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Mandelbrot Set Originally Found In 13th Century (Early April's Fool) 122

Posted by Hemos from the my-history-degree-does-matter! dept.
lines writes "I was amazed to find out that the Mandelbrot Set was discovered by a 13th century monk -- way, way before the advent of non-human computers. Apparently, a mathematician spied a mini-mandelbrot masquerading as the Star of Bethlehem in an illuminated manuscript's depiction of the Nativity scene. It turns out that this particular monk, Udo of Aachen, was attempting to mathematically describe a soul's path to Heaven. (For those unfamiliar with it, here's a quick introduction to the Mandelbrot Set.)" Update 30 mins later by J : Yes, this is an old April Fool's joke - and a cleverly done one, too.
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Mandelbrot Set Originally Found In 13th Century

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  • Re:Oh, come on! (Score:3)

    by Anonymous Coward on Thursday March 22, 2001 @03:16PM (#345976)
    about as well done as most of the "All your base are belong to us" Photoshop jobs, and just about as easy to spot. Hemos really

    You mean those aren't real? Somebody didn't really tattoo 'all your base are belong to us' onto his ass and get chased by cops through a corn field?
  • Yale gave George W. Bush a degree, so they can't be worth much...

    - A.P.

    --
    * CmdrTaco is an idiot.

  • The Europeans at this time (13th century) were still counting with Roman numbers and thus were merely capable to multiply.

    There is a very famous letter from a merchant to a mathematician in Germany were he asks where he should send his son for studying so that he can learn proper mathematics. The reply from the mathematician was that if he were just to learn how to add and substract, it would be sufficient to stay in Germany. But if he wanted to learn how to multiply it would be necessary to go to Florence (in Italy, has a very old university).

    The problem for mathematics in Europe were the Roman numbers. They didn't allow a purely syntactical calculation like the arabian numbers we use now (try to add II and CIIX by writing them in a table like we learn now in school!).

    Arabian numbers were first introduced in Europe with Adam Ries in the 16th century (I think).

    Sebastian
  • For anyone interested: A good introduction about the history of numbers and algorithms can be found in a paper by F. Bauer (I think he has also invented the B+-tree):

    http://www.charlesworth.com/isr/issues/isr231/1379 _18/ [charlesworth.com]

    Those of you familiar with German can also have a look at a short overview of Adam Ries' "Rechnen auff der Linihen" from 1518, which describes how to calculate the multiplication on the Abacus and is considered as the first mathematical book for the common people: Rechnen auff der Linihen [aol.com]

    After "Rechnen auff der Linihen", he wrote "Rechnen auff der Linihen und der Federn" which also is considered as the introduction of the Arabic numbers to Central Europe.

    (see Adam Ries [learnetix.de] - German)

    The Arabic numbers had been introduced to Europe in 1202 by Leonardo Fibonacci (who also found the famous "fibonacci numbers", now a standard algorithm for describing recursion).

    And last but not least, also an article in English: Adam Ries [st-and.ac.uk].

    Sebastian

  • I was almost willing to believe it, despite the extraordinary unlikliness of it all (what can I say, I like unlikely things), until I saw the "infra-red photograph" of the Codex Udolphus.

    Did anyone else notice that the "handwriting" is just a pasted-in snippet of the Voynich Manuscript [att.com]? Clearly Ray Girvan is up on his obscure un-translated early renaissance alchemy texts, at least.

  • 2. The bit about "disputing the bible's claim that pi = 3" really ruins the plausibility. No one except atheists trying to disprove the bible has ever claimed that the bible says pi = 3.

    Actually, there's a bit in the OT about Solomon's Temple where pillars are supposed to be one cubit across, three cubits around, and circular. Jewish scholars debated this in the Middle Ages; generally they agreed that the measures recorded were merely approximate, but one school argued that the presence of God actually changed the geometry of parts of the Temple to a non-Euclidian form where pi really did equal three.

    Steven E. Ehrbar
  • O Fortune,
    like the moon
    you are changeable,
    ever waxing
    and waning;
    hateful life
    first oppresses
    and then soothes
    as fancy takes it;
    first posting
    and taking away
    just an April fool's joke.
  • Yeah, but the colors are determined by the "rate" .. right?
  • (and I skimmed over the article) but does this seem fake to anyone else? :) The only reason I'd think it wasn't fake is simply because it's really not THAT funny of a hoax.. just kind of silly really.

