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Interview With Math Legend Benoit Mandelbrot
Vertigo01 writes "New Scientist is currently featuring an interview with Benoit Mandelbrot the father of the Mandelbrot set, and the man who discovered fractals. 'What motivates me now are ideas I developed 10, 20 or 30 years ago, and the feeling that these ideas may be lost if I don't push them a little bit further.'"
I hope to be like him when I get to be that old. In case any of you haven't heard of Mandelbrot, you should take a look here.
let me guess, dipshit:
one is a surname, one is a forename.
so, PROBABLY NO, dimwit.
Mandelbrot fractal sets are cool, but I think the first fractal discovered should be considered phi, aka the Golden Ratio. It may not be derived from the same mathmatics, but the end result is the same...
OK. How about Benoit Benjamin?
I guess no one ever learned how to make a fractal equation that looked like a given image on the fly.
sigs, as if you care.
I wrote my first Mandelbrot set explorer on an Atari 800. :-) Yeah... fractal exploration in interpreted BASIC at 1.79 Megahertz. Good times.
SLOW times, but good times.
Fuck, I feel old. :-(
--- Ban humanity.
...all this time and I thought he was dead.
This way to the egress...
Haha, me 2 !!!!111one
note to mods (and people scratching their heads): this is funny (or trying to be) because the mandelbrot set is generated by a function over the complex plane, which has one axis of real numbers, and one axis of the "imaginary" numbers, multiples of i=sqrt(-1).
"A witty saying proves nothing." ~Voltaire
"d'Oh!" ~Homer
Gaston Julia, from circa 1920, investigated fractals before Mandelbrot. His work is the basis of Mandelbrot sets as the points in the Mandelbrot set are exactly those parameters for the corresponding Julia sets that are connected. If anyone should attribute fractals to any one man, Julia is more pronounced than Mandelbrot. Granted, Mandelbrot popularized fractals but the analysis stems from Julia's work.
are you retarded?
you ask if benoit mandelbrot ~ chris benoit, then you retort with a surname that's possibly s forename. first, what has this got to do with the original question? second, since when are people likely related when they have the same forname but completely different surnames?
you are a fucking moron.
Wow, I fondly remember the days when I, as a wide-eyed six year old, typed in a Mandlebrot-graphics generation program from Compute! magazine into my Commodore 64.
My friends didn't get it. But I loved it. It made a great backdrop to leave on the screen while I did other, more "normal" kid things. (Legos, drawing, etc.)
Now that I appreciate the mathematics behind it, I must give my respect to the man. Thanks for the childhood brain food, Mandlebrot, even if I didn't get it at the time.
I hope the land around you yields, a crop like all the other fields, and then your waiting might make sense...
New Scientist: How did you feel when you discovered it?
Mandelbrot: Its astounding complication was completely out of proportion with what I was expecting. Here is the curious thing: the first night I saw the set, it was just wild. The second night, I became used to it. After a few nights, I became familiar with it.
I wonder what he means by "saw" it.
What graphics computers were popular in the 1940's?
I sincerely hope that his interview reads easier than his books!
Please, don't feed the trolls.
How about Preperation H topical Benoit-ment?
I don't need no instructions to know how to rock!!!!
Q:Fractals seem to appear all over nature and in economics. Even the internet is fractal. What does that say about the underlying nature of these phenomena?
A:Well, it depends on the field. Circles and straight lines also appear everywhere. Does this mean that all those phenomena have something in common? Of course not. The roughly circular trajectory of a planet around the sun is due to gravitational interactions. Berries are round because a sphere has a smaller skin. The beauty of geometry is that it is a language of extraordinary subtlety that serves many purposes.
Q:So fractals don't point to a single rule underlying reality?
A:There is no single rule that governs the use of geometry. I don't think that one exists.
----
If I believed in a God, I'd say God bless Mr Mandelbrot. As it is, I'll just say, "Damn skippy."
I suppose it's not right that i'm more irritated about the new-age whackos who think fractals really *MEAN* something than the guy who invented the Mandelbrot set is.
(Invented? Discovered? Well, whatever, you know what I mean.)
Now I've got a nice little quote of The Man Himself telling them all they're f-ing idiots.
I LOVE THIS MAN!
