{"id":821,"date":"2008-12-08T10:39:20","date_gmt":"2008-12-08T18:39:20","guid":{"rendered":"http:\/\/www.rudyrucker.com\/blog\/?p=821"},"modified":"2008-12-20T10:22:03","modified_gmt":"2008-12-20T18:22:03","slug":"4d-fractals-and-4d-rotations","status":"publish","type":"post","link":"https:\/\/www.rudyrucker.com\/blog\/2008\/12\/08\/4d-fractals-and-4d-rotations\/","title":{"rendered":"4D Fractals and 4D Rotations"},"content":{"rendered":"

There\u2019s a cute one-panel comic review <\/a>of my novel Mathematicians in Love<\/em> online today.<\/p>\n

<\/p>\n

A programmer named Wiliam Rood has been emailing me about three- and four-dimensional Mandelbrot-set-like fractals. He has a mind-blowing, interactive demo<\/a> on his page\u2014the controls do <\/em>work, but it takes a while to figure them out. Like using an alien iPhone that dropped out of a flying saucer.<\/p>\n

<\/p>\n

I\u2019ve been bugging Rood that he should be working with the Cubic Connectedness Map as described by Douady, Hubbard, Milnor, which is a different take on higher-dimensional fractals than one usually sees. If the images look like taffy, they\u2019re using the Peitgen quaternion approach, which is, I think misguided. What I want to see is spherical warts on warts, as if the regular 2D Mandelbrot set were only a cross-sectional slice.<\/p>\n

<\/p>\n

The cubic connectedness map lets you compute a 2D family of 2D cubic Mandelbrot sets Mk, where k ranges over the complext numbers. If you combined all of the Mk you’d have a 4D object, but first the thing ot look at is a 3D stack of them, like just vary one of the parameters inside k. You can stack to get a 3D object or animate to see a movie. I’d like to see the guy above opening his “mouth” and roaring.<\/p>\n

<\/p>\n

You can also run a diagonalization of the Mk to get a single 2D set I modestly call the Rudy set. I put all of these cubic connectedness map fractals into the old Autodesk Chaos program, still available for free download<\/a> (runs in a DOS window). And I explain the algorithms and the theory on my own alien-scribed tablet<\/a>, which also has a link to Chaos program download.<\/p>\n

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

I\u2019ve also been looking at some great demos by Daniel Piker<\/a>, click on the image agove to se a 4D rotation of a horse. He\u2019s using some software packages called Processing and Rhino, and getting some nice four-dimensional rotation videos, quite unlike any I\u2019ve seen before. <\/p>\n

[I might mention that if you embed a vimeo <\/strong>clip on your web page, the page goes into a continous-download mode with the vimeo site, thereby slaving your page to the corporate masters—which is why I’m not embedding the video.]<\/p>\n

<\/p>\n

That\u2019s all for today. Qeep on Quackin.<\/p>\n","protected":false},"excerpt":{"rendered":"

There\u2019s a cute one-panel comic review of my novel Mathematicians in Love online today. A programmer named Wiliam Rood has been emailing me about three- and four-dimensional Mandelbrot-set-like fractals. He has a mind-blowing, interactive demo on his page\u2014the controls do work, but it takes a while to figure them out. Like using an alien iPhone […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-821","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.rudyrucker.com\/blog\/wp-json\/wp\/v2\/posts\/821","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.rudyrucker.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.rudyrucker.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.rudyrucker.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.rudyrucker.com\/blog\/wp-json\/wp\/v2\/comments?post=821"}],"version-history":[{"count":13,"href":"https:\/\/www.rudyrucker.com\/blog\/wp-json\/wp\/v2\/posts\/821\/revisions"}],"predecessor-version":[{"id":824,"href":"https:\/\/www.rudyrucker.com\/blog\/wp-json\/wp\/v2\/posts\/821\/revisions\/824"}],"wp:attachment":[{"href":"https:\/\/www.rudyrucker.com\/blog\/wp-json\/wp\/v2\/media?parent=821"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.rudyrucker.com\/blog\/wp-json\/wp\/v2\/categories?post=821"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.rudyrucker.com\/blog\/wp-json\/wp\/v2\/tags?post=821"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}