    If it's not a fake, then, well, wow. IIRC, the mandelbrot set is a plot on the real/imaginary axes of the "rate" at which the function approaches infinity for each coordinate.. it seems odd that a monk would use the same technique for describing the fractal. Especially since this technique is just begging for a high amount of computation. Unless I'm missing something, aren't there many possible ways to describe the mandelbrot set other than using this technique? I'd imagine a monk with limited computational resources would decide on a description of the fractal that would be more concise and elegant and less computationally intense than plotting it!
  • Probably just pinching gullible people.
  • Probably not the algorists, as they tend to punch the wrong dots.

    --
  • I'm not really sure how hard it is to go from a picture to a fractal, but it's doable. When you do that, you get a good level of compression. Also, once the picture is encoded as a fractal, you can create much better enlargements than possible with just bicubic interpolation.

    Altamira has a Photoshop plugin, Genuine Fractals [206.63.152.155], that does this. I haven't tested it out yet, but I remember favorable reviews for it. It only requires a "G1" Mac with 32 megs, so the process of generating the fractals can't be too hard (of course, Photoshop users are accustomed to waiting for ages for something to happen).

    For a (seemingly exhaustive) survey of the state-of-the-art (as of 1999) in fractal image encoding, check out this page [ucsd.edu], which Google seems to like a lot.
    --
    How many classes do you have to take

  • I think its fairly good as far as these kind of things go.
    It's semi-plausible and appears to have a lot of details.
    Also, just because its two years old doesn't mean everyone has heard about it.
    What I am trying to say is that hindsight is 20/20.
    Anyone can be a genius after the facts come out.
    Give Hemos a break, at least he spelled everything right!
  • Thelonius was quite real, I assure you. He managed to rescue some older Greek texts that became the Apocrypha [chapters that didn't make it into the Bible] of Biblical fame. Nice fellow too.

  • My soul is trapped in a maze of twisty little passages, all different.
  • Ah, but did you understand the reference to Adventure, the popular text-based game?
  • Would that be the algorists or the abacists?
    ---
  • You're right about the golf course and the arrow. But the writing says "19th hole".

  • To get a taste of what Fractint can do, you could try Fractal Map [samurajdata.se] (basically a web frontend to Fractint).
  • By far and away the best fractal generator for Linux is Xaos [paru.cas.cz] even though it hasn't been updated for a while. Excellent features including:
    • a guided tour of fractals and their maths
    • auto-pilot mode
    • zillions of different formulas to try out
    • very fast rendering engine
    • X or console display

    I've just checked their news page and the team seem to be alive and well and signing copies of the program at SourceForge.

  • Uh, out of all the silliness in the article, that's the one you have to catch the author on? Youch...
  • Too bad he didn't have a good photoshop guy. The digital artifiacts of blending the "star" in were a tad obvious.
  • I've been studying art history and composition (as a way of figuring out how to make my web pages suck less). I think you can date the original pretty accurately this way: after the discovery of perspective, but before the devleopment of advanced methods of composition. Probably mid 15th c to early 16th c.

    Medeival artists followed the classical Roman practice of strict symmetry. Ancient mosaics look like stiffly posed group photos -- the most important figure is placed in the center and larger, flanked by other figures carefully balanced on each size by number, size and importance. This scheme was so engrained that even the greatest artists always followed it slavishly. Leonardo's Last Supper (ca 1495) used the science of perspective, but followed the careful convention of balancing every element on one side with a nearly identical element on another. At the end of the Rennaisance artists began to try alleviate the monotony of exact symmetry by replacing it with symmetrical balance -- several persons on one side might be balanced by a horse on the other.

    By one hundred years later, symmetry was entirely out of the window as artists used perspective, value, and advanced composition techniques subtly draw the eye to the main subject obliquely. Compare a rennaisance painting by Michelangelo [ibiblio.org] or Titian [ibiblio.org] to a baroque painting by Carvaggio [ibiblio.org].

    This illustration is too symmetrical to be late 16th c (although it might have been done in an antique style), but must be at least 15th c due to the use of perspective (although subtle) and the attempt to avoid exact duplication while keeping strict symmetry.

  • Myself, I was noticing the background was very da Vinci-esque, and was thinking late 15th, but willing to grant maybe mid-15th, because the style of illustrating the rocks in the foreground was not sufficiently naturalistic. I was being conservative: 1449 minus 150 equals 1299, or the last moments of the 13th century.

