{"id":4389,"date":"2010-12-28T11:44:46","date_gmt":"2010-12-28T15:44:46","guid":{"rendered":"https:\/\/esa.org\/esablog\/?p=4389"},"modified":"2010-12-28T11:44:46","modified_gmt":"2010-12-28T15:44:46","slug":"the-edges-of-nature","status":"publish","type":"post","link":"https:\/\/esa.org\/esablog\/2010\/12\/28\/the-edges-of-nature\/","title":{"rendered":"The Edges of Nature"},"content":{"rendered":"

This post contributed by\u00a0Nadine Lymn, ESA Director of Public Affairs<\/em><\/p>\n

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
\n\u2014Mandelbrot, The Fractal Geometry of Nature<\/a><\/em><\/span><\/p><\/blockquote>\n

\"\"<\/a> <\/em><\/span>As the year 2010 draws to a close and we find ourselves in the midst of winter\u2019s icy grip, we might pause to marvel at the geometric beauty of a snowflake. \u00a0Earlier this year, the \u201cfather of fractal geometry,\u201d Benoit Mandelbrot, passed away.\u00a0 The New York Times<\/em> <\/span>obituary<\/span><\/a> described how this \u201cmaverick mathematician\u201d proposed a simple but radical way to quantify crookedness by assigning it a \u201cfractal dimension.\u201d\u00a0 Mandelbrot defined a fractal as \u201ca shape made of parts similar to the whole in some way.\u201d\u00a0 This method allowed for a way to quantitatively measure such complex outlines as clouds (or snowflakes) or coastlines and contributed to fields as varied as geology, engineering, medicine, and ecology.<\/span><\/p>\n

A recent <\/span>PBS program<\/span><\/a> explored the world of fractals and its corresponding <\/span>website<\/span><\/a> offers numerous ways to better understand the concept and its applications. \u00a0Described on the website as \u201cirregular, repeating shapes found in cloud formations and tree limbs, in stalks of broccoli and craggy mountain ranges, even in the rhythm of the human heart,\u201d the use of fractals enable the prediction of patterns at different scales.<\/span><\/p>\n

As described on the PBS website, the so-called Mandelbrot set (see above video), which is the \u201cbreeding ground for the world\u2019s most famous fractals,\u201d is an \u201codd-shaped infinite swarm of points clustered on what is known as the \u2018complex number plane.\u2019\u201d\u00a0 To visualize it, the website suggests imaging real numbers such as 1, 2, 3\u2026as spaced out along a number line.\u00a0 Making complex numbers tangible requires two lines (axes) to create a plane and to accommodate the complex numbers\u2019 \u201creal\u201d and \u201cimaginary\u201d parts.\u00a0 The advent of computers and Mandelbrot\u2019s exploratory work at IBM made visualizing fractals possible.\u00a0 This \u201czooming in\u201d on the Mandelbrot set\u2019s boundary reveals its details by \u201cmagnifying it\u201d and allowing people to discover patterns.\u00a0 If you want to try it yourself, the website lets users <\/span>design<\/span><\/a> their own fractal.<\/span><\/p>\n

Applications in ecology include mapping patterns of soils at multiple spatial scales, comparing different landscapes and measuring magnitudes of fluctuations in populations. <\/span><\/p>\n

Ecologists Monica Turner, R.H. Gardner, and Robert V. O\u2019Neill\u2019s 2003 book<\/a> on landscape ecology offers this description of fractals:<\/span><\/p>\n

\u201cThe essence of fractals is the recognition that, for many phenomena, the amount of resolvable detail is a function of scale.\u00a0 An important corollary is that increasing the resolution does not<\/em> result in an absolute increase in precision, but rather it reveals variation that passed unnoticed before.\u201d<\/span><\/p>\n

They go on to note that:<\/span><\/p>\n

\u201cFractals have two important characteristics: (1) they embody the idea of self-similarity, the manner in which variations at one scale are repeated at another; and (2) their dimension is not an integer, but rather a fraction, hence the fractal dimension<\/em>, from which these objects acquired the name.\u201d<\/span><\/p>\n

\"\"<\/a>Ecologist Jim Brown attests that \u201cmuch of life is designed in a fractal-like way.\u201d <\/span><\/p>\n

A Nature<\/em> <\/span>article<\/span><\/a> describes how in the mid-1990s, Brown and fellow ecologist Brian Enquist teamed up with physicist Geoffrey West. The trio scrapped <\/span>Euclidian geometry<\/span><\/a> in favor of fractals to develop a <\/span>theory<\/span><\/a> to explain how organisms use resources.\u00a0 The branching structures of resource distribution networks, such as the xylem that transports water through plants, lends itself well to fractal geometry.\"\"<\/a><\/span><\/p>\n

A later paper by Brown and colleagues, <\/span>\u201cThe fractal nature of nature: power laws, ecological complexity and biodiversity\u201d<\/span><\/a> states that:<\/span><\/p>\n

\u201cNow we are faced with the challenges of understanding the structures and dynamics of the complex systems themselves.\u00a0 We know this cannot be done simply by assembling the parts in ever larger subsystems.\u00a0 There are just too many possibilities.\u00a0 Power laws and other emergent general features of these systems offer invaluable clues to the universal mechanisms that constrain the diversity of life and the complexity of nature.\u201d<\/span><\/p>\n

Photo credits: Trees, Matthew Venn; leaf close-up, kvd<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

This post contributed by\u00a0Nadine Lymn, ESA Director of Public Affairs Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line. \u2014Mandelbrot, The Fractal Geometry of Nature As the year 2010 draws to a close and we find ourselves in the midst of winter\u2019s icy grip,…<\/p>\n","protected":false},"author":41,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[2],"tags":[1099,1100,1101,1102,1103,1104,1105,1106,1107,1108],"class_list":["post-4389","post","type-post","status-publish","format-standard","hentry","category-research","tag-benoit-mandelbrot","tag-brian-enquist","tag-fractal-dimension","tag-fractal-geometry","tag-fractals","tag-jim-brown","tag-landscape-ecology","tag-monica-turner","tag-resource-distribution-networks","tag-self-similarity"],"_links":{"self":[{"href":"https:\/\/esa.org\/esablog\/wp-json\/wp\/v2\/posts\/4389","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/esa.org\/esablog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/esa.org\/esablog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/esa.org\/esablog\/wp-json\/wp\/v2\/users\/41"}],"replies":[{"embeddable":true,"href":"https:\/\/esa.org\/esablog\/wp-json\/wp\/v2\/comments?post=4389"}],"version-history":[{"count":0,"href":"https:\/\/esa.org\/esablog\/wp-json\/wp\/v2\/posts\/4389\/revisions"}],"wp:attachment":[{"href":"https:\/\/esa.org\/esablog\/wp-json\/wp\/v2\/media?parent=4389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/esa.org\/esablog\/wp-json\/wp\/v2\/categories?post=4389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/esa.org\/esablog\/wp-json\/wp\/v2\/tags?post=4389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}