tag:blogger.com,1999:blog-264226589944705290.post7181029450728150972..comments2022-05-19T07:55:48.367-07:00Comments on God Plays Dice: The Mandelbrot monkMichael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-264226589944705290.post-34495342407577308952008-03-31T19:41:00.000-07:002008-03-31T19:41:00.000-07:00It shouldn't be that difficult to actually plot th...It shouldn't be that difficult to actually plot the Mandelbrot set using tools available to a medieval monk, even without invoking complex numbers.<BR/><BR/>Geometrically, computing z^2 is easier when viewed as r(cos θ+i sinθ). Doubling the angle is easy, and squaring the radius can also be easily done. Adding the +c is as simple as completing a parallelogram. All operations easily performed by someone adept with compass and straight-edge.<BR/><BR/>I could easily see showing how to do a single iteration to, say, Archimedes, and saying "If you start with some points, and iterate this procedure, it goes far away quickly. If you start with other points, it never gets very far away. I wonder which points stay close, and which points go far away? It's obvious that if you ever get to a point more than two units away, the procedure will just take you farther away, so we can give up on a point once the iteration falls outside the 2-unit circle."<BR/><BR/>If I have time today, I'll write up a full procedure on my blog and leave a link here.<BR/><BR/>(and, no, my observation isn't an April Fools Day thing, despite the timing.)Buddha Buckhttps://www.blogger.com/profile/17167036913705912859noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-927398076724943692008-03-28T09:10:00.000-07:002008-03-28T09:10:00.000-07:00Awww, c'mon! April 1 isn't close enough yet.Awww, c'mon! April 1 isn't close enough yet.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-47616982160082739692008-03-28T07:16:00.000-07:002008-03-28T07:16:00.000-07:00Yeah, BTW it is a really nicely crafted joke, the ...Yeah, BTW it is a really nicely crafted joke, the first time i've seen it i did not realize it. I was also too happy, being a fractal lover :)Maurizio Mongehttps://www.blogger.com/profile/02742767209544920947noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-19310503674330067232008-03-28T05:37:00.000-07:002008-03-28T05:37:00.000-07:00The "Harvard Journal of Historical Mathematics" do...The "Harvard Journal of Historical Mathematics" doesn't seem to exist. All references to it in Google point to some reference to this page.John Armstronghttps://www.blogger.com/profile/15177732626660057584noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-56008456611311112732008-03-28T05:34:00.000-07:002008-03-28T05:34:00.000-07:00This just screams hoax. He was working with compl...This just screams hoax. He was working with complex numbers, <I>and</I> their geometric representation 300 years before Tartaglia and Cardano hesitantly advanced the former and 500 years before Argand advanced the latter? Not to mention that he's graphing algebraic statements 400 years before Descartes.<BR/><BR/>The Mandelbrot set hangs on so many other things than computer technology -- things almost everyone takes for granted. This story is at the very least horribly oversimplified, and I suspect is actually totally false. I'll check with BenoĆ®t, though.<BR/><BR/>Oh, and Blogger has broken OpenID. Big surprise: Blogger breaking something.John Armstronghttps://www.blogger.com/profile/15177732626660057584noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-41461464648137879952008-03-28T05:32:00.000-07:002008-03-28T05:32:00.000-07:00stregatto,I know that -- but it's close enough tha...stregatto,<BR/><BR/>I know that -- but it's close enough that people should be keeping their eyes open for such things.Michael Lugohttps://www.blogger.com/profile/15671307315028242949noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-10949360137017944422008-03-28T05:31:00.000-07:002008-03-28T05:31:00.000-07:00It is not yet the 1 April :)It is not yet the 1 April :)Maurizio Mongehttps://www.blogger.com/profile/02742767209544920947noreply@blogger.com