{"id":4527,"date":"2023-06-16T01:42:25","date_gmt":"2023-06-16T01:42:25","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=4527"},"modified":"2025-08-26T23:30:44","modified_gmt":"2025-08-26T23:30:44","slug":"fractal-basics-apply-it-1","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/fractal-basics-apply-it-1\/","title":{"raw":"Fractal Basics: Apply It 1","rendered":"Fractal Basics: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Understand self-similarity<\/li>\r\n\t<li>Create a fractal shape<\/li>\r\n\t<li>Change the size of a shape using a formula and measure how complex a shape is and how it changes as it gets bigger or smaller<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h3>Navigating the Intricate World of Fractals<\/h3>\r\n<center>\r\n[caption id=\"attachment_6644\" align=\"aligncenter\" width=\"500\"]<img class=\"wp-image-6644\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12172643\/katya-ross-koyy-5uzlPU-unsplash_50-300x200.jpg\" alt=\"An art studio\" width=\"500\" height=\"333\" \/> Figure 1. Alessandra's art studio[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>Welcome to the studio of Alessandra, a renowned modern artist known for her striking use of geometric shapes, scaling, and fractal concepts in her artwork. She believes that understanding and applying these mathematical principles can add depth and intrigue to her pieces. Today, you are Alessandra's assistant, helping her create her next masterpiece. Alessandra's art often embodies the concept of self-similarity. She loves to take inspiration from the nature that surrounds her. While observing a tree outside her studio, she points out the self-similarity in its structure.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]9544[\/ohm2_question]<\/section>\r\n<p>Alessandra takes a break from her art and tree gazing. During her break, she observes a Romanesco broccoli that she bought from the market for lunch. This peculiar vegetable displays an excellent example of self-similarity. Each bud in the broccoli is composed of a series of smaller buds, all of which are a smaller-scale replica of the whole thing.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]9545[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Understand self-similarity<\/li>\n<li>Create a fractal shape<\/li>\n<li>Change the size of a shape using a formula and measure how complex a shape is and how it changes as it gets bigger or smaller<\/li>\n<\/ul>\n<\/section>\n<h3>Navigating the Intricate World of Fractals<\/h3>\n<div style=\"text-align: center;\">\n<figure id=\"attachment_6644\" aria-describedby=\"caption-attachment-6644\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6644\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12172643\/katya-ross-koyy-5uzlPU-unsplash_50-300x200.jpg\" alt=\"An art studio\" width=\"500\" height=\"333\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12172643\/katya-ross-koyy-5uzlPU-unsplash_50-300x200.jpg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12172643\/katya-ross-koyy-5uzlPU-unsplash_50-1024x683.jpg 1024w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12172643\/katya-ross-koyy-5uzlPU-unsplash_50-768x512.jpg 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12172643\/katya-ross-koyy-5uzlPU-unsplash_50-1536x1024.jpg 1536w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12172643\/katya-ross-koyy-5uzlPU-unsplash_50-2048x1365.jpg 2048w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12172643\/katya-ross-koyy-5uzlPU-unsplash_50-1200x800.jpg 1200w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12172643\/katya-ross-koyy-5uzlPU-unsplash_50-65x43.jpg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12172643\/katya-ross-koyy-5uzlPU-unsplash_50-225x150.jpg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12172643\/katya-ross-koyy-5uzlPU-unsplash_50-350x233.jpg 350w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-6644\" class=\"wp-caption-text\">Figure 1. Alessandra&#8217;s art studio<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Welcome to the studio of Alessandra, a renowned modern artist known for her striking use of geometric shapes, scaling, and fractal concepts in her artwork. She believes that understanding and applying these mathematical principles can add depth and intrigue to her pieces. Today, you are Alessandra&#8217;s assistant, helping her create her next masterpiece. Alessandra&#8217;s art often embodies the concept of self-similarity. She loves to take inspiration from the nature that surrounds her. While observing a tree outside her studio, she points out the self-similarity in its structure.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm9544\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=9544&theme=lumen&iframe_resize_id=ohm9544&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Alessandra takes a break from her art and tree gazing. During her break, she observes a Romanesco broccoli that she bought from the market for lunch. This peculiar vegetable displays an excellent example of self-similarity. Each bud in the broccoli is composed of a series of smaller buds, all of which are a smaller-scale replica of the whole thing.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm9545\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=9545&theme=lumen&iframe_resize_id=ohm9545&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":23,"menu_order":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"copyrighted_video\",\"description\":\"Art studio\",\"author\":\"Katya Ross\",\"organization\":\"Unsplash\",\"url\":\"https:\/\/unsplash.com\/photos\/koyy-5uzlPU\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":74,"module-header":"apply_it","content_attributions":[{"type":"copyrighted_video","description":"Art studio","author":"Katya Ross","organization":"Unsplash","url":"https:\/\/unsplash.com\/photos\/koyy-5uzlPU","project":"","license":"arr","license_terms":""}],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4527"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/23"}],"version-history":[{"count":12,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4527\/revisions"}],"predecessor-version":[{"id":15695,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4527\/revisions\/15695"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/74"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4527\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=4527"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=4527"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=4527"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=4527"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}