{"id":2357,"date":"2019-09-15T12:35:12","date_gmt":"2019-09-15T00:35:12","guid":{"rendered":"https:\/\/www.funk.co.nz\/blog\/?p=2357"},"modified":"2019-09-16T03:05:19","modified_gmt":"2019-09-15T15:05:19","slug":"my-favourite-locations-on-the-mandelbrot-set-fractal","status":"publish","type":"post","link":"https:\/\/www.funk.co.nz\/blog\/visuals\/my-favourite-locations-on-the-mandelbrot-set-fractal","title":{"rendered":"My favourite locations on the Mandelbrot set fractal"},"content":{"rendered":"<p>It's pretty cool that each of these images is defined (minus colour palettes), with just four floating point values:<\/p>\n<ul>\n<li>-0.777120613150274923773<\/li>\n<li>-0.777120273471042550002<\/li>\n<li>0.126857111509958518545<\/li>\n<li>0.126857366062765260933<\/li>\n<\/ul>\n<p>You can make similar ones at the link below...<\/p>\n<div id=\"attachment_2359\" style=\"width: 660px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/firey-pattern.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2359\" class=\"wp-image-2359 size-medium\" title=\"Firey pattern\" src=\"https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/firey-pattern-650x366.png\" alt=\"Firey pattern\" width=\"650\" height=\"366\" srcset=\"https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/firey-pattern-650x366.png 650w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/firey-pattern-600x338.png 600w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/firey-pattern-768x432.png 768w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/firey-pattern-900x506.png 900w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/firey-pattern.png 1600w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/a><p id=\"caption-attachment-2359\" class=\"wp-caption-text\">Firey pattern<\/p><\/div>\n<div id=\"attachment_2361\" style=\"width: 660px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Top-spikey-spires.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2361\" class=\"wp-image-2361 size-medium\" title=\"Top Spikey Spires\" src=\"https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Top-spikey-spires-650x366.png\" alt=\"Top Spikey Spires\" width=\"650\" height=\"366\" srcset=\"https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Top-spikey-spires-650x366.png 650w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Top-spikey-spires-600x338.png 600w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Top-spikey-spires-768x432.png 768w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Top-spikey-spires-900x506.png 900w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Top-spikey-spires.png 1600w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/a><p id=\"caption-attachment-2361\" class=\"wp-caption-text\">Top Spikey Spires<\/p><\/div>\n<div id=\"attachment_2360\" style=\"width: 660px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Smooth-Deep-brot.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2360\" class=\"wp-image-2360 size-medium\" title=\"Smooth Deep Brot\" src=\"https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Smooth-Deep-brot-650x366.png\" alt=\"Smooth Deep Brot\" width=\"650\" height=\"366\" srcset=\"https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Smooth-Deep-brot-650x366.png 650w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Smooth-Deep-brot-600x338.png 600w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Smooth-Deep-brot-768x432.png 768w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Smooth-Deep-brot-900x506.png 900w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/Smooth-Deep-brot.png 1600w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/a><p id=\"caption-attachment-2360\" class=\"wp-caption-text\">Smooth Deep Brot<\/p><\/div>\n<div id=\"attachment_2363\" style=\"width: 660px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/red-yellow-blue.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2363\" class=\"wp-image-2363 size-medium\" title=\"Red Yellow Blue\" src=\"https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/red-yellow-blue-650x366.png\" alt=\"Red Yellow Blue\" width=\"650\" height=\"366\" srcset=\"https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/red-yellow-blue-650x366.png 650w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/red-yellow-blue-600x338.png 600w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/red-yellow-blue-768x432.png 768w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/red-yellow-blue-900x506.png 900w, https:\/\/www.funk.co.nz\/blog\/wp-content\/uploads\/2019\/09\/red-yellow-blue.png 1600w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/a><p id=\"caption-attachment-2363\" class=\"wp-caption-text\">Red Yellow Blue<\/p><\/div>\n<p>Generated by Tom Atkinson using software: <a href=\"http:\/\/math.hws.edu\/eck\/js\/mandelbrot\/MB.html\">http:\/\/math.hws.edu\/eck\/js\/mandelbrot\/MB.html<\/a><\/p>\n<h3>Firey pattern:<\/h3>\n<p><span style=\"font-size: 8px;\"><code>&lt;?xml version='1.0'?