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Fit An Entire Planet In 90k

missingmatterboy points out this "interview with Dr. Ken "Doc Mojo" Musgrave, a computer graphics pioneer who worked with Benoit Mandelbrot generating fractal landscapes and who's designed custom shaders for Hollywood movies. His latest project is called MojoWorld and it uses the power of math to generate infinite-resolution fractal landscapes? one entire planet at a time. It's going to have an open SDK and, to top it all off, a Linux version is also in the works." This is a fascinating project.

122 comments

  1. oops by Anonymous Coward · · Score: 0

    I might be more impressed if their still image gallery page would render in Mozilla 0.9.4.

    1. Re:oops by Anonymous Coward · · Score: 0

      My mozilla 0.9.4 had no problems with it - try it again, the page was pretty slow coming in, maybe you didn't wait long enough.

      Fried

  2. /.ed already! by merlin_jim · · Score: 5, Informative

    Here's the Google cached copy (which isn't doing much better)

    If you have to see the images, BryceWorld got a beta release and posted a gallery of images online.

    And if you want to download it immediately to start playing with it, you can do it by filling out this questionairre

    --
    I am disrespectful to dirt! Can you see that I am serious?!
    1. Re:/.ed already! by PhilHibbs · · Score: 2

      Those pictures are pretty cool, but the stratification is a bit on the heavy side. It works on the plateau sides, but not where the land is shallow - it would be covered by dust or vegetation, hiding the strata.

    2. Re:/.ed already! by AssFace · · Score: 1

      the google cached page is likely just as slow since I'm prety sure they only cache the text, which would be links to the images - so you are going to quickly load the cached text, and still have to wait for the images to come off of the /.'ed server.

      --

      There are some odd things afoot now, in the Villa Straylight.
  3. Rebuild Planet Earth by KrunZ · · Score: 2, Interesting

    MojoWorld:>rebuild Earth.planet

  4. Old news... by chronos2266 · · Score: 5, Interesting

    This has been done quite a few times by quite a few people. Fractal planet 3d engines show up all the time at www.flipcode.com

    I've seen some with complete weather and day/night cycles. Some really inspiring stuff.

    1. Re:Old news... by CaseyB · · Score: 2

      Lucasart's first two games, released in 1984, were Ballblazer and Rescue on Fractalus. Rescue on Fractalus had a fractally generated landscape, in realtime, on 8 bit machines, almost 20 years ago.

    2. Re:Old news... by Saint+Aardvark · · Score: 1
      Can you list an example or two? I'd really like to check them out, and flipcode seems, ah, non-trivial for the uninitiated to navigate...Thanks.

    3. Re:Old news... by malducin · · Score: 5, Informative

      Well the thing is Ken Musgrave is one of the pioneers, if anything a lot of people that have posted code like this out there are based on Ken's numerous papers. He was a researcher with Mandelbrot, kinda developed "multifractals", given SIGGRAPH courses about terrain and procedural modeling, and has written several chapters for a great book "Texturing and Modeling: A Procedural; Approach". He also worked for a time for or at Digital Domain, doing code a for the moon on Apollo 13, and procedural smoke for Dante's Peak (not used) and Titanic.

      Here is his webpage:

      Ken Musgrave's website

      Saw Mojoworld briefly at SIGGRAPH and it looked neat.

  5. Wowee by Insipid+Trunculance · · Score: 1

    Coming Up One Saturn With Rings.....
    Whatch Yuo Want Miss,Betelguese?

    --
    Wanted : A Signature.
  6. Marginal by debrain · · Score: 5, Interesting
    Not really that impressive :) (tongue in cheek). I worked on the preliminary part of a massive multiplayer online game whose universe was a fractal, containing data right down to the shape and size of trees at every point on the planet. The interesting thing was that the modeled universe took time as a variable, and it evolved gradually with small increments of time, thus the universe (which was ultimately nearly infinite from the human perspective), right now was not the same as the universe yesterday, but very similar so those places / things you've become familiar with are still present, but have evolved slightly.

    Planets would move, trees would grow, forests and deserts would change shape, oceans would rise and recede, etc. (Taking into account that the planet is of the type to support something like forests and oceans). The variables that define a "place" as a human looking onto the universe were coordinates and time, and a perspective (direction/angle) from which to project back information. Yet the visual perspective was only minor compared to the actual number of calculable variables, like temperature, and the like. Of course, strange things like density has to be accounted for with Newtonian physics, but that was ironically easy. Choosing what was the cause (is temperature random, ie. fractalish, or a product of Newtonian; really it's a combination; random in a Newtonian'ish thermodynamic space, but random only because we wouldn't actually want to calculate that sort of thing) and what was an effect was the hard part.


    It is an interesting premise, isn't it? Taking a mathematical curiosity (the fractal) and doing something useful with it like creating a universe, or planet in this case. Somewhat matrix'ish.

    1. Re:Marginal by liquidsin · · Score: 1

      That actually sounds really interesting. What game was it you worked on? Is it online still / yet?

