{"id":30578,"date":"2024-10-15T22:50:19","date_gmt":"2024-10-15T14:50:19","guid":{"rendered":"https:\/\/stuif.com\/blog\/?p=30578"},"modified":"2024-10-17T22:07:47","modified_gmt":"2024-10-17T14:07:47","slug":"the-mandelbrot-fractal","status":"publish","type":"post","link":"https:\/\/stuif.com\/blog\/?p=30578","title":{"rendered":"The Mandelbrot Fractal"},"content":{"rendered":"\n

In the 1991 edition of the Guinness Book of Records the Mandelbrot Fractal is mentioned as Most complex object in mathematics? <\/a>, with as explanation: A mathematical description of the shape\u2019s outline would require an infinity of information and yet the pattern can be generated from a few lines of computer code<\/em>.<\/p>\n\n\n\n

Here is the Mandelbrot Fractal.<\/p>\n\n\n\n

\n
\"\"<\/a><\/figure>\n<\/figure>\n\n\n\n

When you zoom in on the outline of the fractal, you will see more and more details.<\/p>\n\n\n\n

\n
\"\"<\/a><\/figure>\n<\/figure>\n\n\n\n

And you will notice that there are smaller copies of the Mandelbrot.<\/p>\n\n\n\n

\n
\"\"<\/a><\/figure>\n<\/figure>\n\n\n\n

Connected to the main shape in a complicated way.<\/p>\n\n\n\n

\n
\"\"<\/a><\/figure>\n<\/figure>\n\n\n\n

Same shape, but often a bit distorted. <\/p>\n\n\n\n

\n
\"\"<\/a><\/figure>\n<\/figure>\n\n\n\n

Infinite detail.<\/p>\n\n\n\n

\n
\"\"<\/a><\/figure>\n<\/figure>\n\n\n\n

I learned about the Mandelbrot fractal around 1985 and got hooked right away ;-). On my PC I wrote programs to generate the Mandelbrot Fractal myself. In 1988 I attended a symposium organised by the Delft University, Fractals and Computed Art<\/em>. I submitted one of my fractal images to a contest but didn’t win a prize :-(. I gave talks about the topic to my students and in 1990 to a group of senior citizens..<\/p>\n\n\n\n

More than ten years later I built my own website<\/a> and of course part of it was about fractals.One page, Fractals<\/a>, describes in more detail than above my experiences with the Mandelbrot fractal. The page has many broken links. but is still worth reading . I also wrote a tutorial<\/a>, (in Dutch). aimed at high school students, It became quite popular, because I had written a number of interactive Java applets, where you could play around with the various aspects of the Mandelbrot Fractal.<\/p>\n\n\n\n

However, in the years that followed, it became more and more difficult (and now even impossible) to run Java applets, because of the security risks involved.<\/p>\n\n\n\n

A few months ago, after talking with friends, I decided to translate the tutorial into English and look for a replacement of my applets. There are many interactive applications on the internet related to the Mandelbrot Fractal, but it took me time to find the ones that fit well with my tutorial.<\/p>\n\n\n\n

I am very pleased with the final result. Click on the screenshot below to enter the tutorial.<\/p>\n\n\n\n

\n
\"\"<\/a><\/figure>\n<\/figure>\n\n\n\n

Enjoy the beauty of mathematics!<\/em><\/p>\n\n\n\n

<\/p>\n\n\n\n

<\/p>\n\n\n\n

<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

In the 1991 edition of the Guinness Book of Records the Mandelbrot Fractal is mentioned as Most complex object in mathematics? , with as explanation: A mathematical description of the shape\u2019s outline would require an infinity of information and yet … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":30596,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[32],"tags":[],"class_list":["post-30578","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/stuif.com\/blog\/wp-content\/uploads\/2024\/10\/Mandelbrot_7.jpg","jetpack_shortlink":"https:\/\/wp.me\/p2LqIR-7Xc","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/stuif.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/30578","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/stuif.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/stuif.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/stuif.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/stuif.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=30578"}],"version-history":[{"count":28,"href":"https:\/\/stuif.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/30578\/revisions"}],"predecessor-version":[{"id":30628,"href":"https:\/\/stuif.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/30578\/revisions\/30628"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/stuif.com\/blog\/index.php?rest_route=\/wp\/v2\/media\/30596"}],"wp:attachment":[{"href":"https:\/\/stuif.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=30578"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/stuif.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=30578"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/stuif.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=30578"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}