{"id":238,"date":"2010-08-20T23:07:00","date_gmt":"2010-08-20T23:07:00","guid":{"rendered":"http:\/\/blog.ronrecord.com\/index.php\/2010\/08\/20\/mandelbox-zoom\/"},"modified":"2019-03-01T12:44:44","modified_gmt":"2019-03-01T20:44:44","slug":"mandelbox-zoom","status":"publish","type":"post","link":"https:\/\/blog.ronrecord.com\/index.php\/2010\/08\/20\/mandelbox-zoom\/","title":{"rendered":"Mandelbox Zoom"},"content":{"rendered":"\n<p>An amazing zoom on the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Mandelbox\">Mandelbox<\/a> made with Mandelbulb 3D v1.53 and VirtualDub.<\/p>\n\n\n\n[embedyt] https:\/\/www.youtube.com\/watch?v=L1joOtob9rc[\/embedyt]\n\n\n\n<p>In mathematics, the\u00a0<strong><a href=\"https:\/\/en.wikipedia.org\/wiki\/Mandelbox\">mandelbox<\/a><\/strong>\u00a0is a\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Fractal\">fractal<\/a>\u00a0with a boxlike shape found by Tom Lowe in 2010. It is defined in a similar way to the famous\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Mandelbrot_set\">Mandelbrot set<\/a>\u00a0as the values of a parameter such that the origin does not escape to infinity under iteration of certain geometrical transformations. The mandelbox is defined as a map of continuous\u00a0<a href=\"https:\/\/en.wikipedia.org\/wiki\/Julia_set\">Julia sets<\/a>, but, unlike the Mandelbrot set, can be defined in any number of dimensions.<\/p>\n\n\n\n<p>The iteration applies to vector&nbsp;<em>z<\/em>&nbsp;as follows:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>function iterate(z):\n    for each component in z:\n        if component > 1:\n            component := 2 - component\n        else if component &lt; -1:\n            component := -2 - component\n\n    if magnitude of z &lt; 0.5:\n        z := z * 4\n    else if magnitude of z &lt; 1:\n        z := z \/ (magnitude of z)^2\n   \n    z := scale * z + c<\/code><\/pre>\n\n\n\n<p>Here,&nbsp;<em>c<\/em>&nbsp;is the constant being tested, and&nbsp;<em>scale<\/em>&nbsp;is a real number.<\/p>\n\n\n\n[embed-vi-ad]\n","protected":false},"excerpt":{"rendered":"<p>An amazing zoom on the Mandelbox made with Mandelbulb 3D v1.53 and VirtualDub. In mathematics, the\u00a0mandelbox\u00a0is a\u00a0fractal\u00a0with a boxlike shape found by Tom Lowe in 2010. It is defined in&hellip; <\/p>\n","protected":false},"author":1,"featured_media":1170,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[101,94,100,25,176],"tags":[705,306,671,670,307,698],"_links":{"self":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/posts\/238"}],"collection":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/comments?post=238"}],"version-history":[{"count":1,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/posts\/238\/revisions"}],"predecessor-version":[{"id":1169,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/posts\/238\/revisions\/1169"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/media\/1170"}],"wp:attachment":[{"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/media?parent=238"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/categories?post=238"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.ronrecord.com\/index.php\/wp-json\/wp\/v2\/tags?post=238"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}