<video><title>Secrets of Sacred Geometry: Tesselations and Lattices</title><description>Join host Sebastian Schepis as he takes you on a journey through the world of Sacred Geometry, exploring the nature of form and examining the unfolding of shape. Lets travel from the Plenum to Multiplicity, enjoying the sights.</description><transcript><transcript><line from="00:00:00,000" to="00:00:03,000">Tesolations and lattices.</line><line from="00:00:03,000" to="00:00:11,000">Tesolations involve covering a surface with a repeated geometric pattern, such that no gaps or overlaps occur between the shapes.</line><line from="00:00:11,000" to="00:00:20,000">The mosaic artworks of the alhambra in Spain exemplify intricate two-dimensional tesolations generated by Islamic geometers.</line><line from="00:00:20,000" to="00:00:24,000">Tesolating the plane reveals the latent order in geometry.</line><line from="00:00:24,000" to="00:00:29,000">How seemingly disjoint shapes interlock into integrated holes.</line><line from="00:00:29,000" to="00:00:34,000">It reflects a metaphysics of interdependence, the Buddhist metaphor of Indra's net,</line><line from="00:00:34,000" to="00:00:38,000">and gestalt principles of perceptual organization.</line><line from="00:00:38,000" to="00:00:43,000">In nature, crystalline structures form lattice-like tesolations.</line><line from="00:00:43,000" to="00:00:49,000">The orderly atomic arrangement within minerals generates beautiful symmetries and diffraction patterns.</line><line from="00:00:50,000" to="00:00:58,000">Quasi crystals discovered in 1982 exhibit exotic, apuriotic tylings, not conventionally considered possible.</line><line from="00:00:58,000" to="00:01:02,000">Lattice formations also undergird biological structures.</line><line from="00:01:02,000" to="00:01:10,000">Cytoskeletal filaments and other protein networks form an intracellular lattice providing structural integrity.</line><line from="00:01:10,000" to="00:01:17,000">Epithelial cells join together in tesolating hexagonal lattices creating cohesive sheets.</line><line from="00:01:17,000" to="00:01:26,000">By mimicking such natural tiling processes, geometrations discern the deeper connections between mathematical ideals and organic forms.</line><line from="00:01:26,000" to="00:01:33,000">Tesolations model the passage from metaphysical unity into the diversity of manifest structures.</line><line from="00:01:33,000" to="00:01:40,000">Just as tiles come together into integral mosaic, nature's beauty springs from its hidden geometric order.</line><line from="00:01:40,000" to="00:01:47,000">The two-dimensional repetition of polygonal units discloses the blueprint underlying physical reality,</line><line from="00:01:47,000" to="00:01:53,000">taught by the self-similarity of molecular lattices and the scaling of the tesolating principle,</line><line from="00:01:53,000" to="00:01:58,000">sacred geometers decipher the transcendental in the commonplace forms of nature.</line></transcript></transcript></video>