markv@gauss.Princeton.EDU (Mark VandeWettering) (01/06/90)
>>Fractals, if a valid measure of nature, say how LITTLE information >>there is. Compilicated appearing patterns actually can be parameterized >>by very few numbers, hence its attractiveness to explanation and information >>compression. Interesting comment, I hadn't pictured it that way. Hmmm... More thinking necessary. >Seems like a matter of semantics, to me. The old "Half full" or "Half empty" >approach. > >>Mitchell appears to be jumbling several types of "new age" mathematics-- >>complexity theory, chaos theory, fractals ...-- each which has precise and >>different definitions and something different to say about nature. Yes! Mathematically speaking, the concept of fractal dimension is rigorously defined. Chaos theory has some very specific results, as does complexity theory. Because of the hype surrounding fractals, one sees grandiose claims about the applicability of fractals to describing natural objects. The problem with this is twofold: a) rarely are such descriptions analytically compared with the objects they describe. Pictures that are generated with fractals are usually evaluated on purely subjective criteria, which is error prone. b) descriptions say nothing about the processes that generated the object in the first place. Fractal mountains don't react to erosion or gravity, fractals trees don't grow with the wind etc.... >The "jumbling" as you call it, was intentional. I was not trying to say >anything specific- just that we should keep an open mind and look for >relationships where we normally wouldn't. And in saying nothing specific, you have said nothing. An open mind is good, but it should be tempered with the ability to critically analyze new ideas and remove hype from your judgement. >>Some may provide USEFUL results and become parts of the scientist's toolkit, >>while others will remain mathematical amusements. Actually, I have nothing against fractals perse, I have several books concerning their mathematics on my shelf. The mathematics of fractals is fascinating. What I combat is the notion that they are somehow most applicable to description (and hence generation) of natural objects. It has never been demonstrated to my satisfaction. >It depends on your orientation. If you want to be analytical, sure, then its >a matter of what TOOL you can apply to what specific problem. But one should >also be able to take a couple of steps back and see the whole picture. What >is the gist of what I am trying to say? Therein lies my message. This is where the "philosophy" in the header enters in. It entirely depends on your view and belief of science. Many scientist have tried to develop general and simple rules that explain the world around us. So far, we have failed. Many of the most elementary questions in science remain unanswered, or answered only in the theoretical sense. Why is this? I would say that it is probably due to the fact that there is a damn lot of information out there, and it doesn't categorize neatly. Also, our ability to observe is improving, so we constantly discover new things about our universe. I don't believe that science will ever gain a view of the "big" picture, only increasingly more complex and intricate views of increasingly smaller and smaller scale effects. So ends the philosophy. >I was trying to elict an appreciation for the BEAUTY of what we have to date >and where they might take us. Unfourtunatly, some are unable to grasp that. Yup. I would rather look at a painting of a mountain than a computer rendering of one. > mitchell@cbmvax.UUCP > "The eyes are open, the mouth moves, but Mr. Brain has long since > departed." - The Black Adder Mark
elf@dgp.toronto.edu (Eugene Fiume) (01/07/90)
In article <12707@phoenix.Princeton.EDU> markv@gauss.Princeton.EDU (Mark VandeWettering) writes: > > >I don't believe that science will ever gain a view of the "big" picture, >only increasingly more complex and intricate views of increasingly smaller >and smaller scale effects. > >So ends the philosophy. > Reductionism doesn't preclude unifying the "big" with the "small". That's the goal, and it's the most effective scientific stance we've got. I'd rather see a hard problem broken up into small pieces than to believe in magic. I guess that's the thing that bugs me most about the fractal bandwagon. Fractals aren't magic. They're cute, fun and frilly mathematical objects that might have something to say about the world (I personally have my doubts). But fractallographers (!) run perilously close to endowing them magical power. [Just go to a populist talk on fractals sometime.] Soon, some yuck will be marketing New Age fractal crystals (-: . -- Eugene Fiume, Dynamic Graphics Project Department of Computer Science, University of Toronto elf@dgp.toronto.edu, (416) 978-5472
rick@hanauma.stanford.edu (Richard Ottolini) (01/07/90)
a Don't abandon "new age" mathematics such as fractals nor worship it. Sometimes years later something will escape from the closet of recreational mathematics and be useful. Two examples: (1) Cellular automata are a serious competitor to differential equations for modeling waves and fluids in the earth sciences. This after years in the "Life" closet. (2) In computer graphics, quaternian transforms may be a superior alternative to homogeneous coordinates for modeling transformations. These have been in the closet over a century.
