garvin@uhccux.UUCP (Jay Garvin) (04/22/88)
In article 811 (David Shinberg) writes: *I am starting a project that will entail displaying and generating fractal *>landscapes on a Mac II...... *>[...] *>Any Help will be greatly appreciated, even just a few good references that *>have some algorithms explained. *> Thanks in Advance *> Dave ------------------------------------------------------------------------------ ---Ok, Dave!, Here are a few of the classics to get you started: NOTE: These books are worth buying a copy to keep for yourself. AUTHOR: Mandelbrot, Benoit B TITLE: The Fractal Geometry of Nature PUBLISHER: San Francisco: W.H. Freeman PUB DATE: (c) 1982 DESCRIPTION: 400p, 1 leaf of plates : ill. (some color) 24cm LANGUAGE: English SUBJECT: Geometry Mathematical models Stochastic processes NOTES: Rev. ed. of: Fractals. (c)1977 Includes indexes BIBLIOGRAPHY: Bibliography: p. [425] 443 AUTHOR: Peitgen, Heinz-Otto, 1945- Richter, P.H. (Peter H.), 1945- TITLE: The Beauty of Fractals: Images of Complex Dynamical Systems PUBLISHER: Barlin; New York: Springer-Verlag PUB DATE: (c) 1986 DESCRIPTION: xii, 199p. :illus. (some color) ; 20cm LANGUAGE: English SUBJECT: Fractals NOTES: includes index. Includes indexes BIBLIOGRAPHY: Bibliography: p. [425] 443 AUTHOR: Mandelbrot, Benoit B TITLE: Fractals: Form, Chance, and Dimension PUBLISHER: San Francisco: W.H. Freeman PUB DATE: (c) 1977 DESCRIPTION: xvi, 365p. : illustr. ; 24cm LANGUAGE: English SUBJECT: Geometry Mathematical models Stochastic processes NOTES: Translation of Les objets Fractals. Includes indexes BIBLIOGRAPHY: Bibliography: p. [333]-346 AUTHOR: Falconer, K. J. TITLE: The Geometry of Fractal sets PUBLISHER: Cambridge [Cambridgeshire] ; New York : Cambridge Univ. Press PUB DATE: (c) 1985 DESCRIPTION: xiv, 162 p. ; 24cm LANGUAGE: English SERIES: Cambridge tracts in mathematics ; 85 SUBJECT: Fractals Geometric measure theory NOTES: Includes index. BIBLIOGRAPHY: Bibliography: p. [150]-160 Magazine Articles: Scientific American, August 1985, Cover Article Computer Recreations: A computer microscope zooms in for a look at the most complex object in mathematics A. K. Dewdney Scientific American, **issue unknown** Computer Recreations: Of fractal mountains, graftal plants and other computer graphics at Pixar A. K. Dewdney BYTE, December 1987 Mimicking Mountains Modeling the curves and surfaces of coastlines, mojntains, and wood grains requires fractal geometry Tom Jeffery (Sorry if there are any errors, as I typed this in by hand...) --Also see the references at the ends of the above books and articles.-- I've done some work at Cornell University at the Computer Aided Design Instructional Facility working with code of my own and that of John Hubbard (of the Hubbard Fractal Research Facility, Cornell) so I'll be glad to help you out and get you started. I'm pretty busy though, so it'll have to be just whenever I have time. I co-authored an article re: fractals in Psych. & Psychophysics but it concerns a different aspect than I think you are interested in, so it probably wouldn't be of much use to you. Are you interested in textures and fractal mountains and the like, or in the Mandelbrot set, a la the landscape on the cover of Peitgen's book (qv.) ? A good starting place might be "the article that started it all" in the August 1985 issue of Scientific American, then move on to the "DO IT YOURSELF" section of Peitgen's book which starts on page 189. Then for Fractal Surfaces check the December 1987 BYTE article and pp 264&5 in Mandelbrot's "The Fractal Geometry of Nature" and be sure not to miss the color plates in the "BOOK WITHIN A BOOK" section... [To the NET:] If anyone has any other references they especially like, please tell me too, ok? I'm always interested in new sources! Likewise, if you have any code which has anything to do with fractals, Mandelbrot set, Julia sets, fractal mountains, Brownian Fractals, Iterated Function Systems, Fluid Flow modeling, Graphics Rendering, and Fractal Music please let me know. Programs for Mac, MacII, AMIGA, IBM-PC, VAX, FPS, IBM, HP, SUN machines are all fine, as are the languages PASCAL, FORTRAN, C, BASIC, MODULA-2, LISP, and COBOL.....