{"id":2639,"date":"2017-04-14T16:33:37","date_gmt":"2017-04-14T16:33:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=2639"},"modified":"2021-02-08T22:34:51","modified_gmt":"2021-02-08T22:34:51","slug":"assignment-fractals-problem-set","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/assignment-fractals-problem-set\/","title":{"raw":"Assignment: Fractals Problem Set","rendered":"Assignment: Fractals Problem Set"},"content":{"raw":"<h2>Exercises<\/h2>\r\n<h3>Iterated Fractals<\/h3>\r\nUsing the initiator and generator shown, draw the next two stages of the iterated fractal.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>1.\r\n\r\n<img class=\"aligncenter size-full wp-image-1741\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/23234524\/exercise1.png\" alt=\"Initiator is a horizontal line. Generator is a horizontal line that then goes up at a right angle, right at a right angle, down at a right angle, and then continues horizontally.\" width=\"190\" height=\"68\" \/><\/td>\r\n<td>2.\r\n\r\n<img class=\"aligncenter size-full wp-image-1742\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/23235224\/exercise2.png\" alt=\"Initiator is a horizontal line. Generator is a zig-zag.\" width=\"203\" height=\"68\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3.\r\n\r\n<img class=\"aligncenter size-full wp-image-1743\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/23235324\/exercise3.png\" alt=\"Initiator is an upward-sloping line. Generator is that line with smaller lines branching off of it.\" width=\"189\" height=\"67\" \/><\/td>\r\n<td>4.\r\n\r\n<img class=\"aligncenter size-full wp-image-1744\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/23235407\/exercise4.png\" alt=\"Initiator is a horizontal line. Generator is two short horizontal lines side-by-side.\" width=\"202\" height=\"51\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5.\r\n\r\n<img class=\"aligncenter size-full wp-image-1745\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/23235611\/exercise5.png\" alt=\"Initiator is a square. Generator is eight more squares arranged to form the border of a large square.\" width=\"187\" height=\"100\" \/><\/td>\r\n<td>6.\r\n\r\n<img class=\"aligncenter wp-image-1746 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/23235831\/exercise6.png\" alt=\"Initiator is an equilateral triangle. Generator is three equilateral triangles that touch each other at an angle.\" width=\"198\" height=\"100\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<ol start=\"7\">\r\n \t<li>Create your own version of Sierpinski gasket with added randomness.<\/li>\r\n \t<li>Create a version of the branching tree fractal from example #3 with added randomness.<\/li>\r\n<\/ol>\r\n<h3>Fractal Dimension<\/h3>\r\n<ol start=\"9\">\r\n \t<li>Determine the fractal dimension of the Koch curve.<\/li>\r\n \t<li>Determine the fractal dimension of the curve generated in exercise #1<\/li>\r\n \t<li>Determine the fractal dimension of the Sierpinski carpet generated in exercise #5<\/li>\r\n \t<li>Determine the fractal dimension of the Cantor set generated in exercise #4<\/li>\r\n<\/ol>\r\n<h3>Complex Numbers<\/h3>\r\n<ol start=\"13\">\r\n \t<li>Plot each number in the complex plane:\r\n<ol>\r\n \t<li>4<\/li>\r\n \t<li>\u20133i<\/li>\r\n \t<li>[latex]\u20132+3i[\/latex]<\/li>\r\n \t<li>[latex]2 + i[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Plot each number in the complex plane:\r\n<ol>\r\n \t<li>[latex]\u20132[\/latex]<\/li>\r\n \t<li>[latex]4i[\/latex]<\/li>\r\n \t<li>[latex]1+2i[\/latex]<\/li>\r\n \t<li>[latex]\u20131\u2013i[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Compute:\r\n<ol>\r\n \t<li>[latex](2+3i)+(3\u20134i)[\/latex]<\/li>\r\n \t<li>[latex](3\u20135i)\u2013(\u20132\u2013i)[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Compute:\r\n<ol>\r\n \t<li>[latex](1\u2013i)+(2+4i)[\/latex]<\/li>\r\n \t<li>[latex](\u20132\u20133i)\u2013(4\u20132i)[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Multiply:\r\n<ol>\r\n \t<li>[latex]3\\left(2+4i\\right)[\/latex]<\/li>\r\n \t<li>[latex](2i)\\left(-1-5i\\right)[\/latex]<\/li>\r\n \t<li>[latex]\\left(2-4i\\right)\\left(1+3i\\right)[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Multiply:\r\n<ol>\r\n \t<li>[latex]2\\left(-1+3i\\right)[\/latex]<\/li>\r\n \t<li>[latex](3i)\\left(2-6i\\right)[\/latex]<\/li>\r\n \t<li>[latex]\\left(1-i\\right)\\left(2+5i\\right)[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Plot the number [latex]2+3i[\/latex]. Does multiplying by [latex]1-i[\/latex] move the point closer to or further from the origin? Does it rotate the point, and if so which direction?<\/li>\r\n \t<li>Plot the number [latex]2+3i[\/latex]. Does multiplying by [latex]0.75+0.5i[\/latex] move the point closer to or further from the origin?\u00a0\u00a0 Does it rotate the point, and if so which direction?<\/li>\r\n<\/ol>\r\n<h3>Recursive Sequences<\/h3>\r\n<ol start=\"21\">\r\n \t<li>Given the recursive relationship[latex]{{z}_{n+1}}=i{{z}_{n}}+1,\\quad{{z}_{0}}=2[\/latex], generate the next 3 terms of the recursive sequence.<\/li>\r\n \t<li>Given the recursive relationship [latex]{{z}_{n+1}}=2{{z}_{n}}+i,\\quad{{z}_{0}}=3-2i[\/latex], generate the next 3 terms of the recursive sequence.<\/li>\r\n \t<li>Using [latex]c=\u20130.25[\/latex], calculate the first 4 terms of the Mandelbrot sequence.<\/li>\r\n \t<li>Using [latex]c=1\u2013i[\/latex], calculate the first 4 terms of the Mandelbrot sequence.<\/li>\r\n<\/ol>\r\nFor a given value of <em>c<\/em>, the Mandelbrot sequence can be described as <em>escaping<\/em> (growing large), a <em>attracted<\/em> (it approaches a fixed value), or <em>periodic<\/em> (it jumps between several fixed values). A periodic cycle is typically described the number if values it jumps between; a 2-cycle jumps between 2 values, and a 4-cycle jumps between 4 values.\r\n\r\nFor questions 25 \u2013 30, you\u2019ll want to use a calculator that can compute with complex numbers, or use <a href=\"http:\/\/www.opentextbookstore\/mathinsociety\/apps\/complexseq.html\">an online calculator<\/a> which can compute a Mandelbrot sequence. For each value of <em>c<\/em>, examine the Mandelbrot sequence and determine if the value appears to be escaping, attracted, or periodic?\r\n<ol start=\"25\">\r\n \t<li>[latex]c=-0.5+0.25i[\/latex].<\/li>\r\n \t<li>[latex]c=0.25+0.25i[\/latex].<\/li>\r\n \t<li>[latex]c=-1.2[\/latex].<\/li>\r\n \t<li>[latex]c=i[\/latex].<\/li>\r\n \t<li>[latex]c=0.5+0.25i[\/latex].<\/li>\r\n \t<li>[latex]c=-0.5+0.5i[\/latex].<\/li>\r\n \t<li>[latex]c=-0.12+0.75i[\/latex].<\/li>\r\n \t<li>[latex]c=-0.5+0.5i[\/latex].<\/li>\r\n<\/ol>\r\n<h3>Exploration<\/h3>\r\nThe Julia Set for <em>c<\/em> is another fractal, related to the Mandelbrot set. The Julia Set for <em>c<\/em> uses the recursive sequence: [latex]{{z}_{n+1}}={{z}_{n}}^{2}+c,\\quad{{z}_{0}}=d[\/latex], where <em>c<\/em> is constant for any particular Julia set, and <em>d<\/em> is the number being tested. A value <em>d<\/em> is part of the Julia Set for <em>c<\/em> if the sequence does not grow large.