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## 1. Geometry

We have published, as an OpenSource project the algorithm implemented in Java that generates the Five Platonic Fractals - that is fractals generated by five most symmetric detector configurations. The algorithm generates self-similar patterns on a sphere of a unit radius. The points on the sphere represent (pure) states of the simplest quantum system - the spin rotator. This spin quantum system is coupled, continuously in time, to a finite number of symmetrically distributed spin-direction detectors. Thus the symmetry of the pattern reflects the symmetry of the detector directions distribution. Each spin direction is characterized by a vector of unit length. Here we study most symmetrical configurations, therefore we chose direction vectors pointing from the origin to the vertices of one of the five platonic solids. We consider the following five detectors configurations: 1. tetrahedron: 4 detectors along the directions {{0, 0, 1.}, {a, 0, -a}, {-a, a, -a}, {-a, -a, -a}}
2. octahedron: 6 detectors along the directions {{0, 0, 1.}, {1., 0, 0}, {0, 1., 0},
{-1., 0, 0}, {0, -1., 0}, {0, 0, -1.}}
3. cube: 8 detectors along the directions {{0, 0, 1.}, {a, 0, a}, {-a, a, a}, {-a, -a, a},
{a, a, -a}, {a, -a, -a}, {-a, 0, -a}, {0, 0, -1.}}
4. icosahedron: 12 detectors along the directions {{0, 0, 1.}, {0.a, 0, a}, {a, a, a}, {-a, a, a},
{-a, -a, a}, {a, -a, a}, {a, a, -a},
{a, -a, -a}, {-a, a, -a}, {-a, 0, -a},
{-a, -a, -a}, {0, 0, -1.}}
5. dodecahedron: 20 detectors along the directions {{0, 0, 1.}, {a, 0, a}, {-a, a, a}, {-a, -a, a},
{a, a, a}, {a, -a, a}, {-a, a, a},
{a, a, a}, {a, -a, a}, {-a, -a, a},
{a, a, -a}, {a, -a, -a}, {-a, a, -a},
{-a, a, -a}, {-a, -a, -a}, {-a, -a, -a},
{a, a, -a}, {a, -a, -a}, {-a, 0, -a},
{0, 0, -1.}}
where the array of real numbers is given in the following table.                    Next: 2. The algorithm Up: 2. EEQT - Quantum Previous: 2. EEQT - Quantum

2002-04-11