      --
      do not read this line twice.
    2. Re:Marginal by iplayfast · · Score: 1

      Your project sounds more interesting then MOJO, do you have a site showing it off?

    3. Re:Marginal by Tide · · Score: 1


      Isn't that Shadowbane? I heard they were doing something similar, being able to add continents in real time over a modem connection, no more massive "EQ-like" downloads. Curious if thats the game you talking about, I havent played it.

      --

      People think Microsoft is the answer. Microsoft is just the question, "No" is the answer.
    4. Re:Marginal by debrain · · Score: 2
      No, not Shadowbane (but that's neat too :)). It has not made it beyond the drawing board yet. That's one of the main advantages of that design, though, saving bandwidth. The other is offline playing, or even sub-universes. "Germ warfare", in the duely literal sense of it, was not entirely out of the question, so long as it was fun. The right choice of fractal would yield the sort of information right down to that nitty-gritty, where human-sponsored/played germs could have plausible effects on larger creatures.


      Thanks to chaos, one could insert minor changes into the variables, so a line of a lorenz equation could be completely changed down the road by adding small (read: negligable) attractors. Lorenz isn't a good choice, IMHO, but it's an example of a simple, obvious case where small attractors would change things invariably. People adding attractors to a game universe fractal is a much niftier idea; just much more complex.

    5. Re:Marginal by JabberWokky · · Score: 2
      Now that he's said it's not off the drawing board, I know it's not WorldForge either, but I know that they did some similar (much less sophisticated from what he says) work - fractal lansdcape that is then iteratively weathered, and fractal floria distribution. Anybody interested might want to check that out too. (FWIW, the running code uses standard matrix maps of data, rather than the fancier fractal code - I'm not involved in the project, so I don't know why)

      --
      Evan

      --
      "$30 for the One True Ring. $10 each additional ring!" -- JRR "Bob" Tolkien
    6. Re:Marginal by Anonymous Coward · · Score: 0

      It is pretty assanine to call MojoWorld, a shipping project, "Marginal" because it doesn't compare to something you came up with which never had a single line of code written ("has not made it beyond the drawing board").

    7. Re:Marginal by DagSverre · · Score: 1

      Interesting in getting a flying start to get that off the drawing board?

      We're aiming for something along these lines at www.legacy-ovwp.org. The goal for now is a single-player story-driven game, however we make every part as reusable as possible and introducing MMORPG to the engine shouldn't be a problem once it's done as we're very aware of the game probably evolving there sometime.

      The site looks somewhat dead and messy because we mostly communicate on IRC and mail these days, it's by no means as dead as it looks! (We have many mails between us a day in laying this out and a well developed source tree). If anyone wants to help us out then simply mail one of us (find mine or JPNotADragon's email address there) and you'll probably have a response the same day.

  7. The galaxy in the palm of your hand by MBCook · · Score: 0, Troll

    Wow! Now I can carry a floppy with me and over 15 planets! OK, so floppy's are passe, but who needs to carry a CD with 7200 planets on it? This seems impossible but I guess since it's nothing but fractals who's equations take up a couple of dozen bytes each, it does make sense. Oh well. Now on to a realistic part of my message:

    <SARCASM><RANT> They can put a dozen planets on a disk but they can't figure out cold fusion! What's the world comming to?</RANT></SARCASM>

    --
    Comment forecast: Bits of genius surrounded by a sea of mediocrity.
    1. Re:The galaxy in the palm of your hand by HiQ · · Score: 2

      Maybe one of these days we're going to find out that our planet, including ourselves, is on someones (or somethings') CD. Talk about freaking people out in a big way :0

    2. Re:The galaxy in the palm of your hand by Anonymous Coward · · Score: 0
      Jesus, then that guy would have the copyright to the entire world!!!.

      I hope he uses it to crush the WTO, RIAA and MPAA, rather than to make a quick buck.

  8. Don't tell Slartibartfast.... by jgerman · · Score: 5, Funny

    ...he took real pride in his fjords, he wouldn't take too kindly to auto planet creation.

    --
    I'm the big fish in the big pond bitch.
    1. Re:Don't tell Slartibartfast.... by Rob.Mathers · · Score: 1

      I dunno, I've seen some fractals that would make great fjords, even appropriate for Norwiegan Blues

      --

      My other sig is funny!
    2. Re:Don't tell Slartibartfast.... by malducin · · Score: 1

      Funny you should mention this. If I remember correctly Ken Musgrave had a terrain renderer called Slartibartfast in the mid nineties while he was at GWU. Unfortunately I think those pages are long gone. You could check some old stuff from his webpage.

    3. Re:Don't tell Slartibartfast.... by Fjord · · Score: 2

      Fjords are magnificent. Just look at me! :)

      --
      -no broken link
  9. Excellent! by Kazmat · · Score: 1

    This is indeed a Good Thing for games such as Elite. Instead of the game designers having to create each world, using minimal detail, as many worlds as are wanted can now be created in infinite detail. I look forward to the first Elite-style game using this technology.