\r\n\r\nFor example, the Julia Set for -2 would be defined by [latex]{{z}_{n+1}}={{z}_{n}}^{2}-2,\\quad{{z}_{0}}=d[\/latex]. We then pick values for <em>d<\/em>, and test each to determine if it is part of the Julia Set for -2. If so, we color black the point in the complex plane corresponding with the number <em>d<\/em>. If not, we can color the point <em>d<\/em> based on how fast it grows, like we did with the Mandelbrot Set.\r\n\r\nFor questions 33-34, you will probably want to use the online calculator again.\r\n<ol start=\"33\">\r\n \t<li>Determine which of these numbers are in the Julia Set at [latex]c=-0.12i+0.75i[\/latex]\r\n<ol>\r\n \t<li>a) [latex]0.25i[\/latex]<\/li>\r\n \t<li>b) [latex]0.1[\/latex]<\/li>\r\n \t<li>c) [latex]0.25+0.25i[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Determine which of these numbers are in the Julia Set at\r\n<ol>\r\n \t<li>a) [latex]0.5i[\/latex]<\/li>\r\n \t<li>b) [latex]1[\/latex]<\/li>\r\n \t<li>c) [latex]0.5-0.25i[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\nYou can find many images online of various Julia Sets[footnote]For example, <a href=\"http:\/\/www.jcu.edu\/math\/faculty\/spitz\/juliaset\/juliaset.htm\">http:\/\/www.jcu.edu\/math\/faculty\/spitz\/juliaset\/juliaset.htm<\/a>[\/footnote].\r\n<ol start=\"35\">\r\n \t<li>Explain why no point with initial distance from the origin greater than 2 will be part of the Mandelbrot sequence<\/li>\r\n<\/ol>\r\n&nbsp;","rendered":"<h2>Exercises<\/h2>\n<h3>Iterated Fractals<\/h3>\n<p>Using the initiator and generator shown, draw the next two stages of the iterated fractal.<\/p>\n<table>\n<tbody>\n<tr>\n<td>1.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1741\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/23234524\/exercise1.png\" alt=\"Initiator is a horizontal line. Generator is a horizontal line that then goes up at a right angle, right at a right angle, down at a right angle, and then continues horizontally.\" width=\"190\" height=\"68\" \/><\/td>\n<td>2.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1742\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/23235224\/exercise2.png\" alt=\"Initiator is a horizontal line. Generator is a zig-zag.\" width=\"203\" height=\"68\" \/><\/td>\n<\/tr>\n<tr>\n<td>3.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1743\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/23235324\/exercise3.png\" alt=\"Initiator is an upward-sloping line. Generator is that line with smaller lines branching off of it.\" width=\"189\" height=\"67\" \/><\/td>\n<td>4.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1744\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/23235407\/exercise4.png\" alt=\"Initiator is a horizontal line. Generator is two short horizontal lines side-by-side.\" width=\"202\" height=\"51\" \/><\/td>\n<\/tr>\n<tr>\n<td>5.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1745\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/23235611\/exercise5.png\" alt=\"Initiator is a square. Generator is eight more squares arranged to form the border of a large square.\" width=\"187\" height=\"100\" \/><\/td>\n<td>6.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1746 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2017\/02\/23235831\/exercise6.png\" alt=\"Initiator is an equilateral triangle. Generator is three equilateral triangles that touch each other at an angle.\" width=\"198\" height=\"100\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol start=\"7\">\n<li>Create your own version of Sierpinski gasket with added randomness.<\/li>\n<li>Create a version of the branching tree fractal from example #3 with added randomness.