The duality of fractals: roughness and self-similarity |
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Authors: | Nicolas Bez Sophie Bertrand |
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Institution: | 1. Institut de Recherche pour le d??veloppement (IRD), UMR 212 EME, CRH, Avenue Jean Monnet, BP 171, 34203, S??te Cedex, France 2. IMARPE, Esquina Gamarra y General Valle S/N Chucuito, Callao, Lima, Peru
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Abstract: | The fractal dimension (D HB) is an interesting metrics because it is supposed to quantify by a single value, scale independence and roughness of ecological objects. However, we show here that those two properties may be quantified by a single dimension only in some specific cases. In general, a non-integer D HB quantifies only the roughness, and self-similarity needs to be evidenced or postulated by other means. Second, we revisit some aspects of the practical estimation of D HB. We recommend the use of madogram instead of variogram for estimations based on geostatistics. We propose a simplification of its estimation for 2D fields and discuss its possible relationship with self-similarity. We finally underline the problem of scale and resolution. Field data recorded during a scientific acoustic survey on the North Sea herring are used for illustrations. The paper concludes on a synthesis of practical recommendations to ecologists when using fractal dimension. |
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