    The means of arranging the subjects was typical of the fifteenth c. and earlier; the landscape and certain foreground elements were probably only technically possible with at least 15th c drawing technique. I expect the schematic way the rock was rendered was due to it coming from an illuminated majiscule and aside from the unwelcome distraction of a carefullly rendered rocky surface in the middle of a letter, it had to be rendered in colored ink instead of paint (it might even be an engraving -- I don't remember). The style would have been highly implausible in the full swing of the baroque era, but allowing that the context demanded a somewhat old fashioned design I'd be willing to grant early baroque. It might also be much, much later and much, much more self consciously old timey(e.g. like Wm Morris [lbwf.gov.uk]). I don't know much about medieval art though.

    Please! They had a different, but not wholly unfathomable aesthetic. They found symmetry beautiful, and it is not merely in their paintings this appears. We find it, for instance, in their dance choreographies: what is done to the left is then done to the right. It was an expression of order and "mesura" (measure, balance, harmony).

    That's a good point, but the painters of the time definitely were really laboring to find ways to break out of symmetry. They experimented with numbers, sizes and values so that compositions maintained an overall visual symmetry while breaking topical symmetry.

    I don't dispute that they found symmetry appealing (nor that they had gorgeous results), but the new techniques of perspective certainly demanded a more naturalistic way of integrating the subject with the background. Works of this era often have the characters almost floating in a plane in front of a carefully rendered perspective landscape. Tremendous compositional energy swirled in the topical plane while the background served as decoration. The baroque masters really found a way to both liberate that energy into three dimensions and integrate perspective into composition -- it was unambiguously and advance in technique if not necessarily aesthetics. I think their closeness to the problem of liberating that energy accounts for the strong diagonal arcs that move through their paintings.

    So to criticise the composition of an early Ren painting by the standards of a Baroque composition, is like criticising a work of prose fiction for not rhyming and having iambic pentameter. That's not what it's supposed to do, not how it's supposed to work, never what it was intended for. It misses the point.

    Well, I'm criticizing in the sense of analyzing, not disparaging. I find the works I cited very pleasing and indeed ingenious. They were less technically sophisticated, but nonetheless innovative.

  • In high school (over 10 years ago - eeek!) me and a friend would set up an Apple IIe hooked to a color monitor in our programming class (we took it for the points, and as a break - nothing more) with a Mandelbrot program written in BASIC (!), utilizing the funky 16 color mode (oooh!) that you could hack if you had an 80 column card. At any rate, we would let it run until our class, in the 5th period or so, where it would complete by the end of class, and save to floppy. We would then work out where we wanted to "magnify", and start the run the next day. Got some pretty neat pictures... for an Apple IIe...

    Worldcom [worldcom.com] - Generation Duh!
  • Nah, the other poster was closer - it was like 89 or 90 when we did this (you see, our programming class was stuck with Apple IIe's, while the Computer class, where one learned how to wordprocess, had 286's, and the Mac lab was, well a Mac lab - best machine was a Mac II color - don't know any other specs on it). Anyhow, you figure 1989 - my home computer was a Tandy CoCo 3 with 512K, 286's were the mid-range machine, and the 386 was top-of-the-line. But a CoCo was cheaper than either, and Apple IIe's were still expensive (but not the ones we had, which broke down more often than not, needing new drives, etc - they were ancient - but a lot of kids learned coding on them)...

    Worldcom [worldcom.com] - Generation Duh!
  • How the hell did I do that? 'T' isn't even close to 'C'. Oy vey!
  • Fractint [fratint.org] is a classic. Runs on DOS (yuck), Linux (supposedly, segfaults on my 2.4 kernel), Win 9x and, I think NT.


  • Myself, I was noticing the background was very da Vinci-esque, and was thinking late 15th, but willing to grant maybe mid-15th, because the style of illustrating the rocks in the foreground was not sufficiently naturalistic. I was being conservative: 1449 minus 150 equals 1299, or the last moments of the 13th century.

    YKYBITSCATLW! I spend a-lot-but-not-enough time looking at early 13th century pictoral evidence of/for women's clothing. If all -- if any 13th century illuminations were as naturalistic and clear as this one, my life would be much, much easier. I confess my first thought was "13th century? Bah! You can tell what she's wearing! I wish!"

    Now, as a med/ren-geek myself, I must take issue with your tone in:

    This scheme was so engrained that even the greatest artists always followed it slavishly.

    Please! They had a different, but not wholly unfathomable aesthetic. They found symmetry beautiful, and it is not merely in their paintings this appears. We find it, for instance, in their dance choreographies: what is done to the left is then done to the right. It was an expression of order and "mesura" (measure, balance, harmony).