<\/li>\n<\/ol>\n<h3>Fractal Dimension<\/h3>\n<ol start=\"9\">\n<li>Determine the fractal dimension of the Koch curve.<\/li>\n<li>Determine the fractal dimension of the curve generated in exercise #1<\/li>\n<li>Determine the fractal dimension of the Sierpinski carpet generated in exercise #5<\/li>\n<li>Determine the fractal dimension of the Cantor set generated in exercise #4<\/li>\n<\/ol>\n<h3>Complex Numbers<\/h3>\n<ol start=\"13\">\n<li>Plot each number in the complex plane:\n<ol>\n<li>4<\/li>\n<li>\u20133i<\/li>\n<li>[latex]\u20132+3i[\/latex]<\/li>\n<li>[latex]2 + i[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Plot each number in the complex plane:\n<ol>\n<li>[latex]\u20132[\/latex]<\/li>\n<li>[latex]4i[\/latex]<\/li>\n<li>[latex]1+2i[\/latex]<\/li>\n<li>[latex]\u20131\u2013i[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Compute:\n<ol>\n<li>[latex](2+3i)+(3\u20134i)[\/latex]<\/li>\n<li>[latex](3\u20135i)\u2013(\u20132\u2013i)[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Compute:\n<ol>\n<li>[latex](1\u2013i)+(2+4i)[\/latex]<\/li>\n<li>[latex](\u20132\u20133i)\u2013(4\u20132i)[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Multiply:\n<ol>\n<li>[latex]3\\left(2+4i\\right)[\/latex]<\/li>\n<li>[latex](2i)\\left(-1-5i\\right)[\/latex]<\/li>\n<li>[latex]\\left(2-4i\\right)\\left(1+3i\\right)[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Multiply:\n<ol>\n<li>[latex]2\\left(-1+3i\\right)[\/latex]<\/li>\n<li>[latex](3i)\\left(2-6i\\right)[\/latex]<\/li>\n<li>[latex]\\left(1-i\\right)\\left(2+5i\\right)[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Plot the number [latex]2+3i[\/latex]. Does multiplying by [latex]1-i[\/latex] move the point closer to or further from the origin? Does it rotate the point, and if so which direction?<\/li>\n<li>Plot the number [latex]2+3i[\/latex]. Does multiplying by [latex]0.75+0.5i[\/latex] move the point closer to or further from the origin?\u00a0\u00a0 Does it rotate the point, and if so which direction?<\/li>\n<\/ol>\n<h3>Recursive Sequences<\/h3>\n<ol start=\"21\">\n<li>Given the recursive relationship[latex]{{z}_{n+1}}=i{{z}_{n}}+1,\\quad{{z}_{0}}=2[\/latex], generate the next 3 terms of the recursive sequence.<\/li>\n<li>Given the recursive relationship [latex]{{z}_{n+1}}=2{{z}_{n}}+i,\\quad{{z}_{0}}=3-2i[\/latex], generate the next 3 terms of the recursive sequence.<\/li>\n<li>Using [latex]c=\u20130.25[\/latex], calculate the first 4 terms of the Mandelbrot sequence.<\/li>\n<li>Using [latex]c=1\u2013i[\/latex], calculate the first 4 terms of the Mandelbrot sequence.<\/li>\n<\/ol>\n<p>For a given value of <em>c<\/em>, the Mandelbrot sequence can be described as <em>escaping<\/em> (growing large), a <em>attracted<\/em> (it approaches a fixed value), or <em>periodic<\/em> (it jumps between several fixed values). A periodic cycle is typically described the number if values it jumps between; a 2-cycle jumps between 2 values, and a 4-cycle jumps between 4 values.<\/p>\n<p>For questions 25 \u2013 30, you\u2019ll want to use a calculator that can compute with complex numbers, or use <a href=\"http:\/\/www.opentextbookstore\/mathinsociety\/apps\/complexseq.html\">an online calculator<\/a> which can compute a Mandelbrot sequence. For each value of <em>c<\/em>, examine the Mandelbrot sequence and determine if the value appears to be escaping, attracted, or periodic?<\/p>\n<ol start=\"25\">\n<li>[latex]c=-0.5+0.25i[\/latex].<\/li>\n<li>[latex]c=0.25+0.25i[\/latex].<\/li>\n<li>[latex]c=-1.2[\/latex].<\/li>\n<li>[latex]c=i[\/latex].<\/li>\n<li>[latex]c=0.5+0.25i[\/latex].