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Complexities in spatial center derivation
Transactions in GIS, 2018AbstractThe center of a spatial object or set of objects is a rather straightforward and well understood descriptor. Beyond providing a statistically oriented interpretation of the middle of something, the center often has much significance in terms of locating services and activities, but may also represent a place of political/historical importance ...
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Spatial Complexity, Visual Complexity and Aesthetics
2020The concept of “visual complexity” is related to spatial complexity. From landscapes to paintings and fractals, aesthetic appeal is directly related to spatial complexity (or, at least, to its determinants). In this chapter, it is examined how and why: (a) neither spatial complexity nor simplicity guarantee aesthetic appeal; (b) quite often, neither ...
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Spatial Complexity, Psychology and Qualitative Complexity
2020How is spatial complexity perceived by humans? The study of spatial complexity is scale-dependent: a spatial entity that may look simple at some spatial level, may reveal many details if examined closer at finer spatial scales. To perceive complexity, we often resort to generalizations: thematic (grouping up similar themes, i.e.
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2020
Spatial complexity is defined here as the difficulty to simplify the structure or form of a 2-and-higher-dimensional surface or object. The study of spatial complexity refers to the geographical space, to mathematically abstract spaces, to physical objects, or to any surface or object, in a n-dimensional space with n equal to two or higher.
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Spatial complexity is defined here as the difficulty to simplify the structure or form of a 2-and-higher-dimensional surface or object. The study of spatial complexity refers to the geographical space, to mathematically abstract spaces, to physical objects, or to any surface or object, in a n-dimensional space with n equal to two or higher.
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2020
Buffon’s needle, Varignon’s theorem, Jung’s theorem, Sylvester's problem, are all hints that random allocations of spatial objects often obey to geometric restrictions. Further, it can be speculated that, so long as population distributions on surfaces might be represented by strings of symbols, there is no apparent reason why the arcsine law and ...
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Buffon’s needle, Varignon’s theorem, Jung’s theorem, Sylvester's problem, are all hints that random allocations of spatial objects often obey to geometric restrictions. Further, it can be speculated that, so long as population distributions on surfaces might be represented by strings of symbols, there is no apparent reason why the arcsine law and ...
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Chaotic spatial bifurcation by complex coupling
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2007A spatial bifurcation (a transition from stationary to oscillatory regime) in a chain of unidirectionally coupled phase systems is studied. It is shown that complication of coupling terms can make this bifurcation spatially chaotic in contrast to the previously observed “regular” and “predictable” type. It is demonstrated that the found type of spatial
Shalfeev, Vladimir D. +2 more
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2020
From Thurston’s geometrization theorem to the Banach-Tarski paradox, spatial complexity can be enigmatic, due to singularities, immersions, infinities (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 ...
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From Thurston’s geometrization theorem to the Banach-Tarski paradox, spatial complexity can be enigmatic, due to singularities, immersions, infinities (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 ...
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Spatial Complexity and the Future
2020Three sets of determinants of spatial complexity have been identified: (i) probabilistic (entropy, randomness), (ii) geometrical (symmetries, intersections, orthogonality, curvature), (iii) topological (boundaries, genus, dimension, knottedness, braiding, knotting, linking, braiding, writhing).
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Spatial and Temporal Complexity
1974In the first section we examined some of the mainly holistic studies of lake benthos that have been undertaken. Opponents of this approach would suggest that no two lakes are, in reality, alike and that the complexity of nature prevents the holistic view from achieving its goal of developing general statements about the nature of lakes. In this section
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Complexity and Spatial Networks
2013The modern spatial economy has a global “networked” character that is generating important socio-economic and political changes. In this respect, new forms of connectivity play a significant role through their dynamic and complex interplay with the economic and political driving forces behind globalization.
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