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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.'"
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...
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.
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 remember typing that program in from one of the Antic magazines. Those were the good ol days. Between 1-2 days to generate each picture. Now we can do it in a matter of seconds on the average PC. Takes all the pride of accomplishment out of it when it's that simple.
I wrote my first fractal in 8-bit color, sucker ! On a MacII no less. In Lightspeed (what's in a name...) C (or was it MPW ? don't remember).
:-)
:-)
The average calculation time was 15min per pixel if i recall correctly. I just left it running the whole weekend and then on monday had to abort it cause someone needed to print and the damd mac couldn't multitask properly (Finder 1.x or so... not even multifinder in those days)
Damd those were the days... I recall spending a whole day trying to find a way to optimize 1 inline asm call... and then re-running a pixel or 2
I also recall my boss being angry about those 120KB image files filling up the 20MB harddisk at breakneck speed
When will I end this grieving ? When will my future begin ?
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?
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.
I remember typing that program in from one of the Antic magazines. Those were the good ol days. Between 1-2 days to generate each picture. Now we can do it in a matter of seconds on the average PC.
Why not do it in real time? A fairly old program, with smooth zooming into various fractals. Worked well on an old Pentium, looks bloody amazing on a modern machine!
Does various tricks to avoid calculating too much, and is rather clever about it...
Tedious Bloggy Stuff - hooray?
Xaos is also a nice way of looking at fractals. It can also work as Xscreensaver.
Life is just nature's way of keeping meat fresh.
In the interview, he says that a lot of interesting mathematics is stuff that's been done by people already, but where the original discoverer didn't go far enough or didn't publish everything. He advocates looking at things that were worked on 150 years ago and then dropped.
Fractals are generally random. They show self-similarity, but the way in which they are not identical but similar is often unpredictable. (E.g., in a period of noise, there will be periods of signal with a certain distribution, but the particular points at which the periods occur and which samples from the distribution appear in a particular trial are unpredictable)
The Feigenbaum number is a bit like the normal distribution, in that is something about how statistics behave in the aggregate rather than depending on the system. The sum of a bunch of independant random variables from the same distribution converges to having a normal distribution as the number of variables goes to infinity, regardless of the original distribution. Similarly, a system with a single state variable and an output linearly proportional to a parameter will show period doublings and regions of chaos in a way governed by the Feigenbaum number. Of course, you've idealized the system to a constrained mathematical model before it behaves that way; it's a property of mathematical models, not a property of all systems.
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.
Yeah, my uncle used to work with him. In those pretty IBM ads that featured some of the fractal work they were doing, IBM put Benoit in front of a screen with a bunch of pretty work my uncle was doing at the time. My uncle got no credit, of course.
-Peter
== Just my opinion(s)
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 dude's name was actually Mitchell Feigenbaum. He was working at LANL at the time. A good read if anyone is interested in the (convoluted) chronology of chaos theory and non-linear dynamics is Chaos: Making a New Science by James Gleick. It gives a feel for how the seperate contributions of people like Lorenz, Julia, Feigenbaum, Mandelbrot, Serpiensky, etc, came together, and the battle Chaos theory fought to be recognized as a legitimate field of mathematics in the 20th century.
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?
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make install -not war