<\/li>\n<li>[latex]c=-0.5+0.5i[\/latex].<\/li>\n<li>[latex]c=-0.12+0.75i[\/latex].<\/li>\n<li>[latex]c=-0.5+0.5i[\/latex].<\/li>\n<\/ol>\n<h3>Exploration<\/h3>\n<p>The Julia Set for <em>c<\/em> is another fractal, related to the Mandelbrot set. The Julia Set for <em>c<\/em> uses the recursive sequence: [latex]{{z}_{n+1}}={{z}_{n}}^{2}+c,\\quad{{z}_{0}}=d[\/latex], where <em>c<\/em> is constant for any particular Julia set, and <em>d<\/em> is the number being tested. A value <em>d<\/em> is part of the Julia Set for <em>c<\/em> if the sequence does not grow large.<\/p>\n<p>For example, the Julia Set for -2 would be defined by [latex]{{z}_{n+1}}={{z}_{n}}^{2}-2,\\quad{{z}_{0}}=d[\/latex]. We then pick values for <em>d<\/em>, and test each to determine if it is part of the Julia Set for -2. If so, we color black the point in the complex plane corresponding with the number <em>d<\/em>. If not, we can color the point <em>d<\/em> based on how fast it grows, like we did with the Mandelbrot Set.<\/p>\n<p>For questions 33-34, you will probably want to use the online calculator again.<\/p>\n<ol start=\"33\">\n<li>Determine which of these numbers are in the Julia Set at [latex]c=-0.12i+0.75i[\/latex]\n<ol>\n<li>a) [latex]0.25i[\/latex]<\/li>\n<li>b) [latex]0.1[\/latex]<\/li>\n<li>c) [latex]0.25+0.25i[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Determine which of these numbers are in the Julia Set at\n<ol>\n<li>a) [latex]0.5i[\/latex]<\/li>\n<li>b) [latex]1[\/latex]<\/li>\n<li>c) [latex]0.5-0.25i[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p>You can find many images online of various Julia Sets<a class=\"footnote\" title=\"For example, http:\/\/www.jcu.edu\/math\/faculty\/spitz\/juliaset\/juliaset.htm\" id=\"return-footnote-2639-1\" href=\"#footnote-2639-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>.<\/p>\n<ol start=\"35\">\n<li>Explain why no point with initial distance from the origin greater than 2 will be part of the Mandelbrot sequence<\/li>\n<\/ol>\n<p>&nbsp;<\/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-2639\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Fractals Problem Set. <strong>Authored by<\/strong>: Lippman, David. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\">http:\/\/www.opentextbookstore.com\/mathinsociety\/<\/a>. <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><hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-2639-1\">For example, <a href=\"http:\/\/www.jcu.edu\/math\/faculty\/spitz\/juliaset\/juliaset.htm\">http:\/\/www.jcu.edu\/math\/faculty\/spitz\/juliaset\/juliaset.htm<\/a> <a href=\"#return-footnote-2639-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":17533,"menu_order":33,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Fractals Problem Set\",\"author\":\"Lippman, David\",\"organization\":\"\",\"url\":\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2639","chapter","type-chapter","status-publish","hentry"],"part":50,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2639","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2639\/revisions"}],"predecessor-version":[{"id":2643,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2639\/revisions\/2643"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/50"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2639\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=2639"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2639"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=2639"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=2639"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}