Death of a Giant
Benoit Mandelbrot, the father of fractals, died on October 14 in Cambridge, Massachusetts, at the age of 85. The cause of death was pancreatic cancer, according to an obituary in the New York Times. Mandelbrot fled Poland ahead of Nazi occupation when he was 11 and moved with his family to Paris. He studied at the Ecole …
I remember being shown some fractal postscript files - a pretty short .ps file that would cause the printer to sit silently for a long time (*) and would then either crash, produce an error page or, occasionally a beautiful fractal. (*) long = an hour or more. Probably would be less time now as this was a few (cough) years ago.
Creator of awesome artworks, explainer of snowflakes and cauliflower, creator of encryption algorithms.
Of course he never did any of the above, but his mathematics enabled others to do these.
If I achieve that much and live to 85 it'll be a ***ing miracle.
Well done Benny. Respect!
So you want to apply this in Physics? This has already happened. Laurent Nottale has tried a fractal approach to spacetime. He gets the expected Higgs mass wrong though and predicts that the large-scale structure of the universe should be self-similar, of which there is not a whole lot of evidence (it's more like a synaptic mess, innit). Maybe he tries too hard:
I was very sorry to hear he had died. We need more like him willing to doggedly work to critically dig through and overturn orthodox paradigms. His dogged promotion of fractals transformed the thinking of so many scientists (often in the face of initial considerable opposition) and yet he has ended up opening up so many new ways to approach problems. Some in the media have classed him as a maverick but I considered his determination inspiring.
Anyway, if you want to see how much impact fractals have had (and are increasingly having), I recommend this fascinating documentary...
Also if you want to play with fractals (zooming in and out (via mouse buttons) in real time on any PC :), I recommended XaoS, i.e.
The man was a genius.
I spent countless hours rendering IFF animations with my Amiga 3000 of interminable zooms inside a Julia set, I even bought more memory to be able to render deeper and deeper.
At the time a big portion of my (Then huge) 50mb SCSI disk was full of fractal zooms.
Some animations took entire weeks to render.
There is something mysterious, easily appreciable, and seemingly impossible to grasp about how fractals work.
What I mean is that if you look at the way nature work, it seems that mother nature has some way to pack a lot of information on a tiny space with a very limited set (see DNA for example).
Fractal Maths give us some insight into how that kind of information compression works.
I remember doing the same thing - except on my 286. Eventually I got tired of the iteration, and did hybrid things where I'd set color based on other aspects, which was kind of interesting.
That eventually got me into chaotic systems ('Computers, Pattern, Chaos, and Beauty' was my bible when I was 12), which I ended up enjoying more; it felt more difficult to understand. With fractals, once I saw where the pattern was, the self-similarity actually bothered me; it *simplified* the whole thing. Once you know how the self-similarity works, you can see all the way down in without really seeing it.
Chaos was more fulfilling, since I could create something I really couldn't predict. I wish I had the time to reimplement some of the code I wrote then; I could probably use a thousand times as many particles and still render a hundred times as fast. Maybe it's time to break out the bible again...
Still, it was Mandelbrot who got the ball rolling on the entire discipline. The vision required to do what he did in an era *without computing hardware* to speak of is little short of breathtaking - a bit like Beethoven's ability to compose a symphony while deaf.
Jo Co said it best...
Mandelbrot Set you’re a Rorschach Test on fire
You’re a day-glo pterodactyl
You’re a heart-shaped box of springs and wire
You’re one badass f*cking fractal
And you’re just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way
Mandelbrot’s in heaven, at least he will be when he’s dead
Right now he’s still alive and teaching math at Yale
He gave us order out of chaos, he gave us hope where there was none
And his geometry succeeds where others fail
If you ever lose your way, a butterfly will flap its wings
From a million miles away, a little miracle will come to take you home
I used to write programs to animate Mandelbrot sets by shifting the starting parameters. Got my old Archimedes to render them in real-time with a mix of fixed-point maths, and laboriously-optimised hand-coded assembly. Wish I still had that program - my inner-loop was a work of art.
