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Post AaUK1iDPnqJvztrf1s by [email protected] |
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More posts by [email protected] |
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Post #AaI8fOs9bmDoF7YiFk by [email protected] |
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If you draw all roots of all polynomials whose coefficients are ±1, you get an… |
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Post #AaI9QRpsPOd92lvaBU by [email protected] |
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At left you see two closeups of the set of all roots of polynomials of some lar… |
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Post #AaICZOzMf96UgOKKZM by [email protected] |
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@johncarlosbaez fun article! Really enjoyed it. 😀 |
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Post #AaICZP3yO0n2ugU0ki by [email protected] |
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@chrisphan - thanks! |
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Post #AaIJkZhHt9ful797s8 by [email protected] |
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@johncarlosbaez there is at least a whole journal on fractal geometry. |
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Post #AaIKjuFS5w5MA4N5yS by [email protected] |
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@Joemoeller - true! And then there's the infamous journal Chaos, Fractals … |
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Post #AaIMK4AameOPJOu9Lc by [email protected] |
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@johncarlosbaez “El Naschie has said "Senior people are above this child… |
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Post #AaIMn6XB4XzH2hJbSC by [email protected] |
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@Joemoeller - bwahaha. He was such an idiot. I loved reading the British jud… |
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Post #AaIN1M3e9VcfF6IV9c by [email protected] |
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@johncarlosbaez IIRC when I played around with drawing this fractal some years … |
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Post #AaIN1M8br3anUUcStE by [email protected] |
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@mathr - a bunch of theorems are known for the set consisting of all roots of L… |
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Post #AaIN3CLJFBUJgtRDVo by [email protected] |
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@johncarlosbaez the implication here is that people submit papers in order to f… |
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Post #AaIOIWc4GHP6r89ICu by [email protected] |
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@johncarlosbaez @mathr Do the boundaries look similar for littlewood polynomial… |
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Post #AaIOPVMRJbBT03AQSm by [email protected] |
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@Joemoeller - since El Naschie published 300 papers in his own journal, and one… |
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Post #AaIOUNFSu933HsE7WK by [email protected] |
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@johncarlosbaez that’s the part that makes this quote double ridiculous |
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Post #AaIOankPIKHdD5lS0O by [email protected] |
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@calculastrology - of course they don't look similar for very small degrees… |
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Post #AaIP6V5yB86GczxuvQ by [email protected] |
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@Joemoeller - he was (and probably still is) a very strange guy. He ran a smal… |
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Post #AaIQDcz5LVG94nhwEy by [email protected] |
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@johncarlosbaez This is super exciting! When I was an undergrad the BIG theorem… |
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Post #AaIQDd4333EHKC1tya by [email protected] |
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@hallasurvivor - wow, so we were destined to meet! In a way the best source of… |
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Post #AaIQWtrcoOL8viPM1I by [email protected] |
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@johncarlosbaez @mathr Thanks! that's what I meant - was making sure that a… |
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Post #AaISGQ99jRBS2RsTom by [email protected] |
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@johncarlosbaez Destiny is funny like that! I don't remember, but if this p… |
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Post #AaISGQDlSIs0Gk2A08 by [email protected] |
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@hallasurvivor - the tale is told here:http://math.ucr.edu/home/baez/roots/Dan … |
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Post #AaISPgJyxqu8oFMENs by [email protected] |
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@johncarlosbaez I took the inspiration from an earlier presentation of yours on… |
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Post #AaISdUhexOSqpZ1E8G by [email protected] |
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@calculastrology - the sets do converge as the degrees get large (i.e. the degr… |
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Post #AaITAGDRqDg1SIVn9c by [email protected] |
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@andrejbauer - cool, I'm glad you're spreading the news about this wond… |
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Post #AaIX2S6GAkUboTgKTg by [email protected] |
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@danielgeisler - Iteration of just \(f_{z,+}\) can't produce, starting from… |
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Post #AaIdfLjQNncV54voq8 by [email protected] |
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@johncarlosbaez There's a clear "handedness" of these patterns - … |
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Post #AaIkNPHL9igeY4BdRo by [email protected] |
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@johncarlosbaez Wow! I was curious how many points are in the set for (say) pol… |
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Post #AaIkbkQzIRdGDQXOPQ by [email protected] |