thomson@cs.utah.edu (Rich Thomson) (01/07/90)
In article <12707@phoenix.Princeton.EDU> markv@gauss.Princeton.EDU (Mark VandeWettering) writes: >Because of the hype surrounding fractals, one sees grandiose claims >about the applicability of fractals to describing natural objects. >The problem with this is twofold: > > a) rarely are such descriptions analytically compared with > the objects they describe. Pictures that are generated > with fractals are usually evaluated on purely subjective > criteria, which is error prone. > b) descriptions say nothing about the processes that generated > the object in the first place. Fractal mountains don't > react to erosion or gravity, fractals trees don't grow with > the wind etc.... In an attempt to bring this back around to graphics, think back on the methods used to generate most computer imagery in use today. Shading equations often contain lots of little parameters that are tweaked by the programmer -- often judged on "purely subjective criteria" in order to get the best looking image. That's what I feel graphics is about -- getting the best image for what you want. If the image you want comes more easily from a fractal model, who cares if it isn't a valid "natural model"? Graphics programmers aren't geologists or biologists or botanists -- they aren't seeking a model for explanatory purposes. They are seeking a model for imaging purposes. The two are very different. Some of these techniques have managed to satisfy both needs (L-systems for example), but mostly graphics is just a "hack" that produces a "nice" image. If you want to completely and accurately model a mountain, you might as well sketch it by hand because the compute time necessary to model the complete developmental cycle of a terrain is prohibitive; not to say that knowledge from the sciences is useless in helping you obtain a good image, but that the technique used to get a good image doesn't necessarily have to come from a "scientifically accurate" model. -- Rich Rich Thomson thomson@cs.utah.edu {bellcore,hplabs,uunet}!utah-cs!thomson More Columbians are killed by American cigarettes than Americans by Columbian cocaine
platt@ndla.UUCP (Daniel E. Platt) (01/08/90)
In article <12707@phoenix.Princeton.EDU>, markv@gauss.Princeton.EDU (Mark VandeWettering) writes: > > Yes! Mathematically speaking, the concept of fractal dimension is rigorously > defined. Chaos theory has some very specific results, as does complexity > theory. Because of the hype surrounding fractals, one sees grandiose claims > about the applicability of fractals to describing natural objects. > The problem with this is twofold: > > a) rarely are such descriptions analytically compared with > the objects they describe. ... [stuff deleted] > > b) descriptions say nothing about the processes that generated > the object in the first place. Fractal mountains don't > react to erosion or gravity, fractals trees don't grow with > the wind etc.... > Actually, it isn't fair to say that the descriptions say nothing about the processes that generate the shapes. While fractality in and of itself doesn't assert causes to things, that doesn't mean that there aren't descriptions that define causes quite effectively in terms of fractal structures. Two examples come to mind. First is the formation of blood-vessels, and the second is the formation of sea-shores. First, blood vessels, during the time when differentiation of cells and all that good stuff is going on, will grow in regions where demand is high; measured by gradients of nutrients and oxygen &c... This implies that the formation of blood vessels would grow in a manner that is diffusion limited. In a retina, the growth is restricted to 2-D (sort of a unique condition). Measurements of the dimensions of retinal vessel patterns compare favorably with Diffusion Limited Aggregation clusters. Second, Sapoval has recently done some simple experiments looking for exitation modes on fractal gaskets. He found that 1) there was little mode coupling between several related regions (where coupled modes could be expected from symmetry), and 2) that this could be expected to be due to very low Q values at any and all length scales. In other words, fractal resonance chambers are great dampers at all length scales. This has also been impirically noticed in acoustical studies where rooms are designed with points and peaks randomly distributed in size and placement (essentially making a fractal even though the designers didn't think of it that way -- they just knew it worked best that way). So, what does this have to do with sea-shores? If a sea-shore starts out with a non-fractal shape, it will probably have a nice resonance at some frequency (as well as an associated length at that frequency). Pounding at that frequency will distort the shore until that resonance disappears. The end result is a shore with very little in the way of a supported resonant frequency -- in other words, fractal. Thus, there are mechanisms where fractal descriptions actually point to a description of the cause. Dan Platt