I like the work the guy has done in the past, but I sometimes I'm dismayed by a little too much self-promotion by academics these days. Recall in his open letter in Wired:
Wired article
Here he mentions the need to conduct fundamental research, which I applaud, but he fails to mention that many, many people are already doing this, and has come across as championing an idea which has already been pursued for decades. If there's one thing I know about life, it's that people with money will almost always do their best to make more of it, and that includes learning how to use the market via financial research. Most mathematically inclined graduate students in Mandelbrot's own university, Yale, go on to financial research.
It reminds me a little of another widely regarded expert, David Gelernter, who has published lots of grandoise nonsense which are devoured readily by people who don't stop to think about what is actually said. For example, in his article about the future ("The Second Coming: A Manifesto"), he says at one point:
"Everything is up for grabs. Everything will change. There is a magnificent sweep of intellectual landscape right in front of us."
Well, that's nice. What's it mean? Perhaps I shouldn't fault the researchers, since getting your name out there seems to be the only way to attract lots of research funds, but every once in a while, it'd be nice to see someone slightly in touch with reality talk about what they want to do and why.
In the article, Mandelbrot says it's simple to understand how some spaces can be more empty than others, once it is explained. Can someone explain it?
Did anyone else feel disapointed that every third leter wasn't missing?
Bwhahahhahahhaha....*sob*...no, it was funny, trust me...
HA! I just wasted some of your bandwidth with a frivolous sig!
The interview reminds me of an old joke that a "mandelbrot" would become a standard unit for measuring ego. Like Farad, one Mandelbrot would be a very large amount of ego, in common usage you would typically see pico- and micro-mandelbrots.
jeff
As someone mentioned above, and I second: Thanks for the brainfood, Mandelbrot!
For years, I have been using Fractint, and generating fractals on my PC, usually for print. I prefer it's zebra pattern, and it's appeal when printed very large -- especially when you can take a magnifying glass to the resulting printed image for more fractal fun!
Zhrodague.net - I do projects and stuff too.
If I renember, there were sone very innovative things done with fractal immage compression, but it sorta dead-ended because of patent issues. see here
New Scientist: What's the mystery?
Mandelbrot: It relates to a rather subtle mathematical property. In simple terms, there are two ways to define the Mandelbrot set. It is rather like proving that 3+1 and 2+2 give the same result. I have always thought that the two definitions were equivalent. But one is easy to study whereas the other is extremely difficult. So far, the proof has defeated many people. The fact that my conjecture is so simple to state, yet baffles everybody, makes it attractive to mathematicians. The conjecture is the mathematical face of the Mandelbrot set, and the T-shirts are the popular face.
.
Hmm... What are these two ways to define the Mandelbrot set?
If anyone is interested, a great book on the subject is Peitgen and Richter's The Beauty of Fractals. It presents a good mathematical background, but it also has tons of pictures demonstrating the math.
(S(SKK)(SKK))(S(SKK)(SKK))
Ignorant American here, but how would you pronounce his name? Ben-wah Mandelbra? or with a hard 't' at the end? Mandlebrot.
Source Output It is an imagemap, so you can click anywhere to zoom in.
Jon Bardin
After all, given the highly chaotic nature of such unpredictable and random subject, who will be able tell what this subject is about, especially where there is a high amount of entropy in the interview? Anyone tries to read it can result in total fractmentalization. Watch dice rolls is a lot less unpredictable, and less risky by comparision.
i got into yale university based on my success in the connecticut science fair for my assembly language project (on the trs-80 color computer! lol) exploring variations on fractals and john conway's game of life
you can imagine my awe when wandering the math building as a 17 year old freshman, i met benoit mandelbrot himself (he was faculty there, and i believe he still is)
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
I spent a significant amount of time in highschool playing with a mandelbrot program and color cycling. In this time, I fell into a trance, and lost a good 4 hours of my life.
When do you plan on giving me these hours of my life back?
*hypnotised by color cycling mandelbrot sets*
*drooool*
no
If you think this guy is one cool dude... nevermind, you belong here
The most interesting part of Mandelbrot's work revolved around the Hausdorff Dimension, which was a way to describe geometry using a real number as opposed to the integers of Euclidian geometry.
I admit I never understood all of the (somewhat convoluted) description Mandelbrot gave in "Fractal Geometry of Nature", but it seemed to boil down to the idea that you could get rid of infinities and zeros if you allowed fractions of a dimension.
ie: A coastline has an infinite length, if you measure it in just one dimension, and zero area if you measure it in two, but a finite value that you can usefully compare to other objects if you use a dimension between 1 and 2.
