{"id":1764,"date":"2017-03-14T00:19:53","date_gmt":"2017-03-14T00:19:53","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=1764"},"modified":"2017-04-18T19:00:19","modified_gmt":"2017-04-18T19:00:19","slug":"introduction-fractal-basics","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/chapter\/introduction-fractal-basics\/","title":{"raw":"Introduction: Fractal Basics","rendered":"Introduction: Fractal Basics"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nBy the end of this lesson you will be able to:\r\n<ul>\r\n \t<li>Define and identify self-similarity in geometric shapes, plants, and geological formations<\/li>\r\n \t<li>Generate a fractal shape given an initiator and a generator<\/li>\r\n \t<li>Scale a geometric object by a specific scaling\u00a0factor using the scaling dimension relation<\/li>\r\n \t<li>Determine the fractal dimension of a fractal object<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the 1980's and 90's fractals were a popular, household idea. \u00a0Their presence in popular culture may have waned in the last 20 years, but their presence in nature, economics, and nearly everything around us has not. In this section, we will introduce some of the fundamental ideas, and terminology that will help you begin to understand the mathematical principles that define fractals.\r\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this lesson you will be able to:<\/p>\n<ul>\n<li>Define and identify self-similarity in geometric shapes, plants, and geological formations<\/li>\n<li>Generate a fractal shape given an initiator and a generator<\/li>\n<li>Scale a geometric object by a specific scaling\u00a0factor using the scaling dimension relation<\/li>\n<li>Determine the fractal dimension of a fractal object<\/li>\n<\/ul>\n<\/div>\n<p>In the 1980&#8217;s and 90&#8217;s fractals were a popular, household idea. \u00a0Their presence in popular culture may have waned in the last 20 years, but their presence in nature, economics, and nearly everything around us has not. In this section, we will introduce some of the fundamental ideas, and terminology that will help you begin to understand the mathematical principles that define fractals.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1764\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Introduction and Learning Outcomes. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Introduction and Learning Outcomes\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"2a9b6968-9194-4583-bbea-36ec8658b31b","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1764","chapter","type-chapter","status-publish","hentry"],"part":50,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/1764","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/1764\/revisions"}],"predecessor-version":[{"id":2757,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/1764\/revisions\/2757"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/parts\/50"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapters\/1764\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/media?parent=1764"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/pressbooks\/v2\/chapter-type?post=1764"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/contributor?post=1764"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-mathforliberalarts\/wp-json\/wp\/v2\/license?post=1764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}