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Introduction to Fractals and Iterated Function Systems (continued)
As a refinement of the process of generating the fern as discussed above, choose the transformations at random, but with probabilities proportional to the relative areas of the associated rectangles. This assures a more homogenous distribution of points and, very importantly, a tremendous reduction in computing time. One is now dealing with Random Iterated Function Systems (RIFSs). (The acronym RIFS has also been used to denote Recurrent IFSs, a different but related concept.)
The amount of data defining the IFS in this case is
the number of transforms (4)
times
[ the number of parameters (6) defining the transform of each smaller rectangle from the original
plus
the probability of choosing the transform (1 number) ],
for a total of 4 x [6 + 1] = 28 numbers.
Thus, to store the complete data needed to generate a one-million pixel image of a fern requires only 28 numbers! Not a bad compression ratio! Even this is understating the case, at least in the program that I am writing, because one can impute what those relative probabilities should be from the transforms themselves. As shown by Barnsley, those relative probabilities are proportional to the determinants of the matrices of the transforms. To see what those matrices are, click on http://www.pha.jhu.edu/~ldb/seminar/ifs.html. Thus, only 24 not 28, input numbers are needed to generate the image. In essence, the larger the absolute value of the determinant, the greater is the number of times that that tramsformation is chosen in our game of biased random choice. And what would it mean if the value of a determinant is negative? It means that the transformation of the starting rectangle into the transformation rectangle has not only in general distorted its shape, but has flipped it upside down!
And to think that the year-2,000 problem could have been postponed (for 1000 years) by storing just one extra byte, such as by calling the year 1998 098 instead of 98, thereby postponing the problem until the year 3,000! I dare say that each penny saved by avoiding the extra byte will cost at least $1 to fix! According to PC Dealer magazine, the Boston transport authority doesn't want people to feel anxious about riding in the subway at the last midnight of 1999. So its directors have approved a five-year (!) plan to ensure that its computers are year-2,000 compliant! Very reassuring! Long before 3000 (by 2020?), thanks to nanotechnology, one should be able to store all of the information of all libraries of the world, uncompressed, and the computer to access it, in the volume of a pocket book. By the way, such a nanocomputer would probably be mechanical, rather than electronic. It could consist of a three-dimensional array of mechanical push-rods and knobs of molecules, as detailed by K. Eric Drexler. See http://www.mitre.org/technology/nanotech/mechanical.html . Charles Babbage would have been proud! (Students at MIT have built a computer out of Tinkertoys that plays tic-tac-toe! Spare the rod? It is one of the few computers around that won't have a year-2000 problem!)
If the technology and economics of manufacturing cars had advanced as much in the last 30 years as that of computers, we should be able to by a new Cadillac for $1.00! If we were still using vacuum tubes, a cell phone would be the size of the Washington monument! (Careful: there is current research into microscopic-sized vacuum devices.) We have just begun the quest to build machines on a molecular scale -- nanotechnology. Three hundred years ago Leonardo da Vinci was asked what one of his sculptures represented. He replied that it was to be a machine that could fly. When asked why he thought that such a ridiculous thing would ever be possible, he replied that we already have machines that can fly -- they' re called birds! When a nanoscientist is asked today why he thinks that we should be able to build submarines (complete with engine and cutting devices) so small that a million of them could float on your thumbnail, the reply could be that we already have machines that small -- they're called enzymes, and we are full of them, and they are busy cutting and pasting molecular chains, at the rate of 5,000 per sec.!
In about 1995, my lawyer at work mentioned to his other client, the Canadian Nuclear Submarine Project, that I had a background in nuclear physics, computers, and contracting. They wanted me to "come aboard" and arranged to interview me, by which time the project was canceled. At about the same time, Japan announced its establishment (to the tune of $200 million) of a micro-machine laboratory, in which the first main project would be to build a submarine, of total length 1 mm. The second stage would be to build one 1,000 times smaller! Just think what a few thousand subs with shape-recognition sensors and cutters could do to fat deposits in your arteries or to the tips of the retinal rods in your eye, to give only two examples of surgery now (crudely) performed. (Shades of Fantastic Voyage!) Now let's work out the cost and the profit margin of these subs on the commercial market. Japan did not intend to lose money building this technology! Would $10.00 each (in lot quantities of 10,000) be too much? Or, eventually, would one cent each be too much? I have just heard, by radio from Germany (in 1998), that a submarine 4 mm long has been on display at the big trade show in Hannover -- that's huge, but give it time! In about 1995 I saw a picture of a working engine 4/1,000 of an inch wide, grown of silicon, with a main wheel that spins at 20,000 rpm. (No, it doen't use WD40 oil!) This is still a leap from the aim of one building molecule-by-molecule (which will happen), but it's a step!