    Furthermore, the positioning of people (and, interestingly, buildings) in Italian (at least) Ren painting had all sorts of complex symbolism which was evident to contemporary viewers, but not to the naive modern viewer. When we moderns look at a painting, we expect to look into a window; we expect to look at the figures of a painting. But the contemporaries of da Vinci read paintings. They expected them not merely to be beautiful, but to have meaning, to, perhaps, tell a story, or express and opinion. When you think about it, they were much more semiotically aware.

    So to criticise the composition of an early Ren painting by the standards of a Baroque composition, is like criticising a work of prose fiction for not rhyming and having iambic pentameter. That's not what it's supposed to do, not how it's supposed to work, never what it was intended for. It misses the point.

  • No, I was too busy marvelling... (Score:3)

    by goliard ( 46585 ) on Thursday March 22, 2001 @02:42PM (#346005)


    ... how an allegedly medieval monk knew how to paint a picture with renaissance perspective.

    Mandlebrot, schmandlebrot. According to the accompanying picture, he figured out the vanishing point 150 years before anyone else!

  • This looks like a hoax. A crafty one, though.
  • Besides, the mandelbrot set relies on a pretty recent advancement in mathematics: the use of complex numbers as (x,y)-coordinates on a plane.

    Complex numbers have been studied for centries, but it was not until 1797 that the Norwegian Casper Wessel, in a paper read before the Royal Academy of Denmark, brought out the fact that since i^2 = -1, and since -1 could be looked upon as a unit vector which has been rotated through 180 degrees, then i could be looked upon as a unit vector which has been rotated halfway, or 90 degrees, or from the x-axis to the y-axis.

    Reference: "Laplace Transforms for Electronic Engineers" by James Holbrook.

    So our 13th century monk would have had to invent the concept of geometry on the complex plane, as well. Smart monk!


    --
  • April fools. From last year.
    Cheers,

    Rick Kirkland

  • Anyone notice this at the bottom (Score:5)

    by ptevis ( 56920 ) on Thursday March 22, 2001 @02:19PM (#346009)
    © Ray Girvan (raygirvan@freezone.co.uk), April 1st 1999.

    I think that sums it up.

  • And shouldn't a book title be underlined?

    Historically underlines were standardized upon as a way of adding emphasis or setting somethign apart only after the typewriter made it impractical to italicize the things you ought. Now that this is no longer the case, I think that that convention is slowly evaporating, and both underlines and italics are considered appropriate.
  • For some reason I thing that Lorentz was one of these people I don't know of Lorenz (I assume that's who you meant) doing any work with fractals directly. However he did a lot for chaos theory, by discovering a normal problem that displayed sensitive dependance on intitial conditions (he had a weather simulator. After seeing some interesting behaviour, he wanted to watch it again, so he typed in the same seeds, but they weren't printed out with the full precision that was used interally, so before long he got qualitatively different results. Trying to isolate this behaviour which struck him as odd (how can 0.000001 difference change everything?) he simplified his system and came up with the Lorenz Attractor [swin.edu.au] - rather than settling on a point or into an oscillating pattern, his system approached a curve of infinite complexity - a strange attractor.

    Sorry, once I start typing, I just can't stop!
  • Any function that approaches infinity can represent all of the stars in the universe (at least as far as counting them.)

    to wit:

    f(x)=1/x

    x->1/n f(x)=n

    Where "n" is the number of stars in the universe.

    As for going from a fractal graph to a formula ... that's a little backwards. You go from a formula to a graph, just like every other graph.
    ____________________

  • In high school (over 10 years ago - eeek!) me and a friend would set up an Apple IIe ... with a Mandelbrot program written in BASIC..., we would let it run until our class..., where it would complete by the end of class, and save to floppy.

    Wow, and at the same time (1990), I was using an Ardent Titan supercomputer, and made a realtime flythrough program. It could generate a 512x512 plot in 1/30th sec, and wherever your mouse was centered, it would zoom in just a little closer for the next frame. Psychedelic.

    Talk about opposite ends of the spectrum. :)

  • How many 17th century computing machines are you familiar with?

    Well, I don't actually know how to operate or build one, but Blaise Pascal built a mechanical computer in the 17th century.
  • 1. It's entirely plausible -- you can get a good approximation with only a few hundred multiplications per pixel. That a 13th century monk would think of it, not too plausible.

    2. The bit about "disputing the bible's claim that pi = 3" really ruins the plausibility. No one except atheists trying to disprove the bible has ever claimed that the bible says pi = 3. It says there was a lake 30 cubits around and 10 across. Maybe St. John the Mushroom Head thought that "I saw a molten lake of fire 30 cubits around and nine and five hundred forty-nine thousanths cubits across" didn't fit the meter very well. Overall, the bit about pi should just be rewritten to make it more plausible.