mitchell@cbmvax.commodore.com (Fred Mitchell - PA) (01/08/90)
In article <12707@phoenix.Princeton.EDU> markv@gauss.Princeton.EDU (Mark VandeWettering) writes: > >>>Fractals, if a valid measure of nature, say how LITTLE information >>>there is. Compilicated appearing patterns actually can be parameterized >>>by very few numbers, hence its attractiveness to explanation and information >>>compression. > >Interesting comment, I hadn't pictured it that way. Hmmm... More thinking >necessary. > >>Seems like a matter of semantics, to me. The old "Half full" or "Half empty" >>approach. >> >>>Mitchell appears to be jumbling several types of "new age" mathematics-- >>>complexity theory, chaos theory, fractals ...-- each which has precise and >>>different definitions and something different to say about nature. > >Yes! Mathematically speaking, the concept of fractal dimension is rigorously >defined. Chaos theory has some very specific results, as does complexity >theory. Because of the hype surrounding fractals, one sees grandiose claims >about the applicability of fractals to describing natural objects. >The problem with this is twofold: > > a) rarely are such descriptions analytically compared with > the objects they describe. Pictures that are generated > with fractals are usually evaluated on purely subjective > criteria, which is error prone. The aim is to classify the form of natural phenomena, rather than to try to describe the mechanism by which the phenomena was generated. For instance, when we say that a trajectory follows what resembles a parabola, the parabola in and of itself does not describe the nature of gravity. > b) descriptions say nothing about the processes that generated > the object in the first place. Fractal mountains don't > react to erosion or gravity, fractals trees don't grow with > the wind etc.... See my above paragraph. >>The "jumbling" as you call it, was intentional. I was not trying to say >>anything specific- just that we should keep an open mind and look for >>relationships where we normally wouldn't. > >And in saying nothing specific, you have said nothing. An open mind is good, >but it should be tempered with the ability to critically analyze new ideas >and remove hype from your judgement. Obviously you miss the point entirely. I am referring to phenoomena that specifically does not lend itself eaisly to analysis. Basically, I am discussing a change in the 'traditional' analytic process itself. Usually, investigators tend to ignore anomlies that does not fit the "accepted" model. There are many cases in history where a person made a significant discovery where others overlooked. X-Rays is one example. >>>Some may provide USEFUL results and become parts of the scientist's toolkit, >>>while others will remain mathematical amusements. > >Actually, I have nothing against fractals perse, I have several books >concerning their mathematics on my shelf. The mathematics of fractals >is fascinating. What I combat is the notion that they are somehow most >applicable to description (and hence generation) of natural objects. >It has never been demonstrated to my satisfaction. Again, you're missing the point entirely. >>It depends on your orientation. If you want to be analytical, sure, then its >>a matter of what TOOL you can apply to what specific problem. But one should >>also be able to take a couple of steps back and see the whole picture. What >>is the gist of what I am trying to say? Therein lies my message. > >This is where the "philosophy" in the header enters in. It entirely >depends on your view and belief of science. Many scientist have tried to >develop general and simple rules that explain the world around us. So >far, we have failed. Many of the most elementary questions in science >remain unanswered, or answered only in the theoretical sense. Failed? I believe that to be a blanket (and incorrect) statement. Many phenomena are well understood. Many others are not. But to say the we have failed is a bit much. It does seem that the general mentality here is to "slash to peices" anyone with a differing point of view, rather than to see how that particular viewpoint reflects on the particular insights of that person and what new ideas may be spawned. I think that if we were face-to-face, we would act in a different manner. But the game here seems to be "who has the biggest stick." Therefore, I will not respond anymore to this particular thread except by direct mail. I tire of the diatribe. > >Mark -Mitchell mitchell@cbmvax.UUCP "My, what big BRAINS you have!" "It's only to take your mind off my mid section, dear."
