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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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The DEDALE system for complex spatial queries
Proceedings of the 1998 ACM SIGMOD international conference on Management of data, 1998This paper presents DEDALE, a spatial database system intended to overcome some limitations of current systems by providing an abstract and non-specialized data model and query language for the representation and manipulation of spatial objects.
Grumbach, Stéphane +2 more
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Spatial complexity metrics: an investigation of utility
IEEE Transactions on Software Engineering, 2005Software comprehension is one of the largest costs in the software lifecycle. In an attempt to control the cost of comprehension, various complexity metrics have been proposed to characterize the difficulty of understanding a program and, thus, allow accurate estimation of the cost of a change. Such metrics are not always evaluated.
Gold, Nicolas, Mohan, A M, Layzell, P J
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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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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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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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Complex spatial patterns on planar continua
Physical Review Letters, 1993The Landau-Ginzburg equations used to describe periodic spatial patterns in two dimensions are extended to a set or spatiotemporal equations. The extension is determined by the requirement that the equations or motion commute with translations, reflections, and rotations in the plane.
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1990
Abstract : The work done with this grant was on the topic of complex spatial dynamics, and included progress in three areas: (1) analysis of the space of cellular automation rules, particularly with an eye toward the question of where complex cellular automata live in this space, and (2) analyzing data from complex spatial systems, and (3) nonlinear ...
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Abstract : The work done with this grant was on the topic of complex spatial dynamics, and included progress in three areas: (1) analysis of the space of cellular automation rules, particularly with an eye toward the question of where complex cellular automata live in this space, and (2) analyzing data from complex spatial systems, and (3) nonlinear ...
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