    3. profanus et animi is great: Material vs. Spiritual. Or maybe better translated as Real and Imaginary.

    4. Fractals don't have "infinite detail" anymore than x*x + y*y 4 has infinite detail. Yes, you can keep bumping up the resolution, but the information content is totally captured in the equation generating it. (i.e. fractal image compression isn't magic.)

    5. The update that this is a hoax should be removed from the summary so that people have an opportunaty to fall for it before they read the comments.
  • You fell for it, but I'm the dumbass?

    Pphhphptthththtpptththt!

  • The only reason I didn't post earlier is that it would have been -1, Redundant. Several others had spotted it before I bothered to read any comments. The idea that a 13th century monk would have invented both the Cartesian coordinate system and complex numbers, both of which are required to draw the Mandelbrot set in the form to which we are accustomed, is ludicrous on the face of it and not at all "semi-plausible." And the copyright date specifying 4/1 when it ordinarily contains only the year should have been a dead giveaway to anyone.

  • Oh, come on! (Score:3)

    by CaptainCarrot ( 84625 ) on Thursday March 22, 2001 @02:31PM (#346018)
    Update 20 mins later by J: Yes, this is an April Fool's joke - very well done, too.

    It's about as well done as most of the "All your base are belong to us" Photoshop jobs, and just about as easy to spot. Hemos really had his head up his butt on this one. It's a two year old joke for crying out loud!

  • Watch out for lightening bolts. (Score:3)

    by nublord ( 88026 ) on Thursday March 22, 2001 @02:20PM (#346019)
    From the article:
    "I was stunned," Schipke says. "It was like finding a picture of Bill Gates in the Dead Sea Scrolls. The colophon [the title page] named the copyist as Udo of Aachen, and I just had to find out more about this guy."

    I don't think the All Mighty is going to be to pleased with this comparison.

  • Ignoring the hoaxiness (oh, the hoaxiness!), it's easy to generate many fractals. My science project my junior year in high school was a program on an Apple ][ to generate simple fractals algorithmically from a couple of basic rules. Here's the easiest one to picture:

    * On the X,Y plane, pick three points which are the corners of an equilateral triangle.
    * Now pick any fourth point, and plot it.
    * Now randomly choose one corner of the triangle, and move the plot point halfway towards it. Plot that point, then pick another corner, move halfway, and plot again. Repeat.

    If you let this run for a while, the points converge into a shape called a Sierpinski Gasket, which is a readily-recognizable series of nested triangles. By varying the location and number of the control points, the transformation rules used to alter your plot point (use different movement rules, for instance, or weigh the probabilities of choosing those rules in some way) you can produce a wide variety of interesting and beautiful fractals.
  • Think before you post, foo.

    Could BSDevel be.... Mr T?
  • oh, please..you're telling me this is new?
    I saw this about 4 years ago..
    And how could it not be a fake.?
    I have to say, there're a lot of things on /. that I'd been looking up around the time I was still playing Dizzy on an Amiga 1200..
  • well, if you're looking at it from a Pratchettesque viewpoint, Capt. Carrot's not exactly the smartest resident of AnkhMorpork.....
  • The word COMPUTER means a human who's job it is to compute. That's why all the old computer names end in -AC (e.g. ENIAC, EDVAC) - it means "Automatic Computer" as apposed to a manual computer, a human being. Only recently (~30 years) has the "automatic" part been taken for granted.
  • Now you've gotten yourself in a fix, 007. Here are my suggestions for extricating yourself: the cyanide capsule located in your tooth -- chew it. If that's unappealing, you can apply Usenet tactics and claim that you really were trolling (no, really!). That might not fly, but since we're only a short spell away, you could try to call it an early April Fool's joke...

    Speaking of April Fool's, you do realize he was pointing out the date and not the copyright?

  • Not that what you did isn't cool or anything. But the guy did say that it was over 10 years ago and the Apple IIe probably places it in the early 80s.

    I mean, I personally frequently find it hard to believe that it was 20 years ago that I got my first computer. I mean, *20 years*? It doesn't seem like that long ago that people who were 20 years old were "old".

    Rich

  • It should be noted that the mathematician's name mentioned in the article can be rearranged to "SHE BE TRICK PRO" Of course that is using Robert instead of Bob, but the point is obvious :)
  • This could be explained by an error of translation, but the florin (the gold coin of Florence) was not coined until 1252. I doubt that they would have been in sufficient circulation within ten or fifteen years for them to be a standard currency of gambling at Irrendorf, even assuming that the gambling took place toward the very end of Udo's life. Given the florin's size and value, it also seems to me unlikely that an abbot would win 32 of them at a time.