    1. Re:Excellent! by flend · · Score: 4, Informative

      Hmmm, an Elite game which uses fractal planets?

      What about, for example, Frontier: Elite2 which pretty much pioneered planet wide fractal terrain gen in a commercial game and ran on a 386.

      Or, its sequel, Frontier: First Encounters which added texturing to make everything look a million times more ugle.

      Or any of the recent fan-made clones, Millenium3 http:://m3fe.com or even The Eternal Project http://compsoc.net/~flend/tep/.

    2. Re:Excellent! by scott1853 · · Score: 2

      Somehow I don't think this is going to make it into games right away. To get high detail, you still need massive amounts of system and video ram for all the textures and vertices. Besides, you still need designers to implement what they want. Just sitting there and hitting a "randomize" button isn't going to work too well unless you have no clue what you want.

    3. Re:Excellent! by Alioth · · Score: 2, Funny
      > The Eternal Project http://compsoc.net/~flend/tep/


      The Eternal Project - what an ironically true to form name ;-)

    4. Re:Excellent! by mellifluous · · Score: 1

      Even earlier, I believe was the "Starflight" series. The first, released in 1986, had several hundred fractally-defined planets in its "universe". The whole thing fit on two 360K floppies. A brilliant design given the storage space limitations of the day.

      On a personal note, that game probably did more to get me hooked on PC gaming than any other.

  10. The earth is in somebody hands for sure by KrunZ · · Score: 1

    The earth is in somebody hands for sure. The big question is if the hand's owner is wearing a turban or a cowboy hat.

  11. Each world is a coordinate in a matrix of worlds by hartsock · · Score: 2, Informative

    Here's the easiest way to think of it: each parameter represents a degree of freedom; an axis you can move back and forth along, as you change the parameter's value. So, for instance, specifying a color in MojoWorld adds three higher dimensions: one for each of the red, green and blue values you use to specify the color. Each of these axes corresponds to a higher dimension in Parametric Hyperspace: it's just a different direction you can move in. You can see that, in getting all the settings right for a scene, you've set a lot of parameters, and thus traveled in many dimensions of Parametric Hyperspace.

    Since the product doesn't store individual worlds, but rather parameters for a procedural system... or a point in parametric hyperspace... the data file for a single world isn't large. Each individual world only needs to be defined with a set of n-dimensional coordinates. I don't do much playing with things like bryce or whatever (can't afford it) but if I'm not mistaken that is a significantly different paradigm. What I didn't see is how large the executable was that generated the worlds dynamically from the n-dimensional parameter vector or hyperspatial coordinates. Technically the program wouldn't have to be large either, but I'm curious...

    --
    Live to Code, Code to Live!
  12. 90K! by TeVi · · Score: 2, Troll

    Wow, 90K!

    I bet a 'make world' will go a lot faster then :-)

  13. 90K? 90K? by Anonymous Coward · · Score: 0

    Elite was rather smaller than 90K. Elite 2 on the other hand...

  14. volumetric pixels by johnjones · · Score: 4, Interesting

    is volumetric pixels this sort of thing ?

    fractals are good for storeing large amounts of information but decompression is hard and how do you then represent the information useing standard methods or volumetric pixels type approach ?

    seems nice but I would like more details before makeing any jugment

    anyone have details ?

    regards

    john jones

    p.s. I am sure a game used this type of thing before

    1. Re:volumetric pixels by kigrwik · · Score: 1

      > p.s. I am sure a game used this type of thing before

      Yep.
      I remember "Strike Commander" built its terrain maps this way. (Fractals + smoothing + texture + objects)
      (back in '92 ? '93 ? )

      ... ten 1.44 Mb disquettes, 1hr of fractal stuff on my good ole 386... ... good memories.

      --
      -- don't discount flying pigs until you have good air defense
    2. Re:volumetric pixels by JohnsonJohnson · · Score: 1

      No volumetric pixels have nothing to do with this, you can render directly to screen coordinates after defining a transformation from world coordinates to screen coorfinates.

      You have it backwards, if you want an exact or even a lossy representation of an image using fractals then compression is a very difficult problem. Decompression on the other hand is simply iterating a usually simple function, or a small set of functions. Since you can estimate the costs of calculating the function and the number off times you iterate is related to the level of detail you present you can calculate the level of detail you can represent given available compute power and time constraints.

      The information is entirely parametric, you specify what region you are interested in and level of detail, then you get a texture back.

      I'm a little lazy so I'm not going to give links, but a simplwe query (like "fractals" or "fractal compression") on Google should provide plenty of jumping off points.

  15. Looks quite cool, but not photorealistic by RNG · · Score: 5, Interesting

    I've just checked out the sample mojo-world gallery (I'm a sucker for any web pages that claims to show me (almost) photo-realistic rendered terrain images) and while the output is quite cool, it still has ways to go before it's going to be photorealistic. On the other hand, the point of MojoWorld is that you don't need a lot of data to re-create your scenes: you just save the seed parameters (which are tiny as compared to a real height-field) and the engine re-creates the scene from these parameters.