IIRC, the Hausdorff Dimension is calculated by measuring the object at different scales. You then took the ratio of the change in scale and the change in measured length. As you went to finer and finer scales, this ratio tends to a limit, which is always equal to or greater than the Euclidian dimension and always strictly less than the Euclidian dimension plus 1.
Where the Hausdorff Dimension is a value strictly greater than the Euclidian dimension, the object is considered a fractal. Fractals are never "random", they are always self-similar. That appears to be a universal law, though I've yet to see a clear explanation as to why.
Another interesting characteristic is that self-similarity does not occur at random intervals. The ratio between the intervals is always an integer multiple of the Feigenbaum Number.
The Feigenbaum Number is itself interesting. It was first observed by Michael Feigenbaum, when he examined chaotic systems that were in an oscillating state. (Chaotic systems, when given insufficient initial conditions to become chaotic will oscillate.) As you increase the inputs, the oscillations exactly double. They don't change smoothly.
The ratio of the change in inputs necessary to double the oscillations is the same between all doublings and between all chaotic systems. This ratio is the Feigenbaum Number. Many properties of chaos and fractals are tightly bound to this value.
The Feigenbaum Number is considered evidence that chaos is not so much a property of the system, but rather that chaos and fractals are the more universal/abstract and the systems are merely products.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
The original name should have been David Benoit.
Hope that clears things up for you.
.
I have mod points right now, but decided to comment on the abysmal state of the mod system instead.
That's not necessarily "abysmalness". The mod system is simply an implementation of a rules based system that gains participation from unpaid participants to create community.
The results of this system?
Democracy, feedback, self-articulation
... there are many nouns that can be applied to the results. Abysmalness is yours.What changes would you make to the mod system?
What would be the results?
I had a friend at the University that made a postscript program that would print a mandelbrot set.
He sent the file to be printed to the laser printer in the mac lab (the original apple laser writer).
And then nothing.
And then nothing.
13 hours later it printed a mandelbrot picture at the very highest resolution.
Pretty cool.
The Internet is full. Go Away!!!
i won 1st prize in the connecticut science fair computer division based on my work doing that and john conway's game of life in assembly language on the trs-80 color computer!
based on that success, i was accepted into yale university
where i met benoit mandelbrot in person... he was on the faculty and still is i believe... 17 year old awe...
this is all for real!
dude, memories of plugging in the assembler cartridge... i had one of those 4 cartridge switchers, so i could also run lode runner and the speech synthesizer LOL
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
Fractal compression is a very intersting technique. However, it's highly assymetric: compression requires an incredible amount of computation while decompression is pretty fast
It's truely a brilliant and elegant technique to compress image. Unfortunately, the results obtained are more or less the same as other compression techniques: DCT (jpeg) or wavelets (jpeg 2000)
It seems the limit has been reached for image compression: since jpeg, there were co real significant improvements on compression/quality ratio.
So, if you looked inside a pico-mandelbrot, would you see more pico-mandelbrots, or femto-mandelbrots? Or would they all look the same?
He really just likes making pretty pictures.
^_^ That program was a massive source of entertainment to me as a child.
This sig has absolutely no significance and serves only to take up screen space and waste the time of the reader.
(Another AC)
Christ, why all the down-mods? Am I the only one who found this thread funny?
I guess no one ever learned how to make a fractal equation that looked like a given image on the fly.
I may be mistaken, but I think somebody did, and called it JPEG.
JPEG and fractal compression are completely different, I'm afraid.
JPEG transforms blocks of the image from the spatial domain to the frequency domain, and keeps only the strongest spatial frequencies. To look at it another way, it tries to express each block as the sum of various functions that look like bands or ripple patterns.
Fractal compression tries to find similarities between different parts of the image, and to express the image as a bunch of these similarity relations (affine transforms, or different types of mapping).
There's more detail for each type of algorithm, but that's the basic approach for each. Some versions of fractal compression to a frequency transform of blocks during the compression stage, but that's just to make it easier to compare blocks to each other when sifting possibilities, as opposed to part of the mechanism of compression itself.
are the names pronounced the same? ben-wah?