(<--Just seeing if you're still awake on that last one! Boy, nothin' like using COBOL for those iterations in the complex plane,eh?? I can see it now......."Lighspeeeeeeeeeed COBOL"! :) Hope this helps you out, Dave. Good Luck! -Jay SIMON SAYS: "Don't do what Simon Says!" ============================================================================= | Jeffrey Jay Garvin _ Electronic Mail: | | Computer Specialist __| | _ BITNET: | | University of Hawaii |__ |_| |__ garvin@uhccux.BITNET | | Computing Center ____| ____| InterNet: | | 2565 The Mall |__ _ |__ garvin@uhccux.uhcc.hawaii.edu | | Keller Hall Rm 201 |_| | __| UUCP: | | Honolulu, HI 96822 |_| {ihnp4,uunet,dcdwest,ucbvax} | | USA Phone: (808) 948-7351 !ucsd!nosc!uhccux!garvin | =============================================================================
paulm@pyr.gatech.EDU (PAUL MILLER) (04/25/88)
In the discussion regarding useful references concerning fractals, I wanted
to mention the following:
Barnsley, M. and Sloan, A. "A Better Way to Compress Images". Byte, Jan. 88.
The gist of the article involves representing ANY image by its IFS codes,
thereby achieving significant image compression ratios (> 10,000 : 1).
Additionally, it includes a simple algorithm (and BASIC program) for quickly
reconstructing the picture from the IFS (the Random Iteration Algorithm).
I'm interested in doing a project involving *rendering 3D fractal surfaces*
(and their measures). The following references have been worthwhile:
Norton, A. "Generation and Display of Geometric Fractals in 3-D". Computer
Graphics, July 1982.
Kajiya, J. "New Techniques for Ray Tracing Procedurally Defined Objects".
Computer Graphics, July 1983.
Reeves, W. "Approximate and Probabilistic Algorithms for Shading and
Rendering Structured Particle Systems". Computer Graphics, July 1985.
Is anyone aware of other references that would be useful ?
Thanks,
Paul Miller
--
Paul Miller
Georgia Insitute of Technology, Atlanta Georgia, 30332
uucp: ...!{akgua,allegra,amd,hplabs,ihnp4,seismo,ut-ngp}!gatech!gitpyr!paulm
ARPA: paulm@pyr.ocs.gatech.edummaclenn@watdcsu.waterloo.edu (Mark MacLennan-Geog.) (04/26/88)
In article 811 (David Shinberg) writes: >> I am starting a project that will entail displaying and generating fractal >>landscapes on a Mac II...... >>Any Help will be greatly appreciated, even just a few good references that >>have some algorithms explained. Here's a quick compilation of a few of the numerous references which describe how to generate fractal "landscapes" (I assume he means topography - there are all sorts of other papers on how to create fractal trees, clouds, craters, etc.) Many recent computer graphics texts now at least mention fractal surfaces. The Lewis (1987) citation is particularly insightful as the author provides an excellent critique of the fractal approach. Voss (1985) summarizes the various algorithms for creating fractal surfaces, of which the midpoint-displacement method is the most widely implemented - e.g. Jeffrey (1987). [Code for generating a fractal mountain is also available in Eric Grosse's "Standard Procedural Database" available from netlib's graphics library - please DON'T send me mail on how to get this code, instead read about netlib in the May 1987 issue of COMMUNICATIONS OF THE ACM, pp. 403-407.] cheers, MARK ----- Fellous, A., J. Granara and J. Hourcade. 1985. "Fractional Brownian Relief: An Exact Local Method", in PROCEEDINGS OF EUROGRAPHICS 85, North Holland, New York, pp. 353-363. Fournier, A., D. Fussell and L. Carpenter. 