The sad thing is that at the time I didn't really understand it. I daresay I could go back to it now and make more sense of the unreal numbers and such, but at the time it just made pretty pictures.
ARM assembly code - that's pure luxury...
When I wrote my first Mandelbrot set program, it was on an Acorn Atom, in 6502 assembly code.
Of course, the Atom wasn't exactly blessed with that many screen colours, so I half-toned the output and sent it straight to my printer - ended up with a few poster sized Mandelbrot sets that took days to produce!
It was only when I finished that I realised that there was a carry error in my 32 bit fixed-point multiply routine, and the zones of divergence had curious scalloped edges to them - but the errors turned out to be nicely fractal too!
Agree w/ zeedee. xfractint is the way to go. When the Mandelbrot *immediately* appears, escape goes to a menu, F1 shows some common options, pageup and pagedown zoom in/out (with arrows and return key setting up the box to zoom in on). This Mandelbrot used to take several seconds on older PCs (up to 15 or 20 on a 486 or so) and overnight on an Atari 800. There's LOADS of fractals to choose from (with mandelbrot and Julia being "the classics". Try the "@" command, this has some nice presets people have found over the years. I'm looking at them now, most used to take so long to generate that I never looked through them all -- now they generate in under a second to a few seconds.
It's too bad the "C" (Color cycle) mode doesn't work (I think it requires 256 color mode), that color cycling mode was a real trip.
You tend to take these mathematicians for granted, don't you. I remember wasting countless hours with FractInt in the early 90s, entering all sorts of command-line parameters and watching the image appear, line by line, down the screen! Makes you wonder where the next mathematical breakthrough will come from?
Well it depends on what you mean "not working well"... the collage theorem was/is very successful in producing very high compression ratios. Of course the problem was finding the right set of iterated function systems that would be a good approximation of what you wanted to compress and do it in a reasonable amount of time (compared to other lossy compression schemes). As for getting money to do the research, I think it was probably worthwhile even if it didn't fulfill the initial promise.
I might be wrong on this point, but I seem to remember Barnsley eventually proving that there wasn't a tractable algorithmic way of searching for the minimal set of coding IFS's. It was always possible for humans to come up with tuned sets of IFSs that would have good compression properties, but without being able to codify that in an algorithm, it wasn't going to work, so the proof was a kind of variation on the Church-Turing thesis, iirc.On the other hand, the wikipedia page seems to contradict this, so I don't really know at this point...
"Of course the problem was finding the right set of iterated function systems that would be a good approximation of what you wanted to compress and do it in a reasonable amount of time (compared to other lossy compression schemes). "
The best generator seemed to be a graduate student locked in a room. IIRC *all* the classic examples (single pictures, not a single mpg amongst them) were the result of this "algorythm"
"As for getting money to do the research, I think it was probably worthwhile even if it didn't fulfill the initial promise."
I was thinking of a company called Iterated Systems which IIRC made a substantial number of clams for their compression tech. AFAIK they ended up supplying a fairly effective (but *very* resource hungry) asymmetric (heavy processing to compress, relatively easy to decompress) website content management systems.
"he did a stint at the Institute of Advanced Studies at Princeton University"
The IAS is in Princeton, NJ, which is also the home of Princeton University; but it is not part of Princeton University. It's a separate organization, founded in 1930 by Louis Bamberger and Caroline Bamberger Fuld to be a new kind of academic institution, where faculty and graduate students could pursue research together without the distraction of those pesky undergrads.
Because of proximity the IAS and PU have a lot of playdates, but they're strictly friends.
There are a couple of anecdotes about Mandelbrot's time at the IAS, and why they never tried to hire him on as a faculty member, in Ed Regis' entertaining history _Who Got Einstein's Office?_.
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