ceb@csli.Stanford.EDU (Charles Buckley) (01/08/90)
In article <6937@lindy.Stanford.EDU> rick@hanauma.stanford.edu (Richard Ottolini) writes: >Don't abandon "new age" mathematics such as fractals nor worship it. >Sometimes years later something will escape from recreational >mathematics and be useful. Two examples: >(1) Cellular automata are a serious competitor to differential equations >for modeling waves and fluids . . . >(2) In computer graphics, quaternian transforms may be superior >to homogeneous coordinates for modeling transformations. Well, not so fast: 1. the applications of cellular automata you cite are easily relatable to differential equations, and anyway CA have been respected for some time - the chief obstacle to their use was simply a lack of hardware. Differential equations (at least some of them) were solvable by hand, and there are tricks you could use when they weren't, so they grew popular when computers were only jokes on and built by the military. 2. Quaternia (singular: quaternion) have also been respectable for quite some time - the chief obstacles to their widespread use were a perceived obscurity and lack of perceived need, plus the fact that much of the best work describing them was done in the Russian hinterlands, and remained obscure due to societal chaos for many years. Fractals are irksome to so many because they produce stunning results similar to those of phenomena we don't well understand, and no one can really say why. This was not true of your companion examples.
markv@gauss.Princeton.EDU (Mark VandeWettering) (01/08/90)
In article <1990Jan7.143923.8647@hellgate.utah.edu> thomson@cs.utah.edu (Rich Thomson) writes: >In article <12707@phoenix.Princeton.EDU> markv@gauss.Princeton.EDU [ I started more of this mess with opinions about the subjective nature of the "realism" of fractal imagery ] >In an attempt to bring this back around to graphics, think back on the >methods used to generate most computer imagery in use today. Shading >equations often contain lots of little parameters that are tweaked by the >programmer -- often judged on "purely subjective criteria" in order to get >the best looking image. Agreed, but this is changing. Witness the work done with radiosity, which attempts to provide an accurate simulation of radiative transfer in the visual spectrum. There is a high element of physics involved in what they do. Many of Kajiya's papers in recent years attempt to deal with problems in lighting and lighting models. Things are improving. >That's what I feel graphics is about -- getting the best image for what you >want. If the image you want comes more easily from a fractal model, who >cares if it isn't a valid "natural model"? Graphics programmers aren't >geologists or biologists or botanists -- they aren't seeking a model for >explanatory purposes. Well, that might be what you feel graphics is all about, but I wouldn't say your classification is universal for all graphics users. Some graphics programmers are botanists, and geologists, and biologists. And physicists and artists and students and..... >They are seeking a model for imaging purposes. The >two are very different. Some of these techniques have managed to satisfy >both needs (L-systems for example), but mostly graphics is just a "hack" >that produces a "nice" image. I think that much of graphics is a hack. More of research is aimed at improving the formality of computer graphics. >If you want to completely and accurately >model a mountain, you might as well sketch it by hand because the compute >time necessary to model the complete developmental cycle of a terrain is >prohibitive; Well, sketching it by hand implies that you have the terrain in front of you, which is certainly not a certain matter. But if you are saying that fractals are good at creating cheap effects at a high level of visual complexity, then I agree. If you say that these are useful in computer graphics I agree that they are useful but not the end of the evolution of graphics modeling. If you try to claim that there is some subjective comparison between fractal models and the objects they mimic, then I might even yield. If however, you claim that fractal models have some analytical relationships to the objects they model, I merely ask to be given proof. >not to say that knowledge from the sciences is useless in >helping you obtain a good image, but that the technique used to get a good >image doesn't necessarily have to come from a "scientifically accurate" >model. There are perhaps two aims to computer graphics: 1. to "describe" a scene visually 2. to "simulate" a scene visually Mr. Thomson appears to say that the aim of computer graphics is 1. I tend to believe that more of 1 is done, but the better aim is to shoot for 2. Yes its complex and nasty, but hey, what else are us researchers supposed to be paid for :-) Mark VandeWettering
markv@gauss.Princeton.EDU (Mark VandeWettering) (01/08/90)