&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;mandelbrot_settings_2&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;image_size width='1600' height='900'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;limits&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;xmin&gt;-0.777120613150274923773&lt;\/xmin&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;xmax&gt;-0.777120273471042550002&lt;\/xmax&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;ymin&gt;0.126857111509958518545&lt;\/ymin&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;ymax&gt;0.126857366062765260933&lt;\/ymax&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;\/limits&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;palette colorType='RGB'&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0' color='0;0;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0.17' color='1;0;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0.83' color='1;1;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='1' color='1;1;1'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;\/palette&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;palette_mapping length='1000' offset='0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;max_iterations value='50000'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;\/mandelbrot_settings_2&gt;<\/code><\/span><\/p>\n<p>&nbsp;<\/p>\n<h3>Smooth Deep Brot:<\/h3>\n<p><span style=\"font-size: 8px;\"><code>&lt;?xml version='1.0'?&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;mandelbrot_settings_2&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;image_size width='1600' height='900'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;limits&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;xmin&gt;-0.1010963735366917967418&lt;\/xmin&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;xmax&gt;-0.1010963735366884924122&lt;\/xmax&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;ymin&gt;0.9562865135190346089334&lt;\/ymin&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;ymax&gt;0.9562865135190364863934&lt;\/ymax&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;\/limits&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;palette colorType='RGB'&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0' color='0;0;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0.2' color='1;0;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0.4' color='1;1;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0.5' color='1;1;1'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0.6' color='1;1;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0.8' color='1;0;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='1' color='0;0;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;\/palette&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;palette_mapping length='1000' offset='0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;max_iterations value='10000'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;\/mandelbrot_settings_2&gt;<\/code><\/span><\/p>\n<h3>Red Yellow Blue<\/h3>\n<p><span style=\"font-size: 8px;\"><code>&lt;?xml version='1.0'?&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;mandelbrot_settings_2&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;image_size width='1600' height='900'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;limits&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;xmin&gt;-0.741536187499999998982&lt;\/xmin&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;xmax&gt;-0.733203562499999999338&lt;\/xmax&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;ymin&gt;0.188327906250000000015&lt;\/ymin&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;ymax&gt;0.194577375000000000015&lt;\/ymax&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;\/limits&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;palette colorType='RGB'&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0' color='0;0;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0.2947882736156352' color='1;0;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0.3583061889250814' color='1;1;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='0.6612377850162866' color='0;0;1'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;divisionPoint position='1' color='0;0;0'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;\/palette&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;palette_mapping length='1000' offset='800'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;max_iterations value='50000'\/&gt;<\/code><\/span><br \/>\n<span style=\"font-size: 8px;\"><code>&lt;\/mandelbrot_settings_2&gt;<\/code><\/span><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It&#8217;s pretty cool that each of these images is defined (minus colour palettes), with just four floating point values: -0.777120613150274923773 -0.777120273471042550002 0.126857111509958518545 0.126857366062765260933 You can make similar ones at the link below&#8230; Generated by Tom Atkinson using software: http:\/\/math.hws.edu\/eck\/js\/mandelbrot\/MB.html Firey pattern: &lt;?xml version=&#8217;1.0&#8242;?&gt; &lt;mandelbrot_settings_2&gt; &lt;image_size width=&#8217;1600&#8242; height=&#8217;900&#8217;\/&gt; &lt;limits&gt; &lt;xmin&gt;-0.777120613150274923773&lt;\/xmin&gt; &lt;xmax&gt;-0.777120273471042550002&lt;\/xmax&gt; &lt;ymin&gt;0.126857111509958518545&lt;\/ymin&gt; &lt;ymax&gt;0.126857366062765260933&lt;\/ymax&gt; &lt;\/limits&gt; &lt;palette colorType=&#8217;RGB&#8217;&gt; [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[33],"tags":[54,48],"class_list":["post-2357","post","type-post","status-publish","format-standard","hentry","category-visuals","tag-fractals","tag-webgl"],"_links":{"self":[{"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/posts\/2357","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/comments?post=2357"}],"version-history":[{"count":0,"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/posts\/2357\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/media?parent=2357"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/categories?post=2357"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.funk.co.nz\/blog\/wp-json\/wp\/v2\/tags?post=2357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}