Drexler foresees the day when, with the help of our home computer and the Net and its collection of succulent recipes, we should be able to construct in our kitchen things like a NY sirloin steak from the raw materials at hand, mainly hydrogen, oxygen, and nitrogen (free in the air) and carbon (from a pile of dirt in the corner)! As for a glass of pinot noir -- why not! "Which vintage shall I manufacture (excuse me, serve) today, sir?" (This may sound like a bit of a pipe dream in an age when we have not even accepted the use of superior Coca-Cola technology (the screw-on plastic cap) to replace cork stoppers on wine bottles! Can you imagine how little cork (and its increasing inferiority) there is left on the trees still remaining in Portugal? Our problem here is not technology, it is misperception, by both the public and many "experts". To illustrate how ludicrous this situation is, I heard an interview with an entrepreneur recently via the Australian Broadcasting Corp. in which he was explaining that, in light of the increasing shortage and price of reasonable cork (i.e., cork without holes), his new stopper had great potential because it would: (1) be made of plastic and cork such that glass would touch only plastic, not cork; (2) wine could touch only cork, not plastic; (3) the stopper would be removable (and replaceable) without using an external tool such as a corkscrew; and (4) it would look like cork. What a remarkable advance in technology, bringing us almost up to the stage that Coca-Cola had surpassed at least 20 years ago, and at twenty times the price of screw-on caps by Coke, I would guess!
Correct me if I am wrong, as I am not a wine expert, but I thought that the purpose of a cork was to keep contaminants such as air and bacteria away from the wine, especially if it is to rest on a shelf for ten years before being sipped. That technology has been in use for about 400 years, and it obviously does not work well at all. About 3% to 7% of wine is contaminated by the cork itself, not to mention the contaminants that manage to work their way from outside through the porous cork into the wine. Coca-Cola would shudder if its failure rate were even as high as 0.0001%, much less 3%, and the problem for Coca-Cola is perhaps more difficult than that facing wine bottlers, what with carbon dioxide and all. But some wine bottlers have solved the problem using the much more reliable srew-on cap, but of course, only for "cheap" wines. It is one of the great ironies of the vino world that wines least in need of quality protection utilize the most effective closures, while high-quality wines that need protection use less-effective closures. For a delightful little essay on this topic, click on Screw This!. We provide the ultimate in safety for a $1.00 bottle of pop (at a cost of $0.005 per botttle for plastic?), but fail miserably to do so for a $100 bottle of wine (at a cost of $.50 per bottle for cork?)!
For a landscape equivalent to an oil painting, one might consider an IFS consisting of 150 to 300 transforms. The difficult part is choosing which particular set of transforms would create a given image. Barnsley has solved this problem, so that his special software can now do this automatically. The procedure is too complex to describe here. Suffice it to say that it consists of an iterative mapping between grids of "domains" and "ranges" of a picture to derive the resulting IFSs. It exploits the fact that it is more probable that one grid element is similar to another than that one picture element is similar to another. Note that IFSs is plural here. Although this is somewhat of a simplification, the key idea is that, rather than even try to express the picture as the result of a single IFS, one instead aims to express several portions of the picture as arising from a single IFS, but that many IFSs will be needed to encode the total picture. For example, in the test picture of Lena, the edge of her cheek might look very similar to an edge of her arm, so why repeat all of the pixel storage for each portion of the picture? Instead, express both as arising from a single IFS. It requires a massive amount of computing. He has produced a special hardware and software system that does the job, all heavily protected by patents. He offers a special board that can be plugged into a PC, consisting of eight math co-processors operating in parallel and application-specific integrated circuits (ASICs). To reduce an 8 x 11" colour photo to an IFS requires 12 seconds (as of about 4 years ago). Having done this, one could then send the IFS parameters by phone line to a remote computer and regenerate the picture in about 2 or 3 seconds using additional regeneration software. For more of an idea as to how this works, click here: http://www.mathcs.carleton.edu/students/stewartj/networking/fbc.html.
Barnsley has contracted with a major oil pipeline system in Africa. Cameras are mounted at remote locations. They periodically snap a picture, reduce it to an IFS, and send the parameters to home base via short-wave radio where the color image is then generated. How's that for pipelining of data! We could be doing a similar thing with chest X-rays from Ninavut!
