Urban Geography Compression Patterns: Non-Euclidean and Fractal Viewpoints
The intersection of fractals, non-Euclidean geometry, spatial autocorrelation, and urban structure offers valuable theoretical and practical application insights, which echoes the overarching goal of this paper. Its research question asks about connections between graph theory adjacency matrix eigen...
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MDPI AG
2025-01-01
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| author | Daniel A. Griffith Sandra Lach Arlinghaus |
| author_facet | Daniel A. Griffith Sandra Lach Arlinghaus |
| author_sort | Daniel A. Griffith |
| collection | DOAJ |
| description | The intersection of fractals, non-Euclidean geometry, spatial autocorrelation, and urban structure offers valuable theoretical and practical application insights, which echoes the overarching goal of this paper. Its research question asks about connections between graph theory adjacency matrix eigenfunctions and certain non-Euclidean grid systems; its explorations reflect accompanying synergistic influences on modern urban design. A Minkowski metric with an exponent between one and two bridges Manhattan and Euclidean spaces, supplying an effective tool in these pursuits. This model coalesces with urban fractal dimensions, shedding light on network density and human activity compression. Unlike Euclidean geometry, which assumes unique shortest paths, Manhattan geometry better represents human movements that typically follow multiple equal-length network routes instead of unfettered straight-line paths. Applying these concepts to urban spatial models, like the Burgess concentric ring conceptualization, reinforces the need for fractal analyses in urban studies. Incorporating a fractal perspective into eigenvector methods, particularly those affiliated with spatial autocorrelation, provides a deeper understanding of urban structure and dynamics, enlightening scholars about city evolution and functions. This approach enhances geometric understanding of city layouts and human behavior, offering insights into urban planning, network density, and human activity flows. Blending theoretical and applied concepts renders a clearer picture of the complex patterns shaping urban spaces. |
| format | Article |
| id | doaj-art-d0f1566d770c4e43adbe4cb772d7ea8f |
| institution | DOAJ |
| issn | 2673-9909 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | AppliedMath |
| spelling | doaj-art-d0f1566d770c4e43adbe4cb772d7ea8f2025-08-20T02:42:45ZengMDPI AGAppliedMath2673-99092025-01-0151910.3390/appliedmath5010009Urban Geography Compression Patterns: Non-Euclidean and Fractal ViewpointsDaniel A. Griffith0Sandra Lach Arlinghaus1School of Economic, Political, and Policy Sciences, University of Texas at Dallas, Richardson, TX 75080, USASchool for Environment and Sustainability, The University of Michigan, Ann Arbor, MI 48109, USAThe intersection of fractals, non-Euclidean geometry, spatial autocorrelation, and urban structure offers valuable theoretical and practical application insights, which echoes the overarching goal of this paper. Its research question asks about connections between graph theory adjacency matrix eigenfunctions and certain non-Euclidean grid systems; its explorations reflect accompanying synergistic influences on modern urban design. A Minkowski metric with an exponent between one and two bridges Manhattan and Euclidean spaces, supplying an effective tool in these pursuits. This model coalesces with urban fractal dimensions, shedding light on network density and human activity compression. Unlike Euclidean geometry, which assumes unique shortest paths, Manhattan geometry better represents human movements that typically follow multiple equal-length network routes instead of unfettered straight-line paths. Applying these concepts to urban spatial models, like the Burgess concentric ring conceptualization, reinforces the need for fractal analyses in urban studies. Incorporating a fractal perspective into eigenvector methods, particularly those affiliated with spatial autocorrelation, provides a deeper understanding of urban structure and dynamics, enlightening scholars about city evolution and functions. This approach enhances geometric understanding of city layouts and human behavior, offering insights into urban planning, network density, and human activity flows. Blending theoretical and applied concepts renders a clearer picture of the complex patterns shaping urban spaces.https://www.mdpi.com/2673-9909/5/1/9Burgess modelfractalManhattan metricMinkowski metricnon-Euclidean geometry |
| spellingShingle | Daniel A. Griffith Sandra Lach Arlinghaus Urban Geography Compression Patterns: Non-Euclidean and Fractal Viewpoints AppliedMath Burgess model fractal Manhattan metric Minkowski metric non-Euclidean geometry |
| title | Urban Geography Compression Patterns: Non-Euclidean and Fractal Viewpoints |
| title_full | Urban Geography Compression Patterns: Non-Euclidean and Fractal Viewpoints |
| title_fullStr | Urban Geography Compression Patterns: Non-Euclidean and Fractal Viewpoints |
| title_full_unstemmed | Urban Geography Compression Patterns: Non-Euclidean and Fractal Viewpoints |
| title_short | Urban Geography Compression Patterns: Non-Euclidean and Fractal Viewpoints |
| title_sort | urban geography compression patterns non euclidean and fractal viewpoints |
| topic | Burgess model fractal Manhattan metric Minkowski metric non-Euclidean geometry |
| url | https://www.mdpi.com/2673-9909/5/1/9 |
| work_keys_str_mv | AT danielagriffith urbangeographycompressionpatternsnoneuclideanandfractalviewpoints AT sandralacharlinghaus urbangeographycompressionpatternsnoneuclideanandfractalviewpoints |