1982. "Computer Rendering of Stochastic Models", COMMUNICATIONS OF THE ACM, 25:6, pp. 371-384. Fournier, A., D. Fussell and L. Carpenter. 1982. "Author's Rely to 'Comments on Computer Rendering of Fractal Stochastic Models' by B.B. Mandelbrot", COMMUNICATIONS OF THE ACM, 25:8, pp. 583-584. Jeffrey, T. 1987. "Mimicking Mountains", BYTE, 12:12, pp. 337-344. Lewis, J.P. 1987. "Generalized Stochastic Subdivision", ACM TRANSACTIONS ON GRAPHICS, 6:3, pp. 167-190. Mandelbrot, B.B. 1975. "Stochastic Models for the Earth's Relief, the Shape and the Fractal Dimension of the Coastlines, and the Number-Area Rule for Islands", PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES USA, 72:10, pp. 3825-3829. Mandelbrot, B.B. 1982. "Comment on 'Computer Rendering of Fractal Stochastic Models'", COMMUNICATIONS OF THE ACM, 25:8, pp. 581-584. Vandepanne, M. 1985. "3-D Fractals", CREATIVE COMPUTING, 11:7, pp. 78-82. Voss, R. 1985. "Random Fractal Forgeries", in FUNDAMENTAL ALGORITHMS FOR COMPUTER GRAPHICS, R.A. Earnshaw (ed.), NATO ASI Series F, Vol. 17, Springer-Verlag, New York, pp. 805-835. ______________________________________________________________________________ | UUCP: {ihnp4,watmath}!watdcsu!mmaclenn | Mark MacLennan | | BITNET: mmaclenn@watdcs.bitnet | Department of Geography | | INTERNET: mmaclenn@watdcs.waterloo.edu | University of Waterloo | | EAN: mmaclenn@watdcs.waterloo.cdn | Waterloo, Ontario | | | Canada N2L 3G1 | ------------------------------------------------------------------------------
rk@cs.strath.ac.uk (Richard Kingslake) (04/26/88)
In article <5595@pyr.gatech.EDU> paulm@pyr.gatech.EDU (PAUL MILLER) writes: > ... > > The gist of the article involves representing ANY image by its IFS codes, >thereby achieving significant image compression ratios (> 10,000 : 1). I am impressed by the ratio of 10,000:1. Can it be true? Anyway, in my very great ignorance, I have never heard of "IFS codes". Can anyone explain? At the moment I compress all my images for storage using PKARC. It often achieves compression ratios of 3:1, but I should certainly like to see 10,000:1. Let's see :- a picture 512 X 512 pixels using one byte per pixel occupies (uncompressed) 262144 bytes. Using the IFS system mentioned this is compressed to just 27 bytes! Fantastic! -- Richard Kingslake JANET: rk@uk.ac.strath.cs ARPA: rk@cs.strath.ac.uk UUCP: !seismo!mcvax!ulcc!strath-cs!rk or rk@strath-cs.uucp
andrea@hp-sdd.HP.COM (Andrea K. Frankel) (04/28/88)
In article <1776@uhccux.UUCP> garvin@uhccux.UUCP (Jay Garvin) writes: >Likewise, if you have any code which has anything to do with fractals, >Mandelbrot set, Julia sets, fractal mountains, Brownian Fractals, >Iterated Function Systems, Fluid Flow modeling, Graphics Rendering, >and Fractal Music please let me know. Ok, I'll byte - what's Fractal Music? what does it sound like? (I've got a dog named Fractal who gets pretty musical sometimes, but somehow I don't think that's what you were alluding to...) Where can I get some to listen to? > SIMON SAYS: "Don't do what Simon Says!" Ooooh, nooooh, Mr. Bill! Yer brain has been fractalized! (And I thought folks only got self-referential from excessive LISP programming...) Andrea Frankel, Hewlett-Packard (San Diego Division) (619) 592-4664 "...I brought you a paddle for your favorite canoe." ______________________________________________________________________________ UUCP : {hplabs|nosc|hpfcla|ucsd}!hp-sdd!andrea Internet : andrea%hp-sdd@hpcea.ce.hp.com (or @nosc.mil, @ucsd.edu) CSNET : andrea%hp-sdd@hplabs.csnet USnail : 16399 W. Bernardo Drive, San Diego CA 92127-1899 USA
doug-merritt@cup.portal.com (04/29/88)
To answer a recent question about IFS encoding achieving a 1:10000
compression ratio of images. Yes, it's true. Although it has its
problems.