<my guess>
Space has dimensionality; a plane has 2 dimensions, a cube exists in 3, hypercube 4... the numbers here are positive. Mandelbrot said he was using negative dimensions to measure "emptiness". He mentions that only one set is considered "empty" (I presume the null set). My guess (and I only minored in math so don't go betting on this) is that a negative dimension is to a positive dimension what a negative number is to a positive one. I'm thinking that if an object existed in -2 dimensions, it would be capable of having negative area. If you could add that object to an object with positive area, you'd reduce the second object's area.
</my guess>
Here's Mandelbrot's homepage at Yale.
Here's more links.
"A witty saying proves nothing." ~Voltaire
"d'Oh!" ~Homer
It is called wavelets
Actually, no.
Wavelet transforms involve expressing the input data as the sum of wavelet basis functions (much as a Fourier transform uses sine/cosine waves).
Fractal compression involves looking for self-similar features in the image itself, removing this redundancy by expressing it as a series of affine transformations, or something similar.
Frequency- and wavelet-transforms can make the search for self-similar structures easier, but they represent fundamentally different approaches (the best you can do to draw an analogy is to consider fractals to be a different type of parameterized basis function that you're doing a transform with).
Mandelbrot Gallery
"We shall party like the Greeks of old! You know the ones I mean." - HedonismBot
Mandelbrot is not the inventor of fractals!
Three people whose work on fractals predated Mandelbrot's by some time, and IMNSHO was infinitely more impressive because it was done without the help of computers, are Felix Hausdorff, inventor of the Hausdorff dimension, Georg Cantor, inventor of the fractal Cantor "middle thirds" Set, and Gaston Julia, who discovered/invented the Julia Set, to which the Mandelbrot Set is closely related.
Think about how amazing the work of these three mathematicians was, given that they, unlike Mandelbrot, didn't have computers to iterate maps or visualize sets, and yet they were able to characterize these sets, including their fractal nature. I find Julia's accomplishment especially impressive.
Mandelbrot is better than these three at self-promotion. When he fiddled a bit with the Julia Set and produced a new set from it, he called it the "M Set" in his work, and waited for somebody else to fill in the remaining 9 letters after "M."
There was a joke among physicists messing around with fractal stuff in the late 1980s that while the most common letter in the English language is "e," the most common letter in Mandelbrot's work was either "I" or "M" (the probable winner, given that "me," "my," "mine," and "Mandelbrot" all begin with "M").
That said, Mandelbrot's work was interesting, and he did acknowledge Julia's work in his own. After all, the Mandelbrot Set is a map where each point on the complex plane represents a Julia Set, where the points inside the Mandelbrot Set represent connected Julia Sets and the points outside represent disconnected Julia Sets. And Mandelbrot took advantage of the computer technology available to him to plot some of these sets, giving us visual representations of these things. But to give him credit for inventing fractals is unfair to the great mathematicians who worked on fractals long before Mandelbrot.
--Mark
"It is nice to know that the computer understands the problem. But I would like to understand it too." --Eugene Wigner
Violence is the last refuge of the incompetent - Salvor Hardin
Ahh yes you have just stated the great benefit of democracy, and also the problems. He makes a point that if the moders were of the intelligence to know what the joke was, we would be fine, but since modders have no clue anymore (or ever?) the system sucks. So True. Educate the public for better democracy... the poor state of our education is something the current administration has used to its benefit over and over again.
It started off at 2, +1 funny, -1 overrated. Current score 1. 2+1-1=1? :) :)
Must be slashcode's way of dinging me for mentioning the root of a negative number
"A witty saying proves nothing." ~Voltaire
"d'Oh!" ~Homer
Q:How many libertarians does it take to stop a Panzer division? A:None, obviously market forces will take care of it.
Libertarians believe in a stong national defence.. not offence. I'm aware a strong offence makes for a stronger defence, but experience shows that we can't trust politicians with deadly force.
-metric
you had me at #!
Could most kids today get their PS2 to draw a mandelbrot set? Does Windows XP provide the tools to acquire and use this knowledge? No.
Like tinyurl, but one letter less! http://qurl.co.uk/
Eg, if you reaped a load of karma in IT, but none in politics, you could mod in IT, but not in politics?
Alternatively, what if moderation wasn't anonymous, and your moderation showed up in your user page, as well as in the comment?
I know I've wished for that on numerous occasions. (the second thing) I think either of these changes would make the moderation system hella better. Although I do like being able to moderate in any topic.. Frankly, I think making moderation non-anonymous would be a giant leap forward. Even if it didn't keep people from modding like five year olds, at least people could know who was smacking them down.