In article <9239@cbmvax.commodore.com> mitchell@cbmvax.commodore.com (Fred Mitchell - PA) writes: >In article <12707@phoenix.Princeton.EDU> markv@gauss.Princeton.EDU (Mark VandeWettering) writes: >Obviously you miss the point entirely. I am referring to phenoomena that >specifically does not lend itself eaisly to analysis. Basically, I am >discussing a change in the 'traditional' analytic process itself. Usually, >investigators tend to ignore anomlies that does not fit the "accepted" >model. There are many cases in history where a person made a significant >discovery where others overlooked. X-Rays is one example. I agree. Witness the growth of research into chaotic systems. When Lorenz published his initial paper, people first of all thought that differential equations couldn't possibly behave that way, and even if they did, REAL systems didn't behave that way. Scientists had developed a model in which they had become too comfortable, and weren't willing to see that there were large numbers of behaviors which were not typically analyzed. >Failed? I believe that to be a blanket (and incorrect) statement. Many >phenomena are well understood. Many others are not. But to say the we >have failed is a bit much. Perhaps. We used to believe that we understood damped and driven oscillators. Many respected scientists believed that either motion would grow without bound, decay to zero, or become cyclic. Now we know that there are no such guarantees. Our understanding of such trivial systems was basically flawed. If such basic understandings are flawed, how can we possibly say we understand anything as complex as cell reproduction or plate tectonics or global warming? >It does seem that the general mentality here is to "slash to peices" anyone >with a differing point of view, rather than to see how that particular >viewpoint reflects on the particular insights of that person and what new ideas >may be spawned. I am merely trying to present an alternative viewpoint. I have received mail about equally split as pro or against my opinion, but so far no one has written me and said "you changed my opinion about fractals" so perhaps it is merely talking into a brick wall. Perhaps you are the voice of insight, and I am the voice of caution. Both are needed for scientific progress, because without the first science stagnates, and without the second, it decays into mindless random motion. >I think that if we were face-to-face, we would act in >a different manner. But the game here seems to be "who has the biggest stick." >Therefore, I will not respond anymore to this particular thread except >by direct mail. I tire of the diatribe. No doubt I will tire of this as well.
thomson@cs.utah.edu (Rich Thomson) (01/09/90)
I wrote: :- In an attempt to bring this back around to graphics, think back on the :- methods used to generate most computer imagery in use today. Shading :- equations often contain lots of little parameters that are tweaked by the :- programmer -- often judged on "purely subjective criteria" in order to get :- the best looking image. In response, markv@gauss.Princeton.EDU (Mark VandeWettering) writes: > Agreed, but this is changing. Witness the work done with radiosity, > [...] There is a high element of physics involved in what they do. :- That's what I feel graphics is about -- getting the best image for what you :- want. > Well, that might be what you feel graphics is all about, but I > wouldn't say your classification is universal for all graphics users. You mean all graphics users don't want to get the "best" image for their needs? That's what I was saying, in case it wasn't clear. In some cases (for the purposes of a short animated film, perhaps) that image may be created from a fractal model with no demonstrable relation to physical processes, while in others it may come from a physically based model. The point is not that fractal models are more "realistic" than other things or that models based on experimental results are better than hacks. The point is that when you're producing an image, you're attempting to get a certain result or effect out of that image. Different users are creating different images with different tools for different needs. I would say that getting the best image for one's needs is universal for all graphics users (within parameters of budget and time, of course). > Some graphics programmers are botanists, and geologists, and > biologists. And physicists and artists and students and..... Right. That is why not every image need be generated from radiosity or ray-tracing techniques -- many times wire-frames will do quite nicely. Suppose an artist sketched that landscape into a paint program. Would you berate the artist because it wasn't realistic and he didn't take the time to accurately model the underlying physical structures? Of course not! :- If you want to completely and accurately :- model a mountain, you might as well sketch it by hand because the compute :- time necessary to model the complete developmental cycle of a terrain is :- prohibitive; > Well, sketching it by hand implies that you have the terrain in > front of you, which is certainly not a certain matter. The point I was trying to make is that there are trade-offs between accuracy and time when modelling objects of the complexity of terrains. For cinematic or theatrical purposes, going to highly accurate geophysical models for terrains aren't worth it. > you are saying that fractals are good