    I have been working on terraform (which is aimed more at the generation and manipulation of digial terrain rather than the rendering of it) for a while now and in the course of doing so have learned a few things about fractal terrain generation. The fact that you can regenerate the terrain from a few seed parameters is not that special (dimension, scale factor, random seed, etc); these are the kind of parameters that are typically passed to these functions anyways. The more interesting thing (to me) is that they have apparently found a compact representation of all the data needed to create a (semi)realistic scene from it. All in all, I think this is quite cool. Hopefully they (at some point) will write a white paper detailing some of the algorithms used by the (closed source) generator.

    1. Re:Looks quite cool, but not photorealistic by Armands · · Score: 1

      Hm, as a few years doing landscapes just for my pleasure, i leave Terragen (most realistic terrain renderer today) and go for Mojo... I see there many new, cool features and photorealism is only matter of time for artists :) Gallery on Pandromeda isn't the best ...

      --
      Armands www.terraescape.com
  16. ok... by donabal · · Score: 1

    not to beat a dead horse... but
    "640K ought to be enough for anyone" ... who wants to model the solar system.

    --donabal

    --
    Safety First Day?
  17. Anyone successfully downloaded yet? by TinheadNed · · Score: 1

    I haven't been able to get anything from them yet. Smacking F5 a lot has got me to almost downloading now.

    Mirrors anyone?

    Very nice screenshots though. Wasn't First Encounters supposed to allow you to fly over planet vistas though?

  18. Just have to wonder... by merlin_jim · · Score: 5, Insightful
    I just wonder how big their problem space is, and does it conform to the genetic algorithm definition of "smooth"... the existance of sliders would seem to indicate that this is so.

    Smooth may be defined as:
    • function: all genotypes code for valid phenotypes
    • injective (compact, nonredundant): different genotypes lead to different phenotypes
    • surjective (universal): all phenotypes are representable
    • continuous: small variations in the genotype produce small variations in the phenotype
    • inversely continuous: small variations in the phenotype can be induced by small variations in the genotype
    Where genotype refers to the parameters and phenotype to the representation of the world.

    If this were true, then one could theoretically evolve (using GA techniques) a planet that is a reasonable facsimile of earth, or any other feature set. Want a detailed map of San Francisco Bay? Let me squirt my survey through my Genetic Algorithm MojoWorld Compression Algorithm. Oh good, it's done. Use these five numbers to recreate the map...

    Hmmm... sounds like it's plausible, but I don't think that small changes in the genotype necessarily result in small changes in the phenotype.
    --
    I am disrespectful to dirt! Can you see that I am serious?!
    1. Re:Just have to wonder... by Anonymous Coward · · Score: 0

      Any algorithm which follows the above 5 definititions will require huge numbers as input.

      You'd need a 1 to 1 mapping of possible maps to possible input space, which would make your input space as big as all possible maps, which is quite big I think.

      To account for this, I think that they use some sort of algorithm that only makes plausible worlds. So their algorithm doesn't produce maps where land and sea are alternated every inch, or where there are a lot of plants on one side of the world, but none on the other.

    2. Re:Just have to wonder... by merlin_jim · · Score: 2

      You are absolutely correct with regards to the 1:1 mapping. You might be able to get some compression in, in that you are storing the idea of a thing and not the thing itself (e.g. information as opposed to data)... but I think you are more accurate in the plausible worlds theory.

      The big question is, is the representation "smooth" enough to encapsulate arbitrary real-life examples?

      --
      I am disrespectful to dirt! Can you see that I am serious?!
  19. Check out these related articles by Kieckerjan · · Score: 3, Informative

    Gamasutra had a couple of articles on the subject of (real-time) procedural formation of planetary bodies. (Free login required.)

    http://www.gamasutra.com/features/20010302/oneil_0 1.htm
    http://www.gamasutra.com/features/20010810/oneil_0 1.htm

    There is a nifty demo available for download. The same code is used in the glElite project.

    --
    Being well balanced is overrated. -- John Carmack
  20. Sing it... by GarryOwen · · Score: 2, Funny

    Come on everybody and sing....

    "I have the whole world, in my floppy"

  21. Does anyone remember Captain Blood? by Anonymous Coward · · Score: 1, Informative
    Been there, and done that in 1987. It was a cool game with 32768 unique plaents... with terrain to fly thru... Hell it even ran on a C64!


    But for some reason the computer industry seems to belive that if there has been a lapse for 10 years, the next sucessor is suddelny 'new'.


    http://www.mobygames.com/game/sheet/gameId,134/



    www.oldskool.org/shrines/captainblood/capblood.htm



    http://argnet.fatal-design.com/bluddian.htm

    1. Re:Does anyone remember Captain Blood? by Anonymous Coward · · Score: 0
      How about Rescue on Fractalus circa 1985.

      http://www.qlam.com/atari/s_rescue.html

      Fractal generated landscapes in 8 bit color.

