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Mutual Regulation in Patch Pattern Dynamics |
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Spatial patch objects such as shrubs, rocks exposures, forests and urban areas form dynamic patterns evolving through patches' expansion, contraction, merge and split while new patches spread by migration, leapfrogging and random colonization. Intrinsic and/or extrinsic forces regulate, control and drive these dynamic most variable spatial phenomena. However, despite their wide presence in natural and anthropogenic landscapes there is limited understanding of their pattern and process relationships. Lack of detail in spatio-temporal information on one hand and of time extents allowing full coverage of slow processes spanning over decades and hundreds of years are among the main reasons for this situation. Another reason concern the complexity of natural and anthropogenic phenomena in terms of the number of factors involved, and their interrelationships across different temporal and spatial scales. Yet, many of these complex systems exhibit common regularities and resilience to structural and peripheral changes in their operational conditions (e.g., urban densification, economic globalization, increasing pollution levels, global warming) and to catastrophic events.
Spatial Duality in Implicit Patch Pattern Evolution is a general hypothesis suggesting that:- Any Gray Level Image may be viewed as an Implicit representation of progressive change in Dichotomic Foreground/ Background patterns.- That there is certain type of mutual regulation between these complementary foreground and background patterns through their evolution, and - That this regulation is embedded within their imagery representations.
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Spatial Duality 
