How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension Export

@article{Mande67, abstract = {Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable. However, many are statistically "selfsimilar," meaning that each portion can be considered a reduced-scale image of the whole. In that case, the degree of complication can be described by a quantity D that has many properties of a "dimension," though it is fractional; that is, it exceeds the value unity associated with the ordinary, rectifiable, curves. 10.1126/science.156.3775.636}, author = {Mandelbrot, Benoit}, citeulike-article-id = {3175474}, citeulike-linkout-0 = {http://dx.doi.org/10.1126/science.156.3775.636}, citeulike-linkout-1 = {http://view.ncbi.nlm.nih.gov/pubmed/17837158}, citeulike-linkout-2 = {http://www.hubmed.org/display.cgi?uids=17837158}, day = {5}, doi = {10.1126/science.156.3775.636}, journal = {Science}, keywords = {fractal, fractal-dimension}, month = {May}, number = {3775}, pages = {636--638}, posted-at = {2008-08-31 01:15:42}, priority = {4}, title = {How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension}, url = {http://dx.doi.org/10.1126/science.156.3775.636}, volume = {156}, year = {1967} }

TY - JOUR ID - Mande67 L3 - citeulike-article-id:3175474 N2 - Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable. However, many are statistically "selfsimilar," meaning that each portion can be considered a reduced-scale image of the whole. In that case, the degree of complication can be described by a quantity D that has many properties of a "dimension," though it is fractional; that is, it exceeds the value unity associated with the ordinary, rectifiable, curves. 10.1126/science.156.3775.636 IS - 3775 JF - Science EP - 638 TI - How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension VL - 156 SP - 636 KW - fractal KW - fractal-dimension AU - Mandelbrot, Benoit PY - 1967/05/05/ UR - http://dx.doi.org/10.1126/science.156.3775.636 ER -