Two systems are in operation for transmitting short bursts (of perhaps a few tens or hundreds of milliseconds) of data by radio from remote sites by bouncing radio waves off meteor trails. This is underway along the west coast of BC, where data from water-level sensors is sent to a central site to help foretell tidal waves. A system is in use throughout the plains of the USA for the tramsmissit\ion of data on ground moisture, temperature, etc., for instant retrieval by the US Department of Agriculture. This is a lot cheaper than leasing land lines, and there is a sufficient supply of meteors! Auditors take note: in this business, one depends not so much on audit trails, as on meteor trails!
Barnsley has collaborated with Microsoft to produce the Encarta Encyclopedia, including 7 hours of sound, 100 animations, 800 color maps and more than 7,000 photographs in less than 600 megabytes of data on a single CD ROM. (See http://www.ippi.com/dir_akp/akp_fracim.html.) I estimate that this was done using a compression ratio of several hundred to one, perhaps 1,000 to one. (IBM is trying to increase the capacity of CD ROMs by a factor of ten, without compression, using ten layers of bits instead of one. Someday, using nanotechnology, we will be using millions or billions of layers!)
Barnsley has produced a short movie, involving a storm over an ocean, using a compression ratio of 1,000,000 to one. For high-resolution images, ratios of 20 to 100 to one are more the norm. His compression technique allows one to choose the quality of resolution desired, including (paradoxical as it may seem) a resolution higher than that of the original!
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Barnsley has contracted with the US Air Force to solve problems such as the following. Given that we have 10,000 photos taken from spy satellites and planes, many of which, such as some over Iraq, seem to show airplanes on runways, what model of plane are they, and exactly where are they? (I came away from his company with a 3.5-inch demo disk containing very detailed zoomable aerial photos of Iraq Base 1 and Pearl Harbour 1 and 2, and 14 seconds worth of color video and sound, all compressed, of course. This is all the more impressive considering that a 600-MB CD can hold only about five minute's worth of uncompressed video!)
Another interesting application is to have a computer observe a corridor through a video camera and raise an alarm whenever an unauthorized person takes a stroll. (A bit more sophisticated than that at least one location in IBM where someone wearing a red badge could get into trouble by walking on a blue carpet instead of a red one! It gives new meaning to being brought up on the carpet! ) With cheap ($100) video-cameras-on-a-chip, Britain is leading the way in installing thousands of surveillance cameras per year in public (and not-so-public!) places to detect naughty people. (Do you think that every place inside of a "public" washroom at Heathrow or in a ATM booth is a "private place" under the law? Think about it!) This will soon escalate to tens of thousands per year. Oh brave new world! So far, the viewers are humans. Will it be more comfortable when computers do the observing instead?
Some homes are now equipped with such cameras, so that one can log onto the Net and spy upon what is happening at home. Nor quite so appealing is the thought that a hacker could arrange to peek into what is happening in someone else's home!
Cameras now stare at people punching PIN numbers into ATM machines. The problem is: how to hack into these images! It has been done, at least once! One has to make a living somehow! (Does PIN stand for Piracy Is Nifty?)
In addition to the use of fractals, several approaches are being taken in how to tell a computer what a face looks like in such a way that it can retrieve it or a close relative. One method is to use a classification system as to width of lip, angle of eyebrow, etc. If one had, say, 200 such characteristics, one could then represent the face as a single point in a 200-dimensional space. The problem of then generating a portrait of a face that appears to be half way between that of John F. Kennedy and Marilyn Monroe then becomes simple: just interpolate between the two points in that space and convert the interpolated point into a portrait. A grad student at MIT has done it. One can even extrapolate to find out who would look twice as different than JFK as Marilyn! In my ConjPic computer program, I can morph an image of a galaxy into that of a pine tree by simply varying a single parameter from frame to frame.
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Several technologies have been vying for years to become standards for High-Definition Television (HDTV). Most of them would require four channels of TV input to produce one channel of output, a profligate use of already scarce bandwidth. Barnsley plans to bring one channel in, reduce each frame to an IFS, and regenerate each frame as an HDTV picture. To do so, the system will have to do the process 30 to 60 times per second instead of the once every twelve seconds noted above, a factor of 720, or about 72,000 times as fast as a PC. I believe that it can be done. For this reason and others, the TV set of the future will consist of a high-resolution monitor and a supercomputer, perhaps one 100 times faster than a Cray. See the chapter "The Death of Television" in the book "Microcosm: The Quantum Revolution in Economics and Technology" by George Gilder (ISBN 0-671-50969-1). Nanocomputers should be able to operate at rates such as one million million instructions per second. A partial advance is underway in that a decision appears to have been made days ago to phase out analog TV and phase in digital TV in parallel. By 2006, all present TV sets will be obsolete.