    Plus, there is no Harvard Journal of Historical Mathematics, or if there is, Harvard's libraries don't know about it.

    My medieval history studies finally serve me well...
  • They're not imaginary numbers, they're complex numbers. If you want to call them imaginary, you might as well call negative numbers imaginary.

  • gee, if you're going to try to strictly parse semantic labels of mathematical terms, they're not really complex, either, they're pretty straightforward. They're all numbers.

    I am, and no they're not. They're complex because they have two parts.

    Besides, imaginary numbers are just the nonreal part of complex numbers; "complex" implies you're going to see both real and imaginary values

    You are, zero is the real number. And before you point out that any real number can just as easily be considered complex because i has a coefficient of zero, you're right, but that doesn't change the fact that imaginary number is a poor label.
  • *laugh* That's all i have to say!
  • It might have been funny... IF IT HAD ACTUALLY BEEN APRIL 1ST.

  • From Merriam-Webster's online dictionary [m-w.com]:

    computer
    Pronunciation: k&m-'pyü-t&r
    Function: noun
    Usage: often attributive
    Date: 1646
    : one that computes; specifically : a programmable electronic device that can store, retrieve, and process data
    bold emphasis mine

    How many 17th century computing machines are you familiar with?

  • Besides, the mandelbrot set relies on a pretty recent advancement in mathematics: the use of complex numbers as (x,y)-coordinates on a plane.

    We didn't even have the X,Y plain back then, either.

    Rate me on Picture-rate.com [picture-rate.com]
  • Read MLP in Kuro5hin [kuro5hin.org] for details.
  • Although I don't see the hoax on the front page at Kuro5hin.org any more, it was in their slashbox earlier today.
    -Mike
  • History is full of instances of powerful organizations suppressing valid work. However, what has been done cannot be undone. What we must do now is insure that no organization ever seeks, or is able to suppress good ideas simply because the individuals in the organization do not understand them. In times past it has been the catholic church. Who is it now? The U.S. Government? Microsoft? The US Patent Office? The American Cancer Society? The Nobel Foundation?
  • Amazon.com still claims that this has no bearing on their patent for a single-click fractal.
  • Yes non-human computers. Go educate yourself on what the work computer meant before WW 2 and the comment will make sense. It is *very* accurate.
  • It's a very, very, very obvious hoax.
  • I went to a talk by Mandelbrot, and he is basically a monster ego with feet and a big mouth.

    I went to a lecture by Mandelbrot, some 10 years ago. He was very self-effacing, and claimed he was embarrassed by the use of his name to describe the set.

    When did you see him? Perhaps someone took him down a peg or two in between the two dates?
    --
  • A monk named Thelonius [achilles.net]? C'mon, guys...my suspension of disbelief was sagging well before I got that far, but that snapped it entirely. It is a pretty funny hoax, though.

    --

  • You don't need imaginary numbers to define the mandelbrot set. Start with point (x[1],y[1]). When you do the iterations, x[next] = x[previous]^2 - y^2 + x[1] and y[next] = -y[previous]^2 + y[1]. And the image shown is most definitely a rendering of the mandelbrot set. Other than that, you're right that complex numbers and cartesian coordinate systems weren't used when this drawing was supposedly made. The article even claims the monk performed 70 iterations on each point to test whether or not it was in the set! It took my Commodore 128 almost 24 hours exactly to do a 320x200 picture that only tested points for 12 iterations. The implication is that the monk performed 1,008,000 calculations just to create the 120x120 grid. April fool.

    Oh, and wouldn't it be nice if slashdot supported the tag?

    --

  • I meant to say <sup> tag

    --
  • and James Gleick eludes to it in "Chaos".

    Don't you mean "alludes"? And shouldn't a book title be underlined?

    All in good fun. And my punctuation is intentional.

    --

  • Yeah but grammar nazi neither underlined nor italicized. He used quotes. I like the grammar nazi, but with a handle like that, you're just asking to be scrutinized.

    --
  • I was once told by a math teacher that a complex enough (mandlebrot?) fractal can represent all of the stars in the universe. Had I paid more attention in that class I would be able to expand on this claim, but I leave that up to wiser heads. I know that they can be used to simulate (or represent) coastlines. How hard is it to go from a fractal graph to a formula?

