{"id":2074,"date":"2009-02-27T08:30:20","date_gmt":"2009-02-27T00:30:20","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=2074"},"modified":"2018-06-26T10:27:28","modified_gmt":"2018-06-26T02:27:28","slug":"friday-math-movie-math-in-art","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/videos\/friday-math-movie-math-in-art-2074","title":{"rendered":"Friday Math Movie - Math in Art"},"content":{"rendered":"<p><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/02\/math-in-art-1.gif\" alt=\"math in art\" title=\"math-in-art-1\" width=\"230\" height=\"230\" \/> <img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/02\/math-in-art-2.gif\" alt=\"math in art\" title=\"math-in-art-2\" width=\"230\" height=\"230\" \/><\/p>\n<p style=\"text-align:center;font-size:0.9em;\">Images from the movie.<\/p>\n<p>Lasse Rempe from the University of Liverpool studies dynamical systems. A dynamical system is:<\/p>\n<blockquote>\n<p>... a physical setting together with rules for how the setting changes or evolves from one moment of time to the next.<\/p>\n<p>One basic goal of the mathematical theory of dynamical systems is to determine or characterize the long-term behavior of the system. (From okstate.edu, link no longer available.)<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.intmath.com\/complex-numbers\/fractals.php\">Fractals<\/a> are one example of a dynamical system. You start with a function that involves complex numbers, and you feed in a number. You feed in the result of the first step to get a second number. And so on.<\/p>\n<p><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/02\/math-in-art-3.gif\" alt=\"math in art\" title=\"math-in-art-3\" width=\"230\" height=\"230\" \/> <img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/02\/math-in-art-4.gif\" alt=\"math in-art\" title=\"math-in-art-4\" width=\"230\" height=\"230\" \/><\/p>\n<p>Another example of a dynamical system is <a href=\"https:\/\/www.intmath.com\/differential-equations\/des-intro.php\">differential equations<\/a>. If you cannot find an algebraic solution for a differential equation, you can use a numerical technique which is quite like what we did for fractals &mdash; enter a number into the equation and get a result, then enter the result into the \"system\" again to get another result, and so on.<\/p>\n<p>This week's movie shows some nice art that results from the study of such dynamical systems.<\/p>\n<p>The movie&rsquo;s over on BBC.com - they don&rsquo;t allow an embed:<\/p>\n<p><a href=\"http:\/\/news.bbc.co.uk\/2\/hi\/science\/nature\/7617191.stm\">The art of mathematics<\/a><\/p>\n<p class=\"alt\">See the <a href=\"https:\/\/www.intmath.com\/blog\/videos\/friday-math-movie-math-in-art-2074#comments\" id=\"comms\">1 Comment<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"<p><a href=\"https:\/\/www.intmath.com\/blog\/videos\/friday-math-movie-math-in-art-2074\"><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2009\/02\/dynamical-system-art.gif\" alt=\"dynamical system art\" title=\"dynamical-system-art\" width=\"128\" height=\"119\" class=\"imgRt\" \/><\/a>This movie shows some beautiful art that comes from the study of dynamical systems in math.<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[105],"tags":[127],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/2074"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=2074"}],"version-history":[{"count":1,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/2074\/revisions"}],"predecessor-version":[{"id":11482,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/2074\/revisions\/11482"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=2074"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=2074"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=2074"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}