Barnsley has coined the term "fractal forgery" to denote the process of generating an image from an IFS because this process can generate a picture that has more detail than the original! Provided that the original picture has elements that are similar or identical at different scales of size, this forged detail can be believable. For example, the branch on the branch of a branch of a tree often appears to resemble the branch of a branch of that tree, possibly sheared or distorted (affine transformation). (If I incorporate a company to exploit this technology, maybe I'll call it IFFY (Iterated Forgery For You)! That way it will not only be iffy, it will sound iffy!)
So, unlike other compression techniques (such as JPEG, MPEG, Wavelets, and DCT), IFSs allow one to generate more detail than that in the original, much of it believable, some not. That is because of an important characteristic of fractal compression: that is, unlike other techniques, it is not pixel-dependent. It also allows for smooth animation by smooth variation of the underlying IFS parameters; hence the ability to morph, i.e., make movies. The reason why the associated Fractal Image Format (FIF) has not become popular is attributed to marketing and patent-law decisions by Iterated Systems, much to the dismay of some critics.
An animated zoom into a fractal image, Bluedive, is available from the following sites:
ftp://fractal.mta.ca/pub/cnam/anim/schol/
ftp://ftp.doc.ic.ac.uk/Mirrors/fractal.mta.ca/pub/cnam/anim/schol/
This was accessed from the following site:
Web 119. Bluedive, from Eric's Fractal Gallery. Fractals: Not by the Numbers, or Fractured Gary Tales by Dr. Gary Kerbaugh: http://www.cs.ecu.edu/~kerbaugh/FractalsNBTN.html Links to related pages.
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I foresee the day, within ten years, in which a new Hollywood film premiers, starring Marilyn Monroe and Joseph Cotton, all creatures of IFSs! The screen credits will include no actors -- only computer programmers and cyber-artists. I have already seen a movie in which the credits included 30 programmers and analysts and interesting chunks of hardware, such as frame grabbers. (In the movie The Last Starfighter, an intricate 20-minute battle between spaceships was generated entirely by computer.) The number of computer analysts required will be exceeded only by the number of patent, copyright, and intellectual property lawyers needed!
When we think today of movie-production factories, we recall names such as MGM, Columbia, 20th Century Fox, and United Artists. Only a few years from now we may more immediately bring to mind names such as Industrial Light and Magic, Lucas Films, Digital Domain, and Dreamworks, fueled by cyberartists from Sheridan College (Toronto), among others.
Why is it that sports and, in particular their heroes, are so popular on TV? Why is Wayne Gretzky a millionaire for contributing what is arguably of little benefit to society? Could it be that, like the Greeks of old, we still need to manufacture heroes? Could it be that, urged on by the propaganda of Molson's, Coke, and Participaction Canada, we attach such ridiculously inflated value to being able to run faster and jump higher? (How ironical it is that Coca-Cola is a major sponsor of the Olympics in order to advertise its main product, a banned substance under the Olympic dictatorship! I can send an essay on Olympic drug testing as an unconstitutional invasion of personal privacy and national sovereignty.)
The closest most of us get to being an athletic hero is to see proxy images on TV. But we do so now with some limitations. First, the picture is not life size. Second, although the picture is in colour, it is only presented in two dimensions, in spite of the fact that technology has existed for years to give us full 3D colour images (not the old red vs green variety). But perhaps the biggest limitation we have vis-à-vis hero-association is that the hero on the screen is not I! With IFS technology it could be! Why shouldn't that athlete on the screen be me, instead of Wayne Gretzky? After all, for purposes of hero worship (and worship at some kind of shrine it appears to be!), all that is needed for me to be the hero is for my picture to be the picture of the hero! After all, to say that you have seen Wayne Gretszky "only" (for most of us) means that you have seen his picture on a screen. What would happen if, instead of his face appearing in that hockey suit on the screen, it were your face? Why would it be any less real? If his face on the screen convinces you that he exists, in spite of the fact that you have never seen him in person, why should the appearance of your face in his suit on the screen not convince you (and, even easier, everyone else) that you are not now the great hockey hero that everyone is talking about?
