According to G. I. Gurdjieff and the Fourth Way, the universe was generated by the Law of 7 (Octaves), and the Law of 3 (the law of relationship). This model is an illustration of the 19 octaves that are said to generate matter, and hence the periodic table. This was developed by Russell Smith (see his book,"Gurdjieff: Cosmic Secrets" on Amazon), and is based on the information in G.I. Gurdjieff's book, "All and Everything". This seems to be a verifiable scientific application of the law of 7 and the law of 3, and as such may be a major breakthrough in providing scientific verification of those laws.
Each octave spirals down, creating notes in the diatonic scale of decreasing frequency. The first octave is 1s, the ‘Supreme’ octave, and is the tallest octave in the attached elevation view. (Frequency - the z axis - is measured by the distance down from the top: see the elevation.) Each octave that contains notes of the same frequency as a note in the first member of each ‘family’, or orbital type, is also in the same family, and is labeled sequentially (e.g. 1s, 2s, 3s, etc). If a subsequent octave has NO notes of the same frequency as notes in a previous first octave of a prior family, it becomes the first octave of a new family. The subsequent families to the ‘s’ octaves (p, d, and f), are each generated in this way, and the families are so labeled to match the common names of the atomic orbitals. Each of the 19 octaves is labeled in the accompanying labeled top view. The intervals between the notes in each octave are colored to indicate the family (orbital type) to which the entire octave belongs (s, p, d, or f). The 19 octaves appear in the following order, in the sequence of decreasing frequency of their initial note 'Do'), as they are generated by preceding octaves, starting with the first "Supreme Octave", 1s: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p. Each new octave begins at one of the 'shock points', La or Fa, of a preceding octave. The order in which the octaves are generated is exactly the order in which the atomic orbitals of the elements are filled with electrons! Therefore, this "Cosmic Weave" model leads directly to the generation of the periodic table. To see how these octaves are generated one at a time, please see my smaller model, "Down Octaves of the Periodic Table", which does not include the notes above the initial ‘Do’ of each octave.Each note of the octave is represented by a different solid (Do-sphere, Ti-Icosahedron, La-Cuboctahedron, So-Dodecahedron, Fa-Octahedron, Mi-Cube, Re-Tetrahedron). This model appears with the permission of Russell A. Smith.