Metaphors of Dissemination and Interaction of morphoCAs

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34 Diagram.nb The rules placed in the first half are the rules of intra-contextural actions. They don’t refer to other contextures. The rules in the upper part represent the trans-contextural actions between different contextures depicted as directed arrows. The compound morphogram of ruleDM[{1, 3, 4, 11, 15}] reflects the mediation of intra- and inter-contextural actions of the flow chart. It is the morphogram compound of the flow chart of the actions of the morphoCA ruleDM[{1, 3, 4, 11, 15}] . ■ ■ ■ - ■ - ■ □ ■ - ■ - ■ □ □ - ■ - ■ ■ □ - ■ - ■ □ ■ - ■ - Non-reducible examples Non-reducible automata definitions might be used as complete irreducible building-blocs for complex morphoCAs. For complete irreducible building-blocs, all entries of the transition table are occupied. In other terminology, all intra-, inter- and trans-contextural sections of the flow-chart scheme are occupied. Irreducible rules are playing the same role for morphoCAs as the irreducible binary functions like NAND, XOR for binary reductions. With NAND or NOR, all other two-valued binary function are defined. Because they are not reducible they are used as elementary devies in electronic circuit consturctions. Unfortunately, there is not yet an algorithmic procedure to minimize (reduce) the functional representation of morphoCA rules. The question for morphic patterns arises: How many irreducible patterns exist for morphoCA (3,3) ? In analogy: “No logic simplification is possible for the above diagram. This sometimes happens. Neither the methods of Karnaugh maps nor Boolean algebra can simplify this logic further. [..] Since it is not possible to simplify the Exclusive- OR logic and it is widely used, it is provided by manufacturers as a basic integrated circuit (7486).” http://www.allaboutcircuits.com http : // memristors.memristics.com // Reduction %20 and %20 Mediation/Reduction %20 and %20 Mediation.pdf Example : ruleDM[{1, 2,12,4,15}] reducible to steps 22 ruleDM[{1, 2, 12, 4, 15}] Reducts {1, 1, 3} → 1, {3, 3, 0} → 3, {0, 2, 0} → 1, {1, 0, 1} → 2, {3, 1, 3} → 2, {2, 1, 1} → 2 {3, 0, 0} → 3, {3, 2, 2} → 3
Diagram.nb 35 Not reduced ruleDM[{1, 2, 12, 4, 15}] Random Analysis Analysis of the interaction patterns
Page 1 and 2: Metaphors of Dissemination and Inte
Page 3 and 4: Diagram.nb 3 Three kinds of morphoC
Page 5 and 6: Diagram.nb 5 intra R1 R2 R3 R4 ■
Page 7 and 8: Diagram.nb 7 Classical Cellular Aut
Page 9 and 10: Diagram.nb 9 k 1 6 l 2 7 m 3 8 n 4
Page 11 and 12: Diagram.nb 11 Hence, the logic devi
Page 13 and 14: Diagram.nb 13 interaction scheme t
Page 15 and 16: Diagram.nb 15 e1 e2 e4 - e3 e5 R1 -
Page 17 and 18: “CA are a parallel rigid model. I
Page 19 and 20: Diagram.nb 19 morphoCA (4,4) = CA1
Page 21 and 22: Diagram.nb 21 yellow C1t + 1 k - C3
Page 23 and 24: Diagram.nb 23 Claviature: ruleDCKV
Page 25 and 26: Diagram.nb 25 {0, 1, 0} -> 0, {1, 0
Page 27 and 28: Diagram.nb 27 step 88 : {0, 0, 1}
Page 29 and 30: Diagram.nb 29 {1, 2, 1} → 0, : sy
Page 31 and 32: Diagram.nb 31 0, 2, 1 → 0, : sys3
Page 33: Diagram.nb 33 {0, 0, 1} → 2 : sys
Page 37 and 38: Diagram.nb 37 {0, 1, 0} → 2, : sy
Page 39 and 40: Diagram.nb 39 Random Analysis ruleD
Page 41 and 42: Diagram.nb 41 Mediation: poly-layer
Page 43 and 44: Diagram.nb 43 {0, 0, 1} → 2 : sys
Page 45 and 46: Diagram.nb 45 {1, 0, 0, 0} → 3, :
Page 47 and 48: All together Diagram.nb 47
Page 49 and 50: Diagram.nb 49 ¨ Full pattern Witho

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