of functions. Hence the boolean values next to the orbital formulae, indicating whether the "negative" value is being used. To maintain a reasonable quality of the view and stay within the limits of OpenSCAD, I needed to optimise the code here and there. So I removed the invisible parts by entering an experimental threshold value (cut-off radius) for the assembled spherical shapes. This mechanism also uses an associative array which is not native but doable in OpenSCAD. Handled by function thresholds() and a 2D array called orbs. Although the parts may be made printable, my primary goal was to visualise the orbitals and see and show their direct relationship with the 3D harmonic oscillations. Feel free using it for demonstration if you are a teacher, also, I'm glad if students will benefit from this exercise. I'm amazed by the experience and I hope so will be others, too. Glad to hear from you if you find it useful and want to share your thoughts. Links of pages used for the formulae and for understanding the background and the shapes: http://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/88.18.html https://en.wikipedia.org/wiki/Spherical_harmonics