  22. Frontier by jafuser · · Score: 2
    I was going to point out this very game, thank you for beating me to it! :)

    This was one of the most amazing games I'd ever seen at the time, becuase the player is completely free to go anywhere in the "universe" and do anything. I think the discovery of "wormholes" (from a 16-bit overflow bug) also added quite an interesting element to it as well (That's not a bug, it's a feature!).

    Don't forget the fractal-nature of the Frontier universe as well. I doubt they could have fit all of that data in the game! It was quite interesting how whole solar systems were created around each star, with different planet types and numbers, different political situations, random natural and manufactured satellites, different star configurations (double and triple systems). I suppose this was all seeded from the same value, or it would have been different every time.

    I wish there were an upgraded game like Frontier, which took advantage of modern computer systems, but still contained all of the elements of the original. I'd love to see such a game as a massive-multiplayer-online sort of game. I'll check those links you provided and see what those are like...

    --
    Please consider making an automatic monthly recurring donation to the EFF
    1. Re:Frontier by Anonymous Coward · · Score: 0

      I'd love to see such a game as a massive-multiplayer-online sort of game.

      Check out Jumpgate (and the fan site Planet Jumpgate)

    2. Re:Frontier by Anonymous Coward · · Score: 0

      The original (BBC Micro) Elite did indeed use seeding of an RNG to create its planets. Never mind a planet in 90K -- Elite "stored" each *galaxy* (planets, names, political systems, pricings of commodities) in 16 bits by storing the RNG seed.

      Peter

    3. Re:Frontier by DevNova · · Score: 1

      Is that how they did it? My theory, which removes the need for even the RNG, was that the program used itself to generate the galaxy. ie: It used the physical program data and used it to compare to a table of locations, planet types, governments, etc. Does that make sense?

  23. A More Practical Application by Jucius+Maximus · · Score: 2, Funny

    All we need now is for someone to encode all the world's pr0n in this fashion and put it on gnutellanet!

  24. Where would one find information? by errorlevel · · Score: 1

    Where would one find information on learning to apply this technology to new games? I saw an earlier post which said the poster had used it for a massively multiplayer online game. I'm very interested in trying to use this technology. Any links about how to implement this or something similar would be highly appreciated.

    --


    The Moo went "Cow!"
  25. Bill Gates was right by Sideways+The+Dog · · Score: 0, Redundant

    Wow, Bill Gates was right. 640K of memory really is enough for anybody.

    --
    "Love is never saying you're too proud." -Tonic
  26. It's a little grandiose by thejake316 · · Score: 1

    They're selling a Holosuite but delivering a View-Master.

    --
    AC's cheerfully ignored
  27. Sierpinksi Gadgets by Quay42 · · Score: 4, Interesting

    On the related note of fractals and their generation; A few years ago while playing around with GWBASIC (!!!) on a Tandy 1000 Color I discovered you could generate sierpinksi gadgets (there's a picture of a 3D one that I managed to find at http://www.angelfire.com/mo3/mysteriesofscience/ga mes.html) by choosing 3 coordinates on the screen (for the vertices) and then choosing a random point somewhere else. Then, choosing between 3 random numbers (or anything that has 3 equally probable events) and plotting the point halfway between the current point and the vertex corresponding to the chosen number, a sierpinski gadget slowly "fades" in.

    To make it look even better, you can choose a color for each vertex. I also found you can do similar things with other shapes (pentagons, squares, etc.) Perhaps this algorithm is a well known way to generate the Sierpinksi Gadget. The amazing thing is how *small* the code is!

    pseudocode (possibly with mistakes...its been a while)

    Sierpinski
    Choose 3 equidistant points on the screen: {x[0],y[0]},{x[1],y[1]},{x[2],y[2]}
    Choose random coordinate on screen (x,y)
    while no user input
    choose random number n from {0,1,2}
    plot ((x+x[n]/2), (y+y[n])/2))
    loop

    Cheers,
    jw

    --
    "Has anything you've done made your life better?" - American History X
    1. Re:Sierpinksi Gadgets by wurp · · Score: 3, Informative

      I think it's:

      Choose 3 equidistant points on the screen: {x[0],y[0]},{x[1],y[1]},{x[2],y[2]}
      Choose random coordinate on screen (x,y)
      while no user input
      choose random number n from {0,1,2}
      x = (x + x[n])/2
      y = (y + y[n])/2
      plot (x,y)
      loop

      and the points don't actually have to be equidistant, any three points will work. You'll just get a warped triangle, which can look kind of cool.

    2. Re:Sierpinksi Gadgets by merlin_jim · · Score: 2

      This is known as the Iterative Fractal System, or IFS, and is actually patented (not sure by who... remember the gentlemen's first name is Michael)

      There was a great chapter in the book, "Programming Tricks of Computer Graphics Gurus" about the subject. Basically, lay out regions on your screen that represent the various parts of the fractal. Make a translation / rotation / scale matrix describing each one. You can make an IDE that applies the matrix to the entire screen (resulting in morphed rectangles at each vertex).