at creating cheap effects > at a high level of visual complexity, then I agree. Well, "cheap" is a subjective term, isn't it? Graphics is full of "cheap" effects -- color cycling animation, for example. I think that you are falling into the trap of thinking every graphics user/programmer is a scientist concerned with the accuracy first. I don't think this is the case YET. Fractals are good at generating complex shapes from simple, concise descriptions (in terms of algorithms, etc.). Not everyone has the time to program extremely sophisticated simulations of terrain generation (I don't even think it's been done to the level needed to get even realistic looking terrains; they are just too complex). > If you say > that these are useful in computer graphics I agree that they are > useful but not the end of the evolution of graphics modeling. I never claimed that; in fact, I believe we are more in agreement than you think. > If you try to claim that there is some subjective comparison between > fractal models and the objects they mimic, then I might even yield. There is always a subjective comparison between a model of an object an the object itself. Science proposes models for which many individuals can arrive at the same subjective comparison, i.e. the results are repeatable. > If however, you claim that fractal models have some analytical > relationships to the objects they model, I merely ask to be given > proof. That is exactly the opposite of my whole posting! My whole point is that fractals are a useful tool in computer imagery in the same tradition as the lighting equation hacks from the early seventies, etc, etc. Sure, now we have radiosity and ray-tracing. Show me a workstation that allows me to rotate objects rendered with a radiosity technique with my knob box in real-time. Analytically and physically accruate models are compute intensive, so we still use those "graphics hacks" to do the job. No, they aren't completely realistic or true to the physics of light. But when a scientist is trying to understand the shape of a complex protein, one doesn't care about realism and physical accuracy in the shading process. They want to be able to manipulate that model freely. Now, on the other hand just because fractals are currently a useful tool with the status of a "hack" in computer imagery doesn't mean they have no bearing on reality. I feel that Chaos theory has more to show us in this area, but even without it similarities between fractal methods and real processes are found. Diffusion limited aggregation is one such area. L-systems (which I referred to in my previous post) are another and they've been around since 1968. :- not to say that knowledge from the sciences is useless in :- helping you obtain a good image, but that the technique used to get a good :- image doesn't necessarily have to come from a "scientifically accurate" :- model. > There are perhaps two aims to computer graphics: > 1. to "describe" a scene visually > 2. to "simulate" a scene visually I feel that the aim of computer graphics is to provide an image that satisfies the needs of the user. Sometimes that means hacking a scene together for a background in a commercial and sometimes that means simulating shock-wave propagation. These are means, not aims. > Mr. Thomson appears to say that the aim of computer graphics is 1. > I tend to believe that more of 1 is done, but the better aim is > to shoot for 2. Yes its complex and nasty, but hey, what else are > us researchers supposed to be paid for :-) Well, I'm flattered that you think I'm so important that you have to refer to me as mister ;-). I agree with you that more of 1 is done than 2 and more for the reasons of economics and finding the best tool for the job than just being sloppy researchers. Again, I think you are confusing graphics researchers with scientists. Scientists definately want simulation to ensure accuracy, yet simulation doesn't imply that you must simulate the physics of everything. Again, molecular models don't need to be ray-traced in order to be useful and accurate. Similarly, terrains and other object capable of being modelled by fractals don't have to be modelled by some other process because fractals haven't been proved to be fundamental to their creation in the real world. Use the best tool for the job. -- Rich Rich Thomson thomson@cs.utah.edu {bellcore,hplabs,uunet}!utah-cs!thomson More Colombians are killed by American cigarettes than Americans by Colombian cocaine
ingoldsb@ctycal.UUCP (Terry Ingoldsby) (01/09/90)
In article <6937@lindy.Stanford.EDU>, rick@hanauma.stanford.edu (Richard Ottolini) writes: > Don't abandon "new age" mathematics such as fractals nor worship it. > Sometimes years later something will escape from the closet of recreational > mathematics and be useful. Two examples: ... > (2) In computer graphics, quaternian transforms may be a superior alternative > to homogeneous coordinates for modeling transformations. These have been in > the closet over a century. If I'm not mistaken, quaternians have been used for at least 10 years in Intergraph systems. I think it was initially to save memory on the old PDP-11. Glad to hear that there are other benefits.