My cats breath smells like cat food!
"A witty saying proves nothing." ~Voltaire
"d'Oh!" ~Homer
Give the man a +1 (either funny or insightful)
"A witty saying proves nothing." ~Voltaire
"d'Oh!" ~Homer
I'm still in therapy...
Try aa-xaos -- now you can view fractals as 80x25 ASCII art. The past is now! Geezers unite!
Two space doubleplusempty.
There are tons of fractal generators out there, my favorite is Chaos Pro. It's windows only, but it's free (as in beer). It supports a ton of advanced features like transparent layering/blending, and generating AVI's, and the author claims it's 100% feature-compatible with Ultra Fractal (a commercial package).
It's also compatible with formula and parameter files from other fractal programs (including the legendary FractInt).
Anyway, if you have a decent photo printer, and any fractal program that can do high resolutions in 32-bit color, you can make some great wall hangings by rendering a fractal image at a high resolution (I use 4000x3000) and then printing it on 8.5x11 glossy photo paper. I have some hanging around my cubicle.
-CausticPuppy "Of all the people I know, you're certainly one of them." -Somebody I don't know
Once we had to draw trees using fractals for scientific C programming class. For almost month after I saw everything in fractals and was troubled about how I would draw them, quite quite mad. It made me very irritable. Still happens occationally.
Now I've got a nice little quote of The Man Himself telling them all they're f-ing idiots.
I get irritated by new-age whackos as much as the next man ("Goddess on Board" bumper sticker anyone?) but I do not feel it is reasonable to claim that seeing something signifigant within fractals makes one a "new-age whacko". What's more, just because Benoit Mandelbrot believes a certain thing, does not make it so.
"A:There is no single rule that governs the use of geometry. I don't think that one exists."
So he believes something different to someone else. I'm pretty sure that covers all humanity. He may be a brilliant man, but he is still just a man. And men are fallible.
I think the first fractal discovered should be... the Golden Ratio. It may not be derived from the same mathmatics, but the end result is the same
Although fractals are self-similar, a self-similar pattern isn't necessarily fractal. Golden spirals/rectangles/triangles aren't fractal because they can be described using classical geometry.
For a detailed breakdown of such distinctions, see Manfred Schroeder's Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise.
It was fucking hilarious.
No article about fractals could be complete without mentioning Elenas excellent ZonXplorer fractal package for AmigaOS 3.5+ and MorphOS (running on the Pegasos PPC). Check out her stuning pictures in her gallery.
I hope her webpage can handle the load, it's sure enough worth a visit.
Mandelbutt (I've got nothing...)
Buy Steampunk Clothing Online!
PEEK and POKE, those were indeed the days
;-)
and don't worry about your gpa, the kind of stuff you learned messing around with the 6809 were probably more useful i would believe
good teenage memories, good memories
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
"Do you do weird things with your coffee to get funky patterns?"
Table-ized A.I.
No, clearly they don't.
And do you know the difference between "it's" and "its"?
[NT]
It really has to be heard to be believed -- you can download an MP3 file when the site is online.
Wow, I wish I could see who modded me down, just to be able to taunt them. What the hell is someone doing modding a discussion about fractals, when they don't even know what the Cantor set is?
HA! I just wasted some of your bandwidth with a frivolous sig!
At UC Berkeley, back in 1990, you told a great story of you and your wife attending a movie premiere which used a fractal landscape effect they'd hired you to produce. (please forgive my repeating old family gossip, especially if I've misremembered the details :) As I recall, it took longer to generate than the producer's patience lasted, so they cropped it rather than wait for its last triangle to completely render. Your wife hadn't heard about the "shortcut", but when your effect came onscreen, she gave you a big pinch. After the movie ended, you asked her what was wrong, and she said, in effect, "That's not a fractal!" - apparently she could recognize even partial fractals as incomplete, therefore nonfractal.
Have you learned more about any other fractal recognition, either people or artificial (eg. software)? Identifying fractals, fractal metrics, noniterative predictions, comparisons without analysis... Have you heard about the recently published African Fractals, a scientific investigation of fractal "sensibility" in traditional African designs, both unconscious and explicit? Do you think human fractal recognition and execution can inform our computer science investigations of this geometry? Perhaps the popularization of fractals in European-rooted design might influence our modern global culture as deeply as it seems to have influenced culture in Africa?