    Yes that is a blank stare.
  • I'd love to get a hold of some progs to do this at home.
    I was always, fascinated by it in school.
    Does anybody have any links ??

    meatplow.

    fuckbunny.org [fuckbunny.org]

  • You have no appreciation for the amount of spare time people in the middle ages must have had. If they had the brains to, they probably would have counted to 10,000 just for fun each day.

    Let's see. What shall we do today? Kill some innocents out of complete ignorance...did that twice this week. Kick some pebbles? Done that. Work slavishly for the fiefdom...every day this week. Guess I'll stare at this wall for a while and then let my imagination run wild to think up some daemons so we can go kill some more neighbors.

  • Just think that the mandelbrot set is the result set of an imaginary numbers equation. When were the imaginary number invented ?

    Furthermore, this image bears only a very remote oliking to a mandelbrot set image in a x-y plane (which in turn is a recent invention too).

    It can be anything artistic, but definitely not a mandelbrot set image.
  • I was *totally* taken in by this one. :) 'course, I don't read Kuro5hin, and I usually don't pay attention to the copyright dates on the pages I read. Frankly, it isn't a particularly *funny* April Fools joke, just kinda strange... well put together, though.
  • Why do I get the feeling some moderators have too much time on their hands?

    (Offtopic!?)
  • whose discovery of jazz was also lost for many ages.
  • This is good in another way too. Mandelbrot is known throughout the dynamical systems community as being a pompous and arrogant jerk. I don't know him personally, but I've heard this from others and James Gleick eludes to it in "Chaos".

    Mandelbrot considers himself the 'father' of fractals.

    This may be just the ego 'punch' that he needs.

  • Actually I knew it was a reference to a text adventure, but I do not know which one. I didn't have the occasion playing it. Your post fitted very well with the description of the souls and fractals thing in the article and that's what it made funny. Too bad the moderators didn't agree, it has cost me some karma, but what the heck...it was worth it :-)
  • wow, im amazed anyone could spend the time to calculate that by hand, belive me, ive tried and after a few points it gets really really boring, i commend him for his effort, but must say im glad i have a computer to do it and dont have to waste a few years doing caculations by hand
  • Fractint. I used it back in college during my Computer Graphics classes, and eventually my teacher just gave everyone else a copy so they would all see what a fractal was, and which fractals were the most popular.

    You can get it at the Fractint WWW pages [triumf.ca].

    Tongue-tied and twisted, just an earth-bound misfit, I
  • I mean, come on, these guys were rather well educated, and besides doing their daily duties, what else did they have to do all day, but persue what ever interested them. I bet monks thought made a lot of interesting discoveries that may have never been passed on. Mendel (also a monk), despite fudging some data, was for example the first to propose the allele concept in genetics, and no one even noticed his work until long after the fact. puck
  • Actually, I think this does: YHBT.
    This one's on Hemos :)

    (end comment) */ }

  • Thelonious Monk... oh that's a good spoof... *wipes tear from eye* ahhh, good piano playing though.
  • Millenium hand and shrimp!

    Bugrit!

    --

  • I can still remember coming up with an idea for an electromagnetically accelerated projectile, when I was 14 (1974). I was somewhat dejected to find it had already been 'invented' sometime in the 50's. Now people call these things Rail Guns. Some ideas are obvious, eh?

    --

  • Is it just me, or does the little "Einstein" picture next to this article look angry?
    ---
  • have you a non-recursuve definition for the Mandelbrot set? I think not... but if you do, post it!!

  • I'll admit it - I fell for it. Reasons why:

    0. Didn't look at the copyright.
    1. It's well written.
    2. Ramajun - if a poor Indian college dropout can come up with hundreds of new mathematical insgights (and rediscover others) in his spare time, it seems plausible that a monk (who could have been copying the bible by hand) could have some astounding mathematical insights.
    3. The stuff about imaginary numbers being associated with the devil reminded me of "true" Greek tales about the gods being angry with the discovery of irrational numbers - the legend may be the source for that part of the hoax.
    4. After enough math courses, the ideas expressed here (except for the Mandelbrot set) strike me as elementary. Imaginary numbers, probability axoims, ordinal infinity, and Cartesian coordinates seem intuitive. They're not, of course, and I would never come up with all of them on my own, but halfway through a math minor they seem like givens.

    OK, I got taken. Just trying to feel less stupid.
  • Nice to see the team are on their toes and checking the stories out.

    The only thing left to prove the integrity of /. is when Timmy or Mikey posts this in a day or so and adds some air head comment.

