fractal
ematics, graphics> A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a smaller copy of the whole. Fractals are generally self-similar (bits look like the whole) and independent of scale (they look similar, no matter how close you zoom in). Many mathematical structures are fractals e.g. {Sierpinski triangle}, {Koch snowflake}, {Peano curve}, {Mandelbrot set} and ef="module.php?name=Lexikon&file=search&eid=1&query=Lorenz attractor">Lorenz attractor. Fractals also describe many real-world objects that do not have simple geometric shapes, such as clouds, mountains, turbulence, and coastlines. ef="module.php?name=Lexikon&file=search&eid=1&query=Benoit Mandelbrot">Benoit Mandelbrot, the discoverer of the ef="module.php?name=Lexikon&file=search&eid=1&query=Mandelbrot set">Mandelbrot set, coined the term "fractal" in 1975 from the Latin fractus or "to break". He defines a fractal as a set for which the ef="module.php?name=Lexikon&file=search&eid=1&query=Hausdorff Besicovich dimension">Hausdorff Besicovich dimension strictly exceeds the ef="module.php?name=Lexikon&file=search&eid=1&query=topological dimension">topological dimension. However, he is not satisfied with this definition as it excludes sets one would consider fractals. {sci.fractals FAQ (ftp://src.doc.ic.ac.uk/usenet/usenet-by-group/sci.fractals/)}. See also ef="module.php?name=Lexikon&file=search&eid=1&query=fractal compression">fractal compression, ef="module.php?name=Lexikon&file=search&eid=1&query=fractal dimension">fractal dimension, {Iterated Function System}. ef="module.php?name=Lexikon&file=search&eid=1&query=Usenet">Usenet newsgroups: ef="module.php?name=Lexikon&file=search&eid=1&query=news:sci.fractals">news:sci.fractals, ef="module.php?name=Lexikon&file=search&eid=1&query=news:alt.binaries.pictures.fractals">news:alt.binaries.pictures.fractals, ef="module.php?name=Lexikon&file=search&eid=1&query=news:comp.graphics">news:comp.graphics. ["The Fractal Geometry of Nature", Benoit Mandelbrot]. [Are there non-self-similar fractals?] (1997-07-02) e="border-width:thin; border-color:#333333; border-style:dashed; padding:5px;" align="left">In addition suitable contents:
[ ef="module.php?name=Lexikon&op=content&tid=31">2 ] [ ef="module.php?name=Lexikon&op=content&tid=134">= ] [ ef="module.php?name=Lexikon&op=content&tid=255">actor ] [ ef="module.php?name=Lexikon&op=content&tid=396">ag ] [ ef="module.php?name=Lexikon&op=content&tid=411">ai ] [ ef="module.php?name=Lexikon&op=content&tid=433">al ] [ ef="module.php?name=Lexikon&op=content&tid=531">alt ] [ ef="module.php?name=Lexikon&op=content&tid=544">am ] [ ef="module.php?name=Lexikon&op=content&tid=592">an ] [ ef="module.php?name=Lexikon&op=content&tid=683">app ] [ ef="module.php?name=Lexikon&op=content&tid=740">ar ] [ ef="module.php?name=Lexikon&op=content&tid=743">arc ] [ ef="module.php?name=Lexikon&op=content&tid=800">as ] [ ef="module.php?name=Lexikon&op=content&tid=894">at ] [ ef="module.php?name=Lexikon&op=content&tid=935">au ] [ ef="module.php?name=Lexikon&op=content&tid=996">av ] [ ef="module.php?name=Lexikon&op=content&tid=1025">B ] [ ef="module.php?name=Lexikon&op=content&tid=1026">b ] [ ef="module.php?name=Lexikon&op=content&tid=1177">bd ] [ ef="module.php?name=Lexikon&op=content&tid=1181">be ] [ ef="module.php?name=Lexikon&op=content&tid=1219">Benoit Mandelbrot ] [ ef="module.php?name=Lexikon&op=content&tid=1269">bi ] [ ef="module.php?name=Lexikon&op=content&tid=1297">binaries ] [ ef="module.php?name=Lexikon&op=content&tid=1334">bit ] [ ef="module.php?name=Lexikon&op=content&tid=1368">bj ] [ ef="module.php?name=Lexikon&op=content&tid=1535">br ] [ ef="module.php?name=Lexikon&op=content&tid=1562">break ] [ ef="module.php?name=Lexikon&op=content&tid=1695">by ] [ ef="module.php?name=Lexikon&op=content&tid=1724">ca ] [ ef="module.php?name=Lexikon&op=content&tid=2001">ch ] [ ef="module.php?name=Lexikon&op=content&tid=2099">ci ] [ ef="module.php?name=Lexikon&op=content&tid=2138">cl ] [ ef="module.php?name=Lexikon&op=content&tid=2247">co ] [ ef="module.php?name=Lexikon&op=content&tid=2330">com ] [ ef="module.php?name=Lexikon&op=content&tid=2471">compress ] [ ef="module.php?name=Lexikon&op=content&tid=2474">compression ] [ ef="module.php?name=Lexikon&op=content&tid=2545">con ] [ ef="module.php?name=Lexikon&op=content&tid=2606">cons ] [ ef="module.php?name=Lexikon&op=content&tid=2791">cr ] [ ef="module.php?name=Lexikon&op=content&tid=2900">cu ] [ ef="module.php?name=Lexikon&op=content&tid=3151">de ] [ ef="module.php?name=Lexikon&op=content&tid=3470">disc ] [ ef="module.php?name=Lexikon&op=content&tid=3565">do ] [ ef="module.php?name=Lexikon&op=content&tid=3568">doc ] [ ef="module.php?name=Lexikon&op=content&tid=3752">du ] [ ef="module.php?name=Lexikon&op=content&tid=3865">ec ] [ ef="module.php?name=Lexikon&op=content&tid=3896">ed ] [ ef="module.php?name=Lexikon&op=content&tid=3929">ee ] [ ef="module.php?name=Lexikon&op=content&tid=4148">er ] [ ef="module.php?name=Lexikon&op=content&tid=4150">era ] [ ef="module.php?name=Lexikon&op=content&tid=4171">es ] [ ef="module.php?name=Lexikon&op=content&tid=4199">et ] [ ef="module.php?name=Lexikon&op=content&tid=4273">excl ] [ ef="module.php?name=Lexikon&op=content&tid=4396">FAQ ] [ ef="module.php?name=Lexikon&op=content&tid=4497">fi ] [ ef="module.php?name=Lexikon&op=content&tid=4520">file ] [ ef="module.php?name=Lexikon&op=content&tid=4700">fo ] [ ef="module.php?name=Lexikon&op=content&tid=4727">for ] [ ef="module.php?name=Lexikon&op=content&tid=4828">fr ] [ ef="module.php?name=Lexikon&op=content&tid=4830">fractal compression ] [ ef="module.php?name=Lexikon&op=content&tid=4831">fractal dimension ] [ ef="module.php?name=Lexikon&op=content&tid=4834">fragment ] [ ef="module.php?name=Lexikon&op=content&tid=4939">Fun ] [ ef="module.php?name=Lexikon&op=content&tid=4983">G ] [ ef="module.php?name=Lexikon&op=content&tid=5057">ge ] [ ef="module.php?name=Lexikon&op=content&tid=5070">gen ] [ ef="module.php?name=Lexikon&op=content&tid=5134">gh ] [ ef="module.php?name=Lexikon&op=content&tid=5141">gi ] [ ef="module.php?name=Lexikon&op=content&tid=5171">gl ] [ ef="module.php?name=Lexikon&op=content&tid=5200">gm ] [ ef="module.php?name=Lexikon&op=content&tid=5291">gr ] [ ef="module.php?name=Lexikon&op=content&tid=5307">graph ] [ ef="module.php?name=Lexikon&op=content&tid=5377">group ] [ ef="module.php?name=Lexikon&op=content&tid=5434">h ] [ ef="module.php?name=Lexikon&op=content&tid=5540">hat ] [ ef="module.php?name=Lexikon&op=content&tid=5690">hole ] [ ef="module.php?name=Lexikon&op=content&tid=5768">hr ] [ ef="module.php?name=Lexikon&op=content&tid=5931">id ] [ ef="module.php?name=Lexikon&op=content&tid=5956">ie ] [ ef="module.php?name=Lexikon&op=content&tid=6013">il ] [ ef="module.php?name=Lexikon&op=content&tid=6064">in ] [ ef="module.php?name=Lexikon&op=content&tid=6413">io ] [ ef="module.php?name=Lexikon&op=content&tid=6482">is ] [ ef="module.php?name=Lexikon&op=content&tid=6558">it ] [ ef="module.php?name=Lexikon&op=content&tid=6560">Iterated Function System ] [ ef="module.php?name=Lexikon&op=content&tid=6760">K ] [ ef="module.php?name=Lexikon&op=content&tid=6789">ke ] [ ef="module.php?name=Lexikon&op=content&tid=6822">ki ] [ ef="module.php?name=Lexikon&op=content&tid=6918">la ] [ ef="module.php?name=Lexikon&op=content&tid=7009">lb ] [ ef="module.php?name=Lexikon&op=content&tid=7023">ld ] [ ef="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ ef="module.php?name=Lexikon&op=content&tid=7107">li ] [ ef="module.php?name=Lexikon&op=content&tid=7151">line ] [ ef="module.php?name=Lexikon&op=content&tid=7291">logical ] [ ef="module.php?name=Lexikon&op=content&tid=7347">Lore ] [ ef="module.php?name=Lexikon&op=content&tid=7349">Lorenz attractor ] [ ef="module.php?name=Lexikon&op=content&tid=7351">lose ] [ ef="module.php?name=Lexikon&op=content&tid=7399">ls ] [ ef="module.php?name=Lexikon&op=content&tid=7410">lt ] [ ef="module.php?name=Lexikon&op=content&tid=7415">lu ] [ ef="module.php?name=Lexikon&op=content&tid=7441">ly ] [ ef="module.php?name=Lexikon&op=content&tid=7457">M ] [ ef="module.php?name=Lexikon&op=content&tid=7463">ma ] [ ef="module.php?name=Lexikon&op=content&tid=7579">mall ] [ ef="module.php?name=Lexikon&op=content&tid=7582">man ] [ ef="module.php?name=Lexikon&op=content&tid=7591">Mandelbrot set ] [ ef="module.php?name=Lexikon&op=content&tid=7822">metric ] [ ef="module.php?name=Lexikon&op=content&tid=7932">mil ] [ ef="module.php?name=Lexikon&op=content&tid=8032">mo ] [ ef="module.php?name=Lexikon&op=content&tid=8040">mod ] [ ef="module.php?name=Lexikon&op=content&tid=8079">module ] [ ef="module.php?name=Lexikon&op=content&tid=8146">mount ] [ ef="module.php?name=Lexikon&op=content&tid=8167">mp ] [ ef="module.php?name=Lexikon&op=content&tid=8384">N ] [ ef="module.php?name=Lexikon&op=content&tid=8386">na ] [ ef="module.php?name=Lexikon&op=content&tid=8460">nc ] [ ef="module.php?name=Lexikon&op=content&tid=8472">ne ] [ ef="module.php?name=Lexikon&op=content&tid=8488">net ] [ ef="module.php?name=Lexikon&op=content&tid=8599">news ] [ ef="module.php?name=Lexikon&op=content&tid=8602">newsgroup ] [ ef="module.php?name=Lexikon&op=content&tid=8627">ng ] [ ef="module.php?name=Lexikon&op=content&tid=8630">ni ] [ ef="module.php?name=Lexikon&op=content&tid=8675">no ] [ ef="module.php?name=Lexikon&op=content&tid=8760">ns ] [ ef="module.php?name=Lexikon&op=content&tid=8819">nz ] [ ef="module.php?name=Lexikon&op=content&tid=8838">object ] [ ef="module.php?name=Lexikon&op=content&tid=8964">om ] [ ef="module.php?name=Lexikon&op=content&tid=9014">op ] [ ef="module.php?name=Lexikon&op=content&tid=9204">pa ] [ ef="module.php?name=Lexikon&op=content&tid=9457">pe ] [ ef="module.php?name=Lexikon&op=content&tid=9550">ph ] [ ef="module.php?name=Lexikon&op=content&tid=9595">picture ] [ ef="module.php?name=Lexikon&op=content&tid=9651">pl ] [ ef="module.php?name=Lexikon&op=content&tid=9908">pr ] [ ef="module.php?name=Lexikon&op=content&tid=10194">py ] [ ef="module.php?name=Lexikon&op=content&tid=10198">Q ] [ ef="module.php?name=Lexikon&op=content&tid=10253">query ] [ ef="module.php?name=Lexikon&op=content&tid=10364">rc ] [ ef="module.php?name=Lexikon&op=content&tid=10385">re ] [ ef="module.php?name=Lexikon&op=content&tid=10390">real ] [ ef="module.php?name=Lexikon&op=content&tid=10754">rl ] [ ef="module.php?name=Lexikon&op=content&tid=10767">ro ] [ ef="module.php?name=Lexikon&op=content&tid=10887">ru ] [ ef="module.php?name=Lexikon&op=content&tid=10918">S ] [ ef="module.php?name=Lexikon&op=content&tid=10922">sa ] [ ef="module.php?name=Lexikon&op=content&tid=11010">sc ] [ ef="module.php?name=Lexikon&op=content&tid=11128">sd ] [ ef="module.php?name=Lexikon&op=content&tid=11150">se ] [ ef="module.php?name=Lexikon&op=content&tid=11281">set ] [ ef="module.php?name=Lexikon&op=content&tid=11307">sg ] [ ef="module.php?name=Lexikon&op=content&tid=11314">sh ] [ ef="module.php?name=Lexikon&op=content&tid=11376">si ] [ ef="module.php?name=Lexikon&op=content&tid=11510">sk ] [ ef="module.php?name=Lexikon&op=content&tid=11556">sm ] [ ef="module.php?name=Lexikon&op=content&tid=11615">sn ] [ ef="module.php?name=Lexikon&op=content&tid=11651">so ] [ ef="module.php?name=Lexikon&op=content&tid=11909">sr ] [ ef="module.php?name=Lexikon&op=content&tid=11934">st ] [ ef="module.php?name=Lexikon&op=content&tid=12090">strict ] [ ef="module.php?name=Lexikon&op=content&tid=12109">struct ] [ ef="module.php?name=Lexikon&op=content&tid=12133">su ] [ ef="module.php?name=Lexikon&op=content&tid=12359">T ] [ ef="module.php?name=Lexikon&op=content&tid=12588">th ] [ ef="module.php?name=Lexikon&op=content&tid=12721">to ] [ ef="module.php?name=Lexikon&op=content&tid=12777">tp ] [ ef="module.php?name=Lexikon&op=content&tid=12787">tr ] [ ef="module.php?name=Lexikon&op=content&tid=12896">tt ] [ ef="module.php?name=Lexikon&op=content&tid=13008">ug ] [ ef="module.php?name=Lexikon&op=content&tid=13018">uk ] [ ef="module.php?name=Lexikon&op=content&tid=13146">up ] [ ef="module.php?name=Lexikon&op=content&tid=13175">us ] [ ef="module.php?name=Lexikon&op=content&tid=13184">Usenet ] [ ef="module.php?name=Lexikon&op=content&tid=13310">ve ] [ ef="module.php?name=Lexikon&op=content&tid=13366">vi ] [ ef="module.php?name=Lexikon&op=content&tid=13672">wf ] [ ef="module.php?name=Lexikon&op=content&tid=13877">ws ] [ ef="module.php?name=Lexikon&op=content&tid=14138">zoo ] [ ef="module.php?name=Lexikon&op=content&tid=14139">zoom ]
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