Titlebook: Spatial Complexity; Theory, Mathematical Fivos Papadimitriou Book 2020 The Editor(s) (if applicable) and The Author(s), under exclusive lic

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Complexity of Binary Maps of Primes and Transcendentals spatial complexity. Sometimes, knowing the numbers behind the spatial structures not only explains a map’s structure, but can also be used to predict how a map might look like if it extended in space (such is the case of transcendental numbers). Assigning black cells to prime numbers produces squar

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Enigmas of Spatial Complexity (e.g. Alexander’s wild knots, Antoine’s necklace, Ford circles, Hilbert curves). Measuring spatial complexity in already “complex” spatial settings constitutes a major challenge for future research, as it should combine algorithmics, computation and topology within a single whole. Further, complete

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Spatial Complexity in Nature, Science and Technology etc. In the bio-medical sciences, spatial complexity is a key descriptor of melanomas and emerges as a decisive factor in some interpretations of MRI imagery, while the complexity of knotting of proteins is important for DNA analyses.

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Spatial Complexity in 4-and-Higher-Dimensional Spacesl complexity might apply to objects in 4d spaces and, more ambitiously perhaps, decide whether the 3d-and-4d-spaces are the ones capable of sustaining the highest spatial complexity among all .-dimensional spaces.

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The Geometric Basis of Spatial Complexityo or more geometric objects and their intersections (regardless of their sizes) result in substantial differences in spatial complexity. Beyond these, research in polyominoes has furnished various computational complexity results, that are useful for the analysis of spatial complexity on squared surfaces.

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The Probabilistic Basis of Spatial Complexitys spatial complexity. Further, the more disordered their allocation, the higher the spatial complexity also. These considerations however, ramify to a series of questions, i.e.: when is a string of symbols a random one? what alternative definitions of random strings are there and how do they impact spatial randomness?