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@johncarlosbaez @robinhouston It is fun to experiment with other sets of coeffi… |
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Post #AaIyUdglNPk4crQ9o0 by [email protected] |
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@johncarlosbaez @Joemoeller I'm sorely tempted to click the link to find ou… |
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Post #AaIyUdl17b92q3PYR6 by [email protected] |
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@TorbjornBjorkman - the link gives an "explanation" but it makes no s… |
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Post #AaIyws7tI9GFVlZX3A by [email protected] |
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@dneary - yes, on my web page about this I wrote:"Inspired by the pictures… |
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Post #AaIzJYD9VAtGPEqaS8 by [email protected] |
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@kalvotom - nice! Is this page yours?The set I wrote about (K = 1, N → ∞) … |
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Post #AaJ1q7j1CH6rj3PbI8 by [email protected] |
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@johncarlosbaez @robinhouston @gregeganSF @jdchristensen Yes, I messed with it … |
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Post #AaJ4ssgrqs6hpNPdDs by [email protected] |
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@kalvotom @johncarlosbaez @robinhouston hmm, if picking a different finite set … |
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Post #AaJ4sslTZjnG3fZJPE by [email protected] |
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@simontatham - sounds fun, but it took Sam Derbyshire 4 days to generate this o… |
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Post #AaJ8W4p6yWg4c6eMU4 by [email protected] |
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@johncarlosbaez I wonder how long a number like 60 would take to calculate. |
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Post #AaJqs4p03ghkxhtldw by [email protected] |
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@johncarlosbaez @simontatham @robinhouston My impression is that Mathematica is… |
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Post #AaJzPL49TyKUX5MCzA by [email protected] |
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@johncarlosbaez @TorbjornBjorkman @Joemoeller it's rather disappointing, j… |
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Post #AaJzPL8PE9jSkHLbcG by [email protected] |
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@dan131riley @johncarlosbaez @Joemoeller OK, against all common sense I clicked… |
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Post #AaJzPLCIzeqqwNAih6 by [email protected] |
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@TorbjornBjorkman - Maybe you do it so we don't have to. 🙃 @dan131riley… |
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Post #AaSdOA56O8pdbcTTpQ by [email protected] |
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@kalvotom - wow, that's great! To me the most exciting part is the way fra… |
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Post #AaSeAcgXLLhUDd5nEm by [email protected] |
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@johncarlosbaez Coefficients ±1 correspond to the first frame (which looks qui… |
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Post #AaSeZTADscUHvepFJY by [email protected] |
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@kalvotom - I'm afraid to figure out what's known about connectedness i… |
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Post #AaUK1hERSXY0wnKxzU by [email protected] |
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@simontatham @johncarlosbaez @robinhouston Do you mean deforming one set of coe… |
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Post #AaUK1i9A3euxmhsGOm by [email protected] |
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@kalvotom @johncarlosbaez @robinhouston or cycling round in a loop. I just hope… |
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Post #AaUK1iDPnqJvztrf1s by [email protected] |
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@simontatham Something like this? There are roots of all polynomials with degre… |
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Post #AfKR1qjMbVicAtlQDw by [email protected] |
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@johncarlosbaez Apparently dynamical systems people call this “the entropy ba… |
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Post #AfKR9RbVuMIcYwiIsa by [email protected] |
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@gregeganSF - should we sue for copyright infringement? |
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Post #AfKRQMwiTnYb2ThY48 by [email protected] |
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@johncarlosbaez Ha! The image in your paper actually shows more detail, so they… |
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Post #AfMS77EJB0rn42EUq0 by [email protected] |
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@johncarlosbaez This paper by William Thurston starts with the same image as th… |
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Post #AfMS77IYvCGlHEDtT6 by [email protected] |
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@johncarlosbaez I don’t think the “entropy bagel” is *quite* the same as … |
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Post #AfMS77M6i16ZSDsizg by [email protected] |
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@gregeganSF @narain - Someone emailed Giulio Tiozzo and he replied:"Of cou… |
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Post #AfMUbEV0ugdwCoXFwW by [email protected] |
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@johncarlosbaez @narain Giulio Tiozzo: “In fact, I proved a few years ago tha… |
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Post #AfMUjGmcJ0cvbcbLWK by [email protected] |
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@johncarlosbaez @gregeganSF I found this hard to believe, because Fig 1 in Thur… |
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Post #AqyYPtNe9QE18z3oHY by [email protected] |
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@johncarlosbaez Damn dragon curves and their relatives. I can't escape them… |
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Post #Aqz2zdoAWTH5thQci0 by [email protected] |
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@geoffl |