To appear to be, or not to be? That is the question. How do we arrange the slings and arrows (IFS vectors) for this to happen, and to make an outrageous fortune? IFS technology and smart entrepreneurs! How much would you be willing to pay so that the whole world watching the next Rosebowl game would see you as the quarterback? I can see several variants of how to do this, involving both technical and commercial considerations. Would you be willing to pay $100,000? After all, those special boxed cubicles in the stadium go for at least that much (at your expense, as corporate tax write-offs). The main technical requirement is to have a few portraits taken of you at several angles, the reduction of your portraits to IFSs, the reduction in each frame of the quarterback's face to an IFS, and the switcheroo of IFSs! That takes care of the video image. Now for the audio image. That gets a bit more complicated. We need to reduce the sonograms of the quarterback's name as spoken by several announcers and post-game interviewers, to audio IFSs, and we are ready to do audio switcheroos, being careful, of course, to use voice recognition to ensure that the audio image of your name is spoken by the appropriate announcer! If we can vote by proxy, why can't we be heroes by proxy? In other words, if an image can be picture-perfect, why can't it also be proxy-perfect? There could be two versions of this process. In one version, John Doe, would appear on all TVs as being Wayne Gretzky. In another version, John would appear as Wayne on only selected TV sets, those which, by prior arrangement, had downloaded the personalized IFSs. Would an IFS by any other name look and sound as sweet?
I dare not even mention this idea to Walt Disney studios or to the advertising agencies! Could you tolerate seeing yourself in the next 100 replays of your worst nightmare of an ad? Could you have foreseen that you did not want to be in that ad, but that someone hacked into your computer, "borrowed" a copy of your personal IFS signature, and sold it on the Net for some e-cash credits? Now he's driving the Mercedes that you saw yourself driving in an ad on TV last night! It's enough to make you want to lose face, for a change!
As a byproduct of these technologies we would no longer need or want to have football stadiums. My wife and I were given free tickets to attend several football games by the Ottawa Roughriders. Although I am not a football fan, I would enjoy watching such games on TV more than at a stadium. The problem with being at the stadium was that, at each exciting part of the game, everyone would stand up, meaning that I could not see what was happening. (Somewhat akin to watching a movie with all of the naughty bits blanked out!) Other shortcomings were: a lack of commentary, no close-up video, no instant replay, and no armchair. Without these, football in real life is not as real or as interesting as that on TV! Even in a real stadium, what does it mean to say that a game of football is real? It is no more real to me than StarTreck! I think that the logical next step is to replace the football stadium by a big TV studio. The next step is to forget the studio and replace it with comfortable computer stations and fractal computer artists. If this seems like a pipe dream, walk into a computer store and ask to see NHL hockey games being generated completely by software. It's not perfect yet, but neither were 45-rpm records a few years ago! Take a look at a recent Sony PlayStation if you want to see some fast 3D graphics. These toys are far faster than the early Cray supercomputers.
Twenty years from now, CDs will be as obsolete as record cylinders. Museum curators and librarians are already worried as to how today's recorded information will even be readable in the future! The CDs may survive, but where have all their players gone? If you had a 45-rpm record, could you play it? (In my work in Federal contracting, I had occasion to arrange for a trade-in credit of a working computer terminal from a government department to a private company so that the company could put it into its museum. In New England three years ago I saw a computer for sale in an antique store.)
Music has been compressed using IFSs. I foresee that IFSs can be invented to produce new music. Another variant would be to create a system to transform a visual image into music using IFSs and computers.
Another possibility that I might pursue is that of converting between visual and musical "images". Lest this be more than a pipe dream, I recall that there is a musical composer (Olivier Messaien, see below) who has a mental condition (synaesthesia) by which he automatically converts visual imagery, mostly triggered by color, into music. It appears to be a kind of "crosstalk" between visual and auditory modes of perception. He composed a major symphony primarily by taking a helicopter ride through a canyon (such as Bryce in Utah) in the southwest USA. This canyon has spectacularly coloured layers of rock. (We visited it a few years ago.) Perhaps not coincidentally, there is a graphics painting program called Bryce, and another one called Fractal Design Painter. Check the Net for some lovely examples. (If you are in the southwest, visit Bryce Canyon if you are moved by colour, or the Grand Canyon if you are impressed by vastness.)
Web 27. Synaesthesia: Music & Art
Synaesthesia: Music & ArtPage for the International Synaesthesia Association: http://nevis.stir.ac.uk/~ldg/ISA/ISAMusicArt.html Dr. John Harrison, Academic Unit of Neuroscience, Charing Cross and Westminster Medical School. Dr. Simon Baron-Cohen.
