tag:blogger.com,1999:blog-87570557717813082522011-11-17T18:47:20.794-08:00Mruivohttp://www.blogger.com/profile/04317578092673812571noreply@blogger.comBlogger11100tag:blogger.com,1999:blog-8757055771781308252.post-71224249293189836022011-09-12T15:13:00.001-07:002011-09-12T15:13:01.808-07:00A <b>fractal</b> is "a rough or fragmented <a href="http://en.wikipedia.org/wiki/Shape" title="Shape">geometric shape</a> that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"<sup class="reference" id="cite_ref-0"><a href="http://en.wikipedia.org/wiki/Fractal#cite_note-0"><span>[</span>1<span>]</span></a></sup> a property called <a href="http://en.wikipedia.org/wiki/Self-similarity" title="Self-similarity">self-similarity</a>. Roots of the idea of fractals go back to the 17th century, while mathematically rigorous treatment of fractals can be traced back to functions studied by <a href="http://en.wikipedia.org/wiki/Karl_Weierstrass" title="Karl Weierstrass">Karl Weierstrass</a>, <a href="http://en.wikipedia.org/wiki/Georg_Cantor" title="Georg Cantor">Georg Cantor</a> and <a href="http://en.wikipedia.org/wiki/Felix_Hausdorff" title="Felix Hausdorff">Felix Hausdorff</a> a century later in studying functions that were <a href="http://en.wikipedia.org/wiki/Continuous_function" title="Continuous function">continuous</a> but not <a class="mw-redirect" href="http://en.wikipedia.org/wiki/Differentiable" title="Differentiable">differentiable</a>; however, the term <i><a class="extiw" href="http://en.wiktionary.org/wiki/fractal" title="wikt:fractal">fractal</a></i> was coined by <a class="mw-redirect" href="http://en.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot">Benoît Mandelbrot</a> in 1975 and was derived from the <a href="http://en.wikipedia.org/wiki/Latin" title="Latin">Latin</a> <i><a class="extiw" href="http://en.wiktionary.org/wiki/fractus" title="wikt:fractus">fractus</a></i> meaning "broken" or "fractured." A mathematical fractal is based on an <a href="http://en.wikipedia.org/wiki/Equation" title="Equation">equation</a> that undergoes <a href="http://en.wikipedia.org/wiki/Iteration" title="Iteration">iteration</a>, a form of <a href="http://en.wikipedia.org/wiki/Feedback" title="Feedback">feedback</a> based on <a href="http://en.wikipedia.org/wiki/Recursion" title="Recursion">recursion</a>.<sup class="reference" id="cite_ref-patterns_1-0"><a href="http://en.wikipedia.org/wiki/Fractal#cite_note-patterns-1"><span>[</span>2<span>]</span></a></sup> There are several examples of fractals, which are defined as portraying exact self-similarity, quasi self-similarity, or statistical self-similarity. While fractals are a mathematical construct, they are found in nature, which has led to their inclusion in <a href="http://en.wikipedia.org/wiki/Work_of_art" title="Work of art">artwork</a>. They are useful in medicine, <a href="http://en.wikipedia.org/wiki/Soil_mechanics" title="Soil mechanics">soil mechanics</a>, <a href="http://en.wikipedia.org/wiki/Seismology" title="Seismology">seismology</a>, and <a href="http://en.wikipedia.org/wiki/Technical_analysis" title="Technical analysis">technical analysis</a>.<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/8757055771781308252-7122424929318983602?l=fractalgeometry.blogspot.com' alt='' /></div>Mruivohttp://www.blogger.com/profile/04317578092673812571noreply@blogger.com0