The basic idea is this: fractals have been used to generate realistic
looking images of certain (many) kinds of things. It turns out that
practically any image of any of those types of objects can be IFS
encoded, loosely speaking. The BYTE article showed a very nice b/w
fern, for example. One of the areas that IFS is particularly *bad*
at is human faces (perspective 3d views of same), because it's not
clear yet how to decompose any face into a fractally self similar
representation (this point appeared in the Scientific American
"Science and the Citizen" news column; I'm not 100% clear on why
this is true, given the Collage theorem discussed below).
In more detail: say you have an image of a black square. It is self
similar: you can create the whole image from four smaller squares,
each of which can be created from ...(etc)
The IFS *decompression* method uses affine transformations in the
plane (affine == polynomial of degree 1 or a 2x2 matrix). For the
example of a square, its encoding consists of a set of affine
transformations that can be used to map any point in the set to any
other point in the set.
Any corner point of the square can be mapped via one or more rotations
to any of the other corner points. It can also be rotated and
"shrunk" to map to a corner point of one of the 4 sub-squares. Similar
mappings apply to the interior of the square.
So you figure out one of the complete self-mapping sets of affine
transformations (it's non-unique), and starting from the origin, apply
all possible transformations to end up with new points inside the
set. Then apply all transformations to each of those new points...
continue infinitely, and you'll have generated all of the points in
the set.
In practice this is too time consuming, and so at each step, just
one of the possible transformations is chosen at random, so that you
keep mapping a single old point to a single new point. I should have
been more careful before, because I missed something important:
you want all of the transformations to contract the figure (I forget
the proper word for this). That way, after a certain number of
iterations, the sub-figures you're generating will be smaller than
a pixel. At which point you repeat, to follow a new probablistic
trajectory through the possible points. After not too many passes,
you'll have generated enough random points within the figure that
it becomes discernable. Eventually you'll have done enough points that
you've drawn essentially 100% of those that are displayable with
any given resolution.
So it looks like the figure is being drawn via a "dissolve", with
random points gradually filling in.
It's a little nonintuitive at first but some thought experiments
help.
The hard part is the *compression* phase where you figure out the
appropriate affine transformations to start with. The author of
the BYTE article has an enormous library of appropriate IFS codes
for various types of objects/features done as part of a sizeable
research project.
The original image is analyzed 7 ways from Sunday (edge detection,
2D FFT, etc, etc), and the subfeatures that are found this way are
looked up in the IFS code library. So for *him* I guess it's relatively
easy, but very time consuming due to the amount of analysis.
The crux of the method is based on something called the Collage Theorem,
which basically means that it's been proved that the method will be
guaranteed to work if you approach it the right way. Even though the
reconstruction process is statistical, the Collage Theorem says that
you can recreate the original to within any desired degree of accuracy
(in terms of pixel resolution and color reproduction, say). THe name
comes from the idea of taking an image and breaking it apart into
affinely distorted subimages. It turns out that it's *always* theoretically
possible to do this.
See the Byte article itself if you want more details.
Doug Merritt ucbvax!sun.com!cup.portal.com!doug-merritt
or ucbvax!eris!doug (doug@eris.berkeley.edu)
or ucbvax!unisoft!certes!dougjfadams@tc.fluke.COM (Jim Adams) (04/29/88)
Here's a book I just bought at my local bookstore that looks fairly inter-
esting:
CHAOS - Making a New Science
by James Gleick, Viking/Penguin Press
ISBN 0670811785
I haven't had the opportunity to read it, so I can't attest to its value as
a fractal reference. It includes color plates of the familiar Pietgen
illustrations (whether they are the same, YOU decide! When you've seen one
rx=1.2,iy=.075:s=1, you've seen them all. :^) )
--
James F. Adams John Fluke Mfg. Co., Inc. Everett, Washington USA
WORLD:jfadams@tc.fluke.COM
UUCP:{ihnp4!uw-beaver,ucbvax!lbl-csam,allegra,decvax!microsoft}!fluke!jfadams
ARPA:fluke!jfadams@uw-beaver.ARPA GEnie:J.F.ADAMS CIS:74036,2517 eugene@pioneer.arpa (Eugene N. Miya) (04/29/88)
In article <1249@hp-sdd.HP.COM> andrea@hp-sdd.UUCP (Andrea K. Frankel) writes: >Ok, I'll byte - what's Fractal Music? what does it sound like? For an idea (actually graftal), it used to be, "For a good time phone: (201)-644-2332" which is the title of a conference paper. P.S. Re: Gleick's Book: Burke (skiing partner and wind surfing converter) like this book. Huberman did not like the book. Jules, it's time to come out with your NO FRACTALs shirt. Another gross generalization from --eugene miya, NASA Ames Research Center, eugene@ames-aurora.ARPA soon to be aurora.arc.nasa.gov at the Rock of Ages Home for Retired Hackers: "Mailers?! HA!", "If my mail does not reach you, please accept my apology." {uunet,hplabs,hao,ihnp4,decwrl,allegra,tektronix}!ames!aurora!eugene "Send mail, avoid follow-ups. If enough, I'll summarize."