eric@batcomputer.tn.cornell.edu (Eric Fielding) (01/09/90)
Just a few comments on this (probably already too long discussion): [sorry if the attributions are mangled] In a recent article thomson@cs.utah.edu (Rich Thomson) wrote: [...] >In response, markv@gauss.Princeton.EDU (Mark VandeWettering) writes: >> Some graphics programmers are botanists, and geologists, and >> biologists. And physicists and artists and students and..... Well, I happen to be a geologist graphics programmer. >Right. That is why not every image need be generated from radiosity or >ray-tracing techniques -- many times wire-frames will do quite nicely. I find that moderately advanced rendering of topography shows me much more information than a wire frame. Synthetic lighting makes much more subtle features visible. My business is to analyze real data. I have not tried any very advanced rendering, but I would guess there is a point of diminishing returns. As a matter of fact, I am mostly CPU limited as it is. (Anyone know how to render a 4000 x 5000 mesh of data ;-) >:- If you want to completely and accurately >:- model a mountain, you might as well sketch it by hand because the compute >:- time necessary to model the complete developmental cycle of a terrain is >:- prohibitive; Actually we are trying to model the development of terrains, but the problem is more a lack of understanding of how mountains are formed and eroded to formulate equations than a lack of computer time. >> Well, sketching it by hand implies that you have the terrain in >> front of you, which is certainly not a certain matter. I have the data in front of me, but it just looks like a computer tape to me. >The point I was trying to make is that there are trade-offs between >accuracy and time when modelling objects of the complexity of terrains. >For cinematic or theatrical purposes, going to highly accurate geophysical >models for terrains aren't worth it. This trade-off is why we end up sub-sampling the data before rendering it. I agree that it would be nice but not necessary to use real data to create terrains for movies or synthetic images. >> you are saying that fractals are good at creating cheap effects >> at a high level of visual complexity, then I agree. Unfortunately, I am rather upset at the number of people taking fractals out of the pretty-picture or effective animation graphics domain and applying them to real data in my field. People can find a 'fractal' in almost every geophysical phenomenon. This does not mean that it is necessarily a new contribution to the science. In most cases, it amounts more to renaming a relationship that was already known, which seems a little silly. >> If you try to claim that there is some subjective comparison between >> fractal models and the objects they mimic, then I might even yield. There are some cases where a fractal model does a good job of describing reality. For instance faults are really made up of fractal levels of smaller and smaller scale faults. My particular peeve is about fractals applied to topography. Somehow it just has not impressed me as a useful measurement, other than the observation that most real topography has the same fractal dimension. So what. How can we tell a recently created mountain from an old one? The fractal dimension is about the same. >> There are perhaps two aims to computer graphics: >> 1. to "describe" a scene visually >> 2. to "simulate" a scene visually There are also two types of scientists: 1. those who look at real data and try to observe how things work 2. those who work from known principles and theorize how other things work I put myself in category 1 for both graphics and science. It takes all types. > More Colombians are killed by American cigarettes > than Americans by Colombian cocaine Great quote. And how many Colombians are killed by American-made guns... ++Eric Fielding
eugene@eos.UUCP (Eugene Miya) (01/09/90)