      Then, assign a probability to each row of the matrix that is the area of the transformation compared to the total area. Use your random number algorithm to pick out which one to apply, and apply it to your point.

      Most of the time this is an arbitrary process, such as "Do it 100 times without plotting to stabilize the jumping point, then do it 1000 times to get a good estimate of the final figure." A lot of people coding it take it one step further and basically end tracing when a certain percent of the last x points drawn were already present...

      --
      I am disrespectful to dirt! Can you see that I am serious?!
    3. Re:Sierpinksi Gadgets by Quay42 · · Score: 1

      Sweet, it has a name! Of course my idea wasn't quite as complex and has many more limits than what you said. But its pretty nifty to know that this is an actual technique, used in some form another.

      Seriously, I need to get back to work now..

      Cheers,
      jw

      --
      "Has anything you've done made your life better?" - American History X
    4. Re:Sierpinksi Gadgets by SurfsUp · · Score: 4, Informative
      This is known as the Iterative Fractal System, or IFS, and is actually patented.

      Iterated function system. Compression by this method is covered by US patent 4,941,193 issued 1990. This is a clearcut example of how a potentially useful mathematical technique has been largely ignored because of its patent encumbrance. Just one more example of how patents are good for lawyers and bad for everybody else. I seriously doubt Barnsley has made any money from the patent, I suspect the book produced more revenue. In any event, whatever usefulness the technique might have is lost to us until the patent runs out in another 8 years or so.

      The word "asshole" comes to mind.

      --
      Life's a bitch but somebody's gotta do it.
    5. Re:Sierpinksi Gadgets by Seth+Leichter · · Score: 1

      I came across this old program of mine recently. When I first read about the algorithm, it was called a "Sierpinski Gasket". So I wrote it up in PostScript. On-screen, you can see the picture fade-in.


      %!
      %%Title: Sierpinski Gasket
      %%CreationDate: 6-21-92
      %%Creator: Seth Leichter
      %%BoundingBox: 0 0 612 792
      %%EndComments

      %%BeginProlog

      /R {rand 3 mod} def

      /plot { /x exch def /y exch def
      x y moveto
      x y lineto
      stroke
      x y moveto
      }def

      /midpoint { /x1 exch def /y1 exch def /x2 exch def /y2 exch def
      x2 x1 add 2 div
      y2 y1 add 2 div
      }def

      %%EndProlog

      /A {306 661}def
      /B {0 131}def
      /C {612 131}def

      /gasket
      {R dup
      0 eq
      {A currentpoint midpoint plot pop}
      {1 eq
      {B currentpoint midpoint plot}
      {C currentpoint midpoint plot}ifelse
      }ifelse
      }def

      1 setlinewidth
      0 setgray
      A moveto

      100000 {gasket} repeat

      showpage

    6. Re:Sierpinksi Gadgets by merlin_jim · · Score: 2

      Yeah, I was actually looking at using this method to do image compression until I ran across the patent. Hopefully the methods that I was looking at will still be valid in 2010... and they won't have been superceded by MPEG-8 or whatever.

      As I remember, one of the major advantages, besides cheap decoding, was hardware encoding could be used relatively easily...

      --
      I am disrespectful to dirt! Can you see that I am serious?!
    7. Re:Sierpinksi Gadgets by Anonymous Coward · · Score: 0

      My version worked a bit differently:

      %!PS-Adobe-3.0 EPSF-3.0
      %%Creator: Anonymous Coward
      %%Title: Sierpinski Triangle
      %%CreationDate: whenever
      %%BoundingBox: 10 10 410 410
      %%EndComments
      /Avg {
      add 2 div
      } def

      /Tri {
      newpath
      moveto
      lineto
      lineto
      closepath
      0 setgray
      fill
      } def

      /Sier {
      dup 0 gt
      {
      6 index 6 index
      1 index 7 index Avg 1 index 7 index Avg
      3 index 7 index Avg 3 index 7 index Avg
      6 index 1 sub

      11 index 11 index
      1 index 12 index Avg 1 index 12 index Avg
      3 index 18 index Avg 3 index 18 index Avg
      6 index

      16 index 16 index
      1 index 23 index Avg 1 index 23 index Avg
      3 index 23 index Avg 3 index 23 index Avg
      6 index

      Sier
      Sier
      Sier
      pop pop pop pop pop pop pop
      }
      {pop Tri} ifelse
      } def

      /x0 20 def
      /y0 200 def
      /x1 350 def
      /y1 50 def
      /x2 300 def
      /y2 390 def

      x0 y0 x1 y1 x2 y2 10 Sier

      showpage
      %%EOF

    8. Re:Sierpinksi Gadgets by Anonymous Coward · · Score: 0
      Wrong, wrong, wrong. The technique of data compression using IFSs is patented. IFS themselves are not. The guy who patented Fractal Image Compressions didn't invent IFSs.


      [And it's called a Sierpinski Gasket, not Gadget.]

