ArticleProceedings of the National Academy of Sciences of the United States of America1975
Stochastic models for the Earth's relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands.
Article in Proceedings of the National Academy of Sciences of the United States of America, 1975. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 38 papers.
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38 citing papers in PubMed.
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- Fractal Texture Enhancement of Simulated Infrared Images Using a CNN-Based Neural Style Transfer Algorithm with a Histogram Matching Technique.Sensors (Basel, Switzerland) · 2022Article
- Fractal dimension of coastline of Australia.Scientific reports · 2021Article
- Statistical physics approaches to the complex Earth system.Physics reports · 2021Review
- Review about the Application of Fractal Theory in the Research of Packaging Materials.Materials (Basel, Switzerland) · 2021Review
- How the cryptocurrency market has performed during COVID 19? A multifractal analysis.Finance research letters · 2020Article
- Fractal analysis of concurrently prepared latex rubber casts of the bronchial and vascular systems of the human lung.Open biology · 2020Article
- The fractal geometry of bronchial trees differs by strain in mice.Journal of applied physiology (Bethesda, Md. : 1985) · 2020Article
- Paradoxical impact of sprawling intra-Urban Heat Islets: Reducing mean surface temperatures while enhancing local extremes.Scientific reports · 2019Article
- Nanopore Structure and Fractal Characteristics of Lacustrine Shale: Implications for Shale Gas Storage and Production Potential.Nanomaterials (Basel, Switzerland) · 2019Article
- Irregular designs and Darwinism in biology: Genomes as the test case.Journal of biosciences · 2017Article
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Abstract
The degree of irregularity in oceanic coastlines and in vertical sections of the Earth, the distribution of the numbers of islands according to area, and the commonality of global shape between continents and islands, all suggest that the Earth's surface is statistically self-similar. The preferred parameter, one which increases with the degree of irregularity, is the fractal dimension, D, of the coastline; it is a fraction between 1 (limit of a smooth curve) and 2 (limit of a plane-filling curve). A rough Poisson-Brown stochastic model gives a good first approximation account of the relief, by assuming it to be created by superposing very many, very small cliffs, placed along straight faults and statistically independent. However, the relative area predicted for the largest islands is too small, and the irregularity predicted for the relief is excessive for most applications; so is indeed the value of the dimension, which is D = 1.5. Several higher approximation self-similar models are described. Any can be matched to the empirically observed D, and can link all the observations together, but the required self-similarity cannot yet be fully explained.
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