In article <11638@csli.Stanford.EDU> ceb@csli.Stanford.EDU (Charles Buckley) writes: >In article <6937@lindy.Stanford.EDU> rick@hanauma.stanford.edu (Richard Ottolini) writes: > >(1) Cellular automata are a serious competitor to differential equations > >for modeling waves and fluids . . . > >(2) In computer graphics, quaternian transforms may be superior > >to homogeneous coordinates for modeling transformations. > >Well, not so fast: >1. the applications of cellular automata you cite are easily > relatable to differential equations, and anyway CA have > been respected for some time - the chief obstacle to their > use was simply a lack of hardware. Not so fast. CA appear fine for 2-D fluid dynamics. They are less so for 3-D. There are 2 reasons: 1) hardware, and 2) investment in existing PDE solvers. A solution does not necessarily consist of a visually based solution, such a some type of single figure of merit, say Q. CA's are kind of a fad, too, but they need more work by serious scientists. >2. Quaternia (singular: quaternion) have also been respectable for > quite some time - the chief obstacles to their widespread use were > a perceived obscurity and lack of perceived need, plus the fact > that much of the best work describing them was done in the Russian > hinterlands, and remained obscure due to societal chaos for many years. I posted qhwc(1), the source code to a quaternion calculator developed by Bill Burke [Williams's quaternion hoc calculator] some time ago to comp.sources.misc a derivative of the hoc6 calculator in Kernighan and Pike. It handled complex arithmetic (obviously) as well. Two people expressed interest. It was Bill's acknowledgement that he had effectively learned lex and yacc. Bill is in Gleick's Chaos book, he uses quaternions for his cosmology and gravitation work. He only asks that the users of qhwc let him know (thru me, so if you are going to ask me for a copy, I have to ask this) what they are using qhwc for: i.e., graphics, astronomy [in one case, etc.]. Bill is the author of "Applied Differential Geometry" and "Cosmology." Another gross generalization from --eugene miya, NASA Ames Research Center, eugene@aurora.arc.nasa.gov resident cynic at the Rock of Ages Home for Retired Hackers: "You trust the `reply' command with all those different mailers out there?" "If my mail does not reach you, please accept my apology." {ncar,decwrl,hplabs,uunet}!ames!eugene
park@usceast.UUCP (Kihong Park) (01/12/90)
>Yes! Mathematically speaking, the concept of fractal dimension is rigorously >defined. Chaos theory has some very specific results, as does complexity >theory. Because of the hype surrounding fractals, one sees grandiose claims >about the applicability of fractals to describing natural objects. >The problem with this is twofold: > > a) rarely are such descriptions analytically compared with > the objects they describe. Pictures that are generated > with fractals are usually evaluated on purely subjective > criteria, which is error prone. > b) descriptions say nothing about the processes that generated > the object in the first place. Fractal mountains don't > react to erosion or gravity, fractals trees don't grow with > the wind etc.... This being the comp.graphics newsgroup, it is natural to emphasize fractals from the computer generation of images point of view. But there is a "physical" aspect to the issue as well which lends the fractal approach to modeling certain aspects of natural phenomena additional credence. It is well known that cellular automata behavior can exhibit fractal structures in terms of the time-evolution of their global configuration patterns. Such properties are observed in some of the class 3 cellular automata as empirically classified by S. Wolfram. An ensemble of simple elements interacting with one another locally can exhibit complex global behavior. If an analogy is made between such systems and certain natural phenomena, then attributes such as erosion, friction, and gravity can be modeled within such a framework by suitably modifying the CA transformation rules(modeling fluid dynamics uses in essence such rules). Moreover, A. Lindenmayer has developed grammatical systems(Lindenmayer systems), the parallel realization thereof on a cellular substrate is regarded as very good models of plant growth. The fact that plants do not grow unboundadly in part due to gravitational forces can also be incorporated into the overall framework. Similar observations are also applicable to cellular growth such as the limbs of homo sapiens. One should not loose sight that fractal object generation via simple iterative functions systems(Barnsley), or probabilistic iterative automata(Culik), are computational descriptions which do not exclude other forms of realization as illustrated above.