  28. Far out by Dyolf+Knip · · Score: 3, Insightful

    I tried zooming out to a few thousand km to try and get a good full planet view and was rather disappointed. Only two terrain features were still visible (green and snow); nearly all the lakes and rivers had vanished and there were no large bodies of water no matter how high I set the water level. Didn't look anything at all like a planet when it had finished rendering.

    --
    Dyolf Knip
  29. Very cool for video game development by ackthpt · · Score: 1
    One of my old favorites was Seven Cities of Gold, which had a crude world builder in it. I've played a number of games which have some sort of landscape development aspect in it, but usually they're pretty cheesey when you really get a good look at them.

    I've expiremented with various algorithms to try creating landscapes, some of which have relied upon fractal and Mandelbrot math, but often with mixed results. I'll follow this with interest.

    --

    A feeling of having made the same mistake before: Deja Foobar
  30. Name taken? by sammy+baby · · Score: 2

    Dear lord - did they have to call it Mojoworld?

    I hope that Mojo Nixon doesn't decide to sue, seeing as how he's already written songs about it, and all.

    1. Re:Name taken? by Indomitus · · Score: 1

      I don't know anything about Mojo Nixon (your link is broken) but if you're an X-Men fan you'll probably remember the TV obsessed villian Mojo and his planet was also called Mojoworld IIRC. This was more than 10 years ago, probably closer to 20.

  31. Elite: Frontier and First Encounters by szyzyg · · Score: 2

    These games had fractally generated universes with starsystems, planets, cities and whatnot. Because they are elite games you could literally fly anywhere you wanted. It's now possible to download the shareware version of First Encounters from the Elite Club, and the game is so popular some clever fellow went and reverse engineered the binary, fixed a load of bugs and made releases of the game engine for Windows and Linux.

  32. Reminds me of old ideas... by Mike+McTernan · · Score: 1

    Seems like a reverse approach to what people believed in the past; that the universe was dictated by some huge equation that one day would be found and understood (turns out that chaos theory means it is impossible to know the starting state to an accuracy where todays universe can be known).

    Just this seems to be the other way around - make a formula and find the universe it creates.

    --
    -- Mike
  33. One word: Starflight by Anonymous Coward · · Score: 1, Funny

    Rolf Harris tells a joke about a lawyer from a long-established firm. Over the decades that he and his family had practiced law in the same building, the constant foot traffic over their doorstep had worn a big depression into the solid granite. So the lawyer had a stonemason come in and give him an estimate on a new doorstep. It came out to a lot of money. So our boy thought his best lawyerish money-saving thoughts, and came up with an idea. He said to the stonemason, "Well, how much would it be to not replace the stone but just flip it over? It's just a solid rectangular block, so nobody would be any the wiser if we got some wear out of the bottom as well as the top." And as it happened, that would cost rather less money. So that was what the lawyer decided to have the stonemason do.

    So the stonemason goes to work, hammering and chiselling and doing all the usual activities of his trade, and then after about an hour the lawyer hears a knock on his door. He hurries to open it and there's the stonemason with a cheeky grin on his face, saying, "Yer grandfather thought of that fifty years ago!"

    Fractal planet generators are indeed a good idea, but they're not so new as all that. Starflight, people, starflight.

  34. This really isn't that impressive... by Anonymous Coward · · Score: 4, Interesting
    Generating fractal landscapes is really pretty well understood these days and I'm afraid that Ken Musgraves latest efforts, whilst good, are really nothing special. The standard at the moment is set by Terragen - which is an order of magnitude better than Musgrave's efforts.

    Musgrave is also extremely annoying in the way he dismisses enhancements as trivia and gives the impression that he's done the hard work. He hasn't - he's done the easy bit. For example placing vegetation on his landscapes is a very, very hard problem. Lets see him place a forest of oak trees besides a river, with realistic rendering of sunlight through the leaves, the roots in the soil, and the shadows of the leaves on the ground then I'll be impressed.

    There are packages that are attempting to do this - World Construction Set, WorldBuilder and GenesisII come to mind - there are many more (including the granddaddy of them all Vistapro). None look as realistic as Terragen though - again something that can probably be ascribed to the fact that terragen, like Mojoworld, chooses a particular type of landscape in which to work. Unlike Mojoworld though, Terragen is photorealistic.

    Creating a general-purpose photorealistic terrain renderer is probably on of the hardest problems still available in computer graphics. And while Musgrave deserves respect for what he has achieved over the years, sadly he's one of those people who simply isn't as good as he thinks he is.

    1. Re:This really isn't that impressive... by Anonymous Coward · · Score: 1, Interesting
      You're missing the obvious here. MojoWorld is attempting to do this in real time. TerraGen does not.

      In any case, TerraGen is pretty fucking far from photorealistic. Get the right camera angle and it looks great; get the wrong angle and you're in polygon hell.

      I'm not impressed with any of this shit.

  35. Ihara-grub algorithms, anyone? by cryptochrome · · Score: 1, Redundant

    Forget planets, what we need are algorithms that can generate everyday objects like people.