--
make install -not war
(Chaitin in pretty similar too. And come to think of it, so's Latham. These IBM Research Fellows are an untrustworthy bunch.)
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
When Scienctific American Mathematical Recreations published the Mandelbrot algorithm circa 1986, everybody tried to program it and look for interesting zooms and seeds. I know our lab tied its computers for weeks. And you saw it everywhere at trade show demos.
his book ("The Fractal Geometry of Nature") contains at least one oversight that is really staggering, and throws a bizarre light on his abilities beyond pure math (and other posters here have speculated at length about the originality of his mathematical work as well).
;-)
In that book is a high-res picture of one of the fractal landscapes he did (one of the high-gloss images in the center), and the caption reads something like "this image does not look particularly realistic, since real valleys have much smoother floors than the ridges around them - and I have no idea why". Either he was joking, or the whole concept of erosion (and common sense along with that) had completely passed him by.
I first read that book when I was about 15, and this has bothered me ever since then - how come that such an icon can make such stupid mistakes?
Apart from that I found the whole book to be remarkably long on convoluted talk at the time, and remarkably short on actual insight. But who are we to question an icon of modern math...
Just my 0.2EUR
A.W.
Optimal Fractal Coding is NP-Hard:t ml
http://theory.lcs.mit.edu/~ruhl/papers/1997-dcc.h
Might be a reason why it never took off...
Do you really have to resort to such nonsensical hyperbole for an eye-catching headline? Leave that crap for Fox News.
---- I have nothing more to add.
While we're on the subject, my website http://www.moneyscience.org/ also published a short piece by Mandelbrot recently - about the article which made most of an impact on him.e .php?articleId=12
http://www.moneyscience.org/tiki/tiki-read_articl
read some (in fact, any) of his earlier papers, and you'll find them to be full of acknowledgments of his antecedents. If with advancing age he can no longer be bothered to preface every sentence with an extensive bibliography, this is only understandable. We all get a little tired over the years.
In fact, your implying that any Westerner who omits the obligatory deferential nod to Plato is suffering from lack of intellectual integrity motivated by desire for self-promotion. Grow up!!
His talks are nothing but self-aggrandisement. I've been to talks by countless intellectuals ranging from people like Witten, Hawking, Bell and Feynman. Nobel prize winners. Fields medal winners. None of them promoted themselves in the way Mandelbrot does. Quite frankly, Mandelbrot talks like a complete asshole. I don't expect a bibliography from everyone. Mandelbrot is different from any other speaker I've known. He's obnoxious, and also a complete bullshitter. He talks endlessly about applications of his work that actually come to nothing. He's a fake riding on the success of his earlier years. And his earlier work is merely technicalities. FInd me the mathematician who actually cares about Mandelbrot's work. They are few and far between. His work is a dead-end that has had little impact anywhere. And yet he continues to give talks on applications of his work to things like financial markets (he's been doing that very recently) that are complete and utter bull. None of this stuff works. But he wows people with pretty pictures and once you're famous you're treated with undue reverence whatever you say.
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
yeah but my gallery has *animated* fractals.. and not just static zooms either.
Hmm, do you remember a demo that took hours to run that drew a 3-D graph that looked like a hat? I seem to recall the listing describing it as plotting an "Archimedes Spiral", it was only about 10 lines long. The final image was used as the title screen of the package "Printwiz". I've tried to no avail to find it on the 'net.
o/~ Join us now and share the software
Here's the song and the Lyrics
:)
:)
Now, take a musicians web server to its knees will ya!
Fine, here, have a mirror:
"You're one badass fucking fractal "
-- There is no sig line, only Zuul.
Ah, yes, those *were* the days...
/. lurker and occassional AC; too much laziness and tinfoil to login (which is a shame when I see how much low UID's sell for... =)
Reminds me of the time (high school?) I wanted the most accurate zero-crossing timer I could invent for a CoCo software SSTV decoder (sending the amateur radio's audio output into the CoCo's cassette port). I *needed* a 16-bit counter, but instructions like ADDD were sooo slow (6 cycles?).
It eventually dawned on me there was one really fast 16-bit counter in the machine... the program counter! I filled memory with NOPs and sent the zero-crossing output into an interrupt (FIRQ?). Subtract the stacked PC from the start of the NOPs and you had 2~ accuracy! I thought it was the coolest thing ever: the machine was churning through NOPs as fast as it could... and the NOPs *were* the computation!