    'News for nerds. Stuff that matters.' That was a long, long time ago. Now it should read, 'News for herds, Stuff that generates ad revenue'
  • Calculus de agony dx/dt :-)
  • I'm sorry to say it comes naturally. It seems we must have a common ancestor :-)

    I've read the FAQ, and notable by it's omission is any forum for a discussion on /. its self! Also the FAQ contains inaccuracies, deletion of comments being one such area.

    But back to the point at hand, /. seems to be slipping from when I first started reading. Prehaps, it's me that's changed or the site has grown. I'm not sure, but I am aware that other users feel the same way.

    The /. crew stead fastly refuse to answer or discuss this. At the same time they are starting to ask for comments on how /. should be funded.
  • the mandelbrot set is a plot on the real/imaginary axes of the "rate" at which the function approaches infinity for each coordinate.

    Actually, the mandelbrot set itself doesn't take into account the rate. The mandelbrot set is just the set of all points that don't escape to infinity ever. You cannot actually have a picture of this, without computing for an infinite amount of time (at least with current methods). All the computer pictures of the Mandelbrot set are just approximations. Anyway, in a normal Mandelbrot fractal picture, the actual Mandelbrot set is everything in black.

  • One of the best fractal generator programs around, even if the interface is somewhat clunky: Fractint [triumf.ca]

    Another good one that even lets you compile your own fractal algorithms into it. For Mac only though. Fractal Designer [unige.ch]

  • Kind of, they are determined by the number of iterations that it takes to get past the radius 2 circle. You can consider that a rate of a kind. But, as I said, that isn't part of the Mandelbrot set.
  • Formulas are different than algorithims. With Fractal Designer you could concievably make a faster algorithm for a formula it already had. Besides, its got a better interface.
  • I think you should read up a little more on the history of fractals before you post things like

    The guy lucked out in my opinion. He had an interest in something already known and other people developed the technology for him to take the credit. The sad thing is that this is worse than patent law since Mandelbrot will always get way more credit than he deserves.

    Gaston Julia did not discover the Mandelbrot set. He discovered the Julia sets. These are related to the Mandelbrot set, but are not the same. For every point in the Mandelbrot set, there is a corresponding Julia set.

    Both sets use the formula z := z^2 + c, but they differ in what z0 and c are. In the Julia Sets, z0 is the point on the plane and c is a constant that defines which Julia set it is. For the Mandelbrot set however, z0 is always 0, and c is the point on the plane. In this way, the Mandelbrot set is a table of contents for the Julia sets. Each point on the plane that is in the Mandelbrot set corresponds to a Julia with that point's coordinates as its c that is connected. All the points not in the Mandelbrot set correspond to Julia sets that are not connected. This was the work that Mandelbrot did, and that is why the fractal is rightfully named after him, just as the Julia fractals are named after Gaston Julia.

    Lorentz was not working on either the Mandelbrot or Julia fractals. He was working on simplified differential equations for modeling weather. This led to his discovery of the Lorentz attractor. Basically, his work showed that fractals and chaos were abundant in nature. The fact that we will never be albe to accurately predict the weather more than a month in advance also stems from his work. This is commonly known as the Butterfly effect, i.e. a butterfly flaps its wings in Central Park and a 3 months later, a hurricane doesn't hit Japan.

    To the best of my knowledge he never acknowledged the work done by the meterologists. When I saw him he also claimed the results of the conjectures as his own and went out of his way to disparage the people who did the real work.

    I've never heard Mandelbrot try to disparage anyone in anyway. In fact, its mostly the other way around. People disparaged him because he would write papers in many different journals in widely varying fields, although really they were all in the field of non-deterministic systems, or whatever they are calling it now. People viewed him as an outsider, and therefore dismissed his work without considering it.

  • .."I was amazed to find out that the Mandelbrot Set was discovered by a 13th century monk -- way, way before the advent of non-human computers".

    as compared to those pesky human computers. Smartasses is what we call them suckers.

  • Well, this story is clearly a joke. But what I want to remark is that in truth lifetimes of impassioned research were sometimes driven by things akin to the search for the mathematics of "a soul's path to Heaven". You only have to remember Johannes Kepler, who devised the Laws of Planetary Motion (Astronomia Nova 1600-1609), which later became the basis for much of Newton's astrophysics. The funny thing is, Kepler was only pursuing a fancy that the planets in the Solar system are arranged in proportion to the classical Pythagorian hierarchy of the 5 fundamental polygons. Of course, this was only a pipe-dream, and the purported relationships merely accidental. Nevertheless, in 30 years of work, Kepler, using primitive pre-calculus mathematics, made one of the great advances in planetary physics ever. Nothing would sound strange to me after this ...

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