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Emergence theory is a unified first-principles quantum gravity unification theory currently in development by a Los Angeles-based team of scientists. Emergence theory weaves together quantum mechanics, general and special relativity, the standard model and other mainstream physics theories into a complete, fundamental picture of a discretized, self-actualizing universe. Visit QUantum gravity research
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A quasicrystal is a three-dimensional structure that exhibits long-range order but lacks periodicity. Such structures have symmetries that are not present in traditional periodic crystals.
Penrose tiling is a specific type of non-periodic tiling that can be constructed from a kite and a dart shape. These tiles can be arranged in a pattern that has a five-fold rotational symmetry, which is not possible in traditional periodic tilings.
The connection between a 3D quasicrystal and the Penrose pattern arises from the fact that the projection of a 3D quasicrystal onto a 2D surface can result in a pattern that exhibits the same five-fold rotational symmetry as the Penrose pattern.
The kite and dart shapes of the Penrose pattern can be seen as the result of projecting the three-dimensional structure of the quasicrystal onto a two-dimensional plane. The resulting pattern retains some of the symmetries of the original quasicrystal and has the same local ordering principles. This projection process is analogous to the process of taking a shadow of an object.
Therefore, the kite and dart Penrose pattern can be seen as a two-dimensional projection of a three-dimensional quasicrystal. This connection has been used to explain the structural properties of some quasicrystals, and also to design materials with interesting physical properties.
Penrose tiling is a specific type of non-periodic tiling that can be constructed from a kite and a dart shape. These tiles can be arranged in a pattern that has a five-fold rotational symmetry, which is not possible in traditional periodic tilings.
The connection between a 3D quasicrystal and the Penrose pattern arises from the fact that the projection of a 3D quasicrystal onto a 2D surface can result in a pattern that exhibits the same five-fold rotational symmetry as the Penrose pattern.
The kite and dart shapes of the Penrose pattern can be seen as the result of projecting the three-dimensional structure of the quasicrystal onto a two-dimensional plane. The resulting pattern retains some of the symmetries of the original quasicrystal and has the same local ordering principles. This projection process is analogous to the process of taking a shadow of an object.
Therefore, the kite and dart Penrose pattern can be seen as a two-dimensional projection of a three-dimensional quasicrystal. This connection has been used to explain the structural properties of some quasicrystals, and also to design materials with interesting physical properties.
By 1200 C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons (girih tiles) decorated with lines. These tiles enabled the creation of increasingly complex periodic girih patterns, and by the 15th century, the tessellation approach was combined with self-similar transformations to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in the West."
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