johng@ecrcvax.UUCP (John Gregor) (04/29/88)
In article <931@stracs.cs.strath.ac.uk> rk@cs.strath.ac.uk writes: >In article <5595@pyr.gatech.EDU> paulm@pyr.gatech.EDU (PAUL MILLER) writes: >> The gist of the article involves representing ANY image by its IFS codes, >>thereby achieving significant image compression ratios (> 10,000 : 1). >I am impressed by the ratio of 10,000:1. Can it be true? > >PKARC. It often achieves compression ratios of 3:1, but I should certainly >like to see 10,000:1. Let's see :- a picture 512 X 512 pixels using one >byte per pixel occupies (uncompressed) 262144 bytes. Using the IFS system >mentioned this is compressed to just 27 bytes! Fantastic! Unfortunately, the search space is ~ 2 ^ (27*8) or 2 ^ 216. And even then the compression will be destructive (i.e. the uncompressed picture won't be the same as the original. I've only seen it work on demonstration pictures that looked very fractalish to begin with. So I can "compress" the Mandelbrot set into a handfull of bits, big deal. It still takes a couple of hours to get at the areas of the set I want to see. (* inews laxative *) (* inews laxative *) (* inews laxative *) -- pqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpqpq bdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbdbd John Gregor johng%ecrcvax.UUCP@germany.CSNET
saponara@batcomputer.tn.cornell.edu (John Saponara) (05/02/88)
In article <4644@watdcsu.waterloo.edu> mmaclenn@watdcsu.waterloo.edu (Mark MacLennan-Geog.) writes: >[Code for generating a fractal mountain is also available in >Eric Grosse's "Standard Procedural Database" available from netlib's graphics >library - please DON'T send me mail on how to get this code, instead read about >netlib in the May 1987 issue of COMMUNICATIONS OF THE ACM, pp. 403-407.] Coincidentally enough, I was just using my SPD program mentioned above to generate some fractal mountains. I set the fractal dimension down to 2.02 to get a milder landscape and noticed some repetition in the pattern. Looking into it, I found my hashing function had a misplaced parenthesis and would blow up on landscapes with a size factor greater than 7, to boot. So, attached at the end is the `diff' to fix the SPD package. If you don't have the package, here's the 10 second rundown (my apologies to all who've read this before): The "Standard Procedural Database" package is a set of 6 database generators, including the recursive tetrahedron, a fractal mountain, and a tree grower. For images produced by the databases and more information on the concept, see the article in IEEE Computer Graphics & Applications, November 1987, p. 3-5. To get the package, send mail to Netlib (which has a lot of other worthwhile free stuff) at `netlib@anl-mcs.arpa' or at `research!netlib'. Send the one line message `Send Haines from Graphics' and the program which receives your message will send you a copy of the package. If you send the message (on a separate line) `Send Index' you'll get the index and more information about Netlib in general. Eric Grosse and Jack Dongarra run Netlib. I (Eric Haines) simply wrote the SPD package. OK, so for the rest of you who already have the package, here's the diff. Note that you should have version 2.3 to correctly update your package. Eric (not John Saponara) Haines p.s. The diff is indented for obscure `rn' reasons - please unindent. diff old/README README 4c4 < Version 2.3, as of 3/1/88 --- > Version 2.4, as of 5/1/88 20a21 > Version 2.4 released May, 1988 - fixed hashing function for mountain.c. diff old/mountain.c mountain.c 7c7,15 < * Version: 2.2 (11/17/87) --- > * NOTE: the hashing function used to generate the database originally is > * faulty. The function causes repetition to occur within the fractal > * mountain (obviously not very fractal behavior!). A new hashing function > * is included immediately after