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The seal of Solomon in three dimensions - A fractal pattern for massive parallel architecture progra
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The two dimensional seal of Solomon or Magen David (star of King David) is made of two symmetrical equilateral triangles of same center. The Solomon's seal in three dimensions is composed of four Magen David. It is obtained by browsing a cube-octahedron. A cube-octahedron is a three dimensional solid described by Archimede. This solid is composed of 8 triangles and 6 squares. Each triangle has a symmetrical triangle respective to the center of the solid, and if you project theses two triangles on a plane, you obtain a two dimensional Magen David. The three dimensional Magen David is so obtained by browsing the three apexes of a triangle, then diving in the center of the solid to emerge on the opposite side triangle, then browsing the three apexes of this triangle in a symmetrical path; this browsing draws in perspective a Magen David; in order to complete the three dimensional figure, the browsing continues with two other triangles (for example moving on a vertical axe from the first Magen David) then repeating this with the left and right Magen David. This browsing can be looped into the first Magen David in order to develop an infinite orbit browsing the cube-octahedron. If a word is associated to each apex, the browsing described can build a poem of 24 words composed of 8 sentences of 3 words each (a subject, a verb and an object). Giving a title to that poem, this title can be used as an apex for a bigger seal, composed of 12 cube-octahedrons. This repetition of the browsing pattern and cube-octahedron defines a fractal. Here is such a poem in French with the corresponding mapping on a cube-octahedron: Here is the poem in French: Le physique exprime le comportement Le don connaît le sens Le sens agît sur le psychologique La logique caractérise le physique Le langage agît sur le comportement Le don caractérise le moteur Le moteur exprime le psychologique La logique connaît le langage. Here is an approximative translation: Physical express behavior Gift knows sense Sense acts on psychologic Logical caracterize physical Language acts on behavior Gift caracterize drive Drive express psychologic Logical knows language. A fractal structure of 64 poems and cube-octahedrons is developed in the French electronic book "Journal intime d'un schizophrène". Further investigations are needed in order to determine if our brains use this pattern as a neuronal structuring pattern and how it can be used as an algorithm for massive parallel programming. 
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