With the double-speed POKE to run at 1.78MHz that got you ~1 microsecond resolution from 0 out to ~0.07s. A serial cable connected the CoCo (RS-232 Program Pak) to my Mac IIsi and a crazy MPW program displayed the incoming image (I think by directly writing to IIsi screen memory).
I had written a SSTV transmitter on the IIsi, recorded a test image to audio tape, and successfully received a tiny bitmap image of Jupiter. It looked pretty good-- there wasn't much jitter and the gray levels came out decent!
A mystery to me how all that early advantage seems to have been squandered...
Surely you meant `EDTASM' instead of `MASM'?
--Longtime
And hell, I will even let the "technology pioneer" thing go .... yeesh get over yourself
Slashdot, where armchair scientists get shouted down and armchair theologians get modded up.
Sounds like Google used to troll here for new hires.
--grendel drago
Laws do not persuade just because they threaten. --Seneca
Mandel, is THE man these days for math. And he hasn't said much recently. Good to hear at least some legends are still around to study.
sometimes when a challenge like this comes along I've got to take it up. Just got a mandelbrot demo working on my ps2 with the 6yo. It was based on the sample demo program that shipped with the demo disk
howwith yabasic of course. with every ps2 shipped into AUS (and UK and some other euro countries with PAL TV systems) a copy of the yabasic interpreter was bundled along with the demo disk.
The ps2 homebrew programming community is pretty strong with yabasic and ps2linux.
input and pongbtw the input via the ps2 controller is as bad as my ZX80 bubble keyboard. I don't have a USB keyboard (or a Datel PS2 XPort). Now for pong. It takes slashdot to get the young bloke to input games I played 25yrs ago :)
peterrenshaw ~ Another Scrappy Startup
Look at how he consistently keeps calling it Chaitin complexity even though everybody else calls it Kolmogorov complexity. AFAIK, Kolmogorov discovered it first.
"sweet dreams are made of this..."
MojoWorld from Pandromeda is a world-generation engine that generates fractal-based worlds with "pixel-perfect quality" (that is without obvious pixelation artefacts and loss of details in closeups). It's not yet photorealistic, but already very impressive (Gallery)
Future Wiki -- If you don't think about the future, you cannot have one.
This is probably the most irrelevant and stupid comment I have ever read. Seriously.
Oh, I disagree. As irrelevant and stupid as it was, there are far more irrelevant and stupid things here on Slashdot. Some of them are quite entertaining in their own way, and that's what keeps me coming back. Whenever I'm feeling a bit low for any reason, I just come to www.slashdot.org, read a few of the more ignorant comments and my innate sense of mental superiority returns full-force. Kind of like Web-enabled Prozac.
The higher the technology, the sharper that two-edged sword.
*searches*
Argh!
Which one was the paper you read? I'm afraid to click on some of the links :)
++
Within 100 years the act of thinking will require royalty payments.
So if the company fails, does that mean free software can begin using the patent? Or, does another company invariably sneak in and file a very similar patent (hoping the existence of prior art is not noticed) so as to prevent that from happening?
No reciepe. All she wanted to know was how to bake this Mandelbrot.
I doubt that we will ever figure out - and I suspect that even if we did figure out we couldn't do much about it
I am really impressed with the knowledge which /. moderators bring to the table. The parent of this post corresponds to the opinion of the majority of mathematicians, which is that Mandelbrot has done some good work but is a self-promoter, does not always acknowledge the work of others and probably is not considered a Math Legend by most mathematician.
I am a peon with a Ph.D. in math who has been doing research for less than 30 years; I have only one paper which received a
Featured Review and I consider myself to be a fairly ordinary person with three kids.
Slashdot moderators know much more than do I about contributions to geometric measure theory, Hausdorff measures, self-similar sets, fractals, etc. and I accept that my previous post was flamebait since I am ignorant. However, lots of other people deserve credit for their work on fractals. I will just mention two, John Hutchinson and Michael Barnsley. I just met John when I visited ANU recently; I believe I also saw Michael. I do not think they invented fractals or claim to be the smartest people in the world but they did some interesting work. Since our slashdot moderators are so smart, they can even tell you about this research. (Just in case they are too busy, here are some recent papers.)