the old one: merely define NEW_HASH if > * you want to use a good hashing function. To perform ray tracing > * comparison tests you should still use the old, faulty database (it may > * have repetition, but it's still a good test image). > * > * Version: 2.4 (5/1/88) 26a35,37 > /* to use the corrected hashing function, uncomment this next line */ > /* #define NEW_HASH */ > 41c52,56 < /* hashing function to get a seed for the random number generator */ --- > #ifndef NEW_HASH > > /* Hashing function to get a seed for the random number generator. */ > /* This is the old, buggy hashing function - use it if you wish to > * obtain the same image as in the November 1987 IEEE CG&A article. */ 44a60,77 > #else > > /* New, corrected hashing function. Use for a true fractal mountain */ > /* 134456 is M1 in routine lib_gauss_rand() */ > #define hash_rand(A,B,C) ( ( C <= 15 ) ? \ > ( ABSOLUTE( \ > ((A)<<(31-(C))) \ > + ((B)<<(15-(C))) ) \ > % 134456 ) \ > : \ > ( ABSOLUTE( \ > ((A)<<(31-(C))) \ > + ((B)>>((C)-15)) ) \ > % 134456 ) \ > ) > > #endif > 56d88 <
wecker@child.dec.com (Official DEC Houseplant) (05/02/88)
The technique IS interesting.. (I got as much as I could up and running based
on the Byte article) but it seems pretty useless unless you can get your
hands on a reasonable IFS library.
So the next obvious question: "Is there a PD affine library, or information
on how to generate one for reasonably common objects?"
___________________________________________________________________________
dave ENET: CHILD::WECKER - DTN: 522_3873 - MS: CXO1-2/N22
USENET: decwrl!child.dec.com!wecker
ARPA: wecker%child.dec.com@decwrl.dec.com
SNAIL: 115 Palm Springs Drive, Colorado Springs CO 80921
Disclaimer: The opinions expressed are my own and in no way should be taken
as representative of my employer Digital Equipment Corporation.
___________________________________________________________________________carlson@aftac.tis.llnl.gov (John Carlson) (05/04/88)
In article <8805012132.AA16548@decwrl.dec.com> wecker@child.dec.com (Official DEC Houseplant) writes: >The technique IS interesting.. (I got as much as I could up and running based >on the Byte article) but it seems pretty useless unless you can get your >hands on a reasonable IFS library. Also, hardware support is necessary. They quoted 30 minutes decoding time in the article. John Carlson
sn@otter.hple.hp.com (Srinivas Nedunuri) (05/09/88)
/ otter:comp.graphics / paulm@pyr.gatech.EDU (PAUL MILLER) / 6:14 pm Apr 24, 1988 / Paul Miller writes: > I'm interested in doing a project involving *rendering 3D fractal surfaces* >(and their measures). The following references have been worthwhile: >Norton, A. "Generation and Display of Geometric Fractals in 3-D". Computer > Graphics, July 1982. >Kajiya, J. "New Techniques for Ray Tracing Procedurally Defined Objects". > Computer Graphics, July 1983. > >Reeves, W. "Approximate and Probabilistic Algorithms for Shading and > Rendering Structured Particle Systems". Computer Graphics, July 1985. > Is anyone aware of other references that would be useful ? >Thanks, >Paul Miller ---------- Hope you find the following useful: :-) :-> Wiseman N and Nedunuri S : "Computing Random Fields", Computer Journal, V29, No.4, pp 373-377, 1986. (Presents a method for building fractal meshes using coroutines) Nedunuri S : "Displaying Random Surfaces" Computer Journal, V30, No.2 pp 163-167, 1987. (cheap display technique for above surfaces with hidden surface elimination and shadowing)
sn@otter.hple.hp.com (Srinivas Nedunuri) (05/10/88)
/ otter:comp.graphics / sn@otter.hple.hp.com (Srinivas Nedunuri) / 12:00 pm May 9, 1988 / >Nedunuri S : "Displaying Random Surfaces" Computer Journal, V30, No.2 >pp 163-167, 1987. Sorry, that should read : Nedunuri S & Wiseman N E : "Displaying Random Surfaces" ... Just an attack of meglomania, thats all ! ---