The composer Olivier Messaien gives a particularly florid description of his colour sound associations in his 1947 account of "the gentle cascade of blue-orange chords" in the piano part of the 2nd movement of Quator pour la fin du temps. He is later more specific about the nature of his synaesthesia when he states he sees "colours which move with the music, and I sense these colours in an extremely vivid manner".
I cannot resist a further digression in relation to crosstalk of perceptions. I have discovered only recently, by accident on the Internet (a fortuitous collision on that highway, don't you think?) that Richard P. Feynman, one of my heroes, when reading equations printed in black ink on white paper, would perceive that different aspects of the equations would appear to be in different colours, in a systematic way. One might characterize this as letter-colour synaesthesia. Curious! Here are two interesting sites.
Web ?. Richard Feynman's Synaesthesia
Richard Feynman's Synaesthesia. by Ian Watson. Richard Feynman (1918-1988), winner of the 1965 Nobel Prize in Physics, was a letter-color synesthete as . . . http://nevis.stir.ac.uk/~ldg/ISA/Feynman.html
Web ?. Quote by Richard Feynman: http://golem.physics.ucsb.edu/~mikefalk/poems/feynman.html An Intriguing Quote by Richard Feynman. It will be difficult. But the difficulty really is psychological and exists in the perpetual torment that results . . .
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Yes, fractals are everwhere! They are buried in time series, such as electrical noise, the rise and fall of the Nile River, the growth of cities and dendrites, the sublime music of Bach, and in stock-market prices.
See the book Chaos and Order in the Capital Markets by Edgar E. Peters, for how one can apply complexity theory, fractals, genetic algorithms, and wavelets to market prices. Don't buck the trend -- make a buck from the trend!
Web ?. Wiley Finance--Frontiers in Finance Chaos and Order in the Capital Markets. Edgar E. Peters. http://www.wiley.co.uk/products/subject/finance/finance/front01.htm "The bible of market chaologists." -- BusinessWeek.
Web ?. Chaos and Order in the Capital Markets: http://www.amazon.com/exec/obidos/ISBN=0471139386/spiffynetA A New View of Cycles, Prices, and Market Volatility (Wiley Finance Editions) by Edgar E. Peters. List:.
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9. Database Access via Fractal Compression
(This summarizes a separate document sent to Richard earlier: C:\Up\CrossZ1.doc.)
Listed below (at Web 900, Web 901, …) are some hyperlinks to sites dealing with fractal databases, that is, database-access methods that use fractal data compression as part of the access method, rather than databases of fractals as a subject, per se. They were garnered using searches for Cross&Z (120 docs), Cross&Z&International (65), "Cross/Z International" (41), and QueryObject (96).
The following article perked my interest in this subject beyond my ongoing interest in fractals as applying primarily to images: Fractal Databases – New Horizons in Database Management, by Lisa Lewinson, PC AI Magazine, March/April 1994, pages 30 to 33. The article summarizes the work of Andre Szykier, Chief Technology Officer of Cross/Z International, and his cousin, Mark Chroscielewski, Senior Marketing Executive at Chase Manhattan Bank.
Andre had been developing a proposal involving constructing a map of the last stretch of terrain that a cruise missile would fly over. Szykier proposed the use of a fractal equation (more likely, a set of affine transformations) to represent coordinates for longitude, latitude, and terrain altitude.
Mark’s problem was to build a massive customer database for the bank, involving 30 million names, with data from five credit bureaus that would have to handle up to seven levels of data. Within two weeks they had built a prototype fractal database, compressing 30 million records onto a PC. They found that they could do exact counts instantaneously, as compared to queries on a mainframe, which took several days.
The key to the technique is that, for example, one could represent 10,000 to 20,000 hourly temperature observations as a shape represented as a single fractal data point of eight bytes. This single point can be used to reproduce any or all of the original data points exactly. Thus, one can discard the original data. (I have some detailed material on this subject of fractal interpolation and construction of fractal curves.) They are exploiting 64-bit chip technology to achieve data-compression ratios of 10,000 to 1. In 1994 they were upgrading their system to display segment counts for an array of 22 by 22 variables, 7 levels deep. Their system requires about 15 minutes to create views of a 40-million record database, after which each query takes less than one second on a PC.
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End of 9. Database Access via Fractal Compression. _______ Continued at 10. Web Sites
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You can e-mail me at waynerp@sympatico.ca