    --

    ---If you can't trust a nerd, who can you trust?

    1. Re:Ihara-grub algorithms, anyone? by Anonymous Coward · · Score: 0

      Check out Poser

    2. Re:Ihara-grub algorithms, anyone? by Anonymous Coward · · Score: 0

      check out http://www.haptek.com
      for some realtime human animation.

  36. Fractal Planets... Literally. by Buran · · Score: 1
    A Photoshop plugin called LunarCell does this a bit more literally -- it creates planets, not landscapes on planets, also by means of fractals. What's more, it can download actual cloud patterns from satellites to create even more realistic images by combining real bitmapped data with fractals.

    My Fractal Planet Gallery might interest some people...

    (The most recent one uses another plugin, developed by the same people -- to add a nebula background. Yes, I know the planet should drown the stars and nebula out. It looks cool, and I created that pic to be my desktop background image!) :-)

  37. Impacts for Non-computer gaming and other things.. by BluePenguin · · Score: 1
    When I read this one of the first things I thought was: "Great, now when I generate worlds for my Rifts/Alternity/Anything group, I can actually give my players something to explore!" In tabletop gaming, one of the great advantages to campeign settings has (IMO) been maps. Maps tend to make any fantasy setting easier to explore, and at 90k, it's fairly easy to e-mail my players and say "Here, DL a copy of the world map!"

    It also brings to mind some of the Illustrated Guide to XYZ fantasy universe books that so many fans crave. With software like this becoming more common, could we begin to see CDs o' Fractal images with such publications? Or (again with file sizes of 90k), will we see printed URLs with a "Go here do DL the complete wold..."

    Still, while thier limited viewer is free, and the professional viewer (with unlimited resolution) is only $30, I think the $250 SRP (even the $200 intro price)the hobbyist may stay off this platform for a while.

    :q!

    --
    If I can't see it in Lynx I'm not interested.
  38. Power of math by bloo9298 · · Score: 1

    Is the power of math something like the power of Oxyclean?

  39. Sorry if I'm skeptical by donglekey · · Score: 2

    But fractal landscapes? Holy shit stop the presses! Landscapes are the classic use for fractals. This is really nothing special. Sorry to be so harsh.

  40. Want some good rendered scenery? by Anonymous Coward · · Score: 0

    http://www.mikebonnell.com
    http://www.digitalblasphemy.com

    It might not be fractally generated but who cares, its damn good stuff.

  41. I can see it now... by chinton · · Score: 1

    Kirk is preparing a presentation on Genesis. Spock can be seen in the background in front of a bank of computers.

    Kirk: Spock, is the Genesis planet demo ready?

    Spock: I am in the process of building the last piece of the rendering software now, Admiral. It will be completed in 7.182 seconds...

    Kirk: (smirking) Could you be a little more specific, Spock?

    Spock: (cock's an eyebrow at something on his display)

    Kirk: Problem, Spock?

    Spock: Yes, Admiral. The rendering software requires an ancient version of something called "GTK". This is not logical... "GTK" fell out of disuse in the early 21st century following the advent of the Quantum Display...

  42. Hmph (proprietaryware seller!) by Chris+Johnson · · Score: 3, Informative
    I've done this too... difference is, when I realised it didn't really lead towards personal Cadillacs etc. rather than immediately decide to take the project proprietary, I just sort of drifted away towards other things... have always meant to return one day, and I will.

    What you're seeing in the mpeg videos behind that link is flyover scenes that generate a terrain grid with dynamic level of detail concentrated near the camera, overlaid onto an entirely synthetic and repeatable world which is derived from multiple pointer math on a large (16M) data file. That means FAST- it was only implemented in REALbasic and still runs reasonably fast, and is a natural for C.

    I also spent some time producing universe distributions- one stumbling block that I ran into that I hadn't got around to solving was what I was keeping world space in, as the universe is very big and at the same time the actual planets would go down to roughly 1/8" level of detail using some approaches for data synthesis. In particular, one of the techniques for positioning stuff would go down to 1/8" level of detail with four pointer-like operations using no kind of higher math. The difficulty is that you don't get a list of objects- instead if you wanted to synthesise, say, blades of grass, you'd go over a ten mile view by scanning across your view grid and every eighth of an inch, would do the fairly quick lookup of whether there was a blade of grass or some similar object on that eighth-inch spot. On the bright side, it would at least be repeatable, being entirely procedural.

    The thing about these projects, and I can see that many people have done them, is that you can get grandiose about them but the bottom line is: this is not a game. This is not inherently fun, or interesting. One thing I'd thought of for _my_ approach is to apply some Warcraft-like game (scaled to MMORG, of course ;) I think that's a rule for all people coding virtual worlds) and make use of the fact that you can have a world-sized area with (perpetual) resources laid out irregularly and down to an extraordinary level of detail. So you could be in a game, and have to dig for gold or iron or something, and go by people's reports of where that resource could be found- including "There's this planet out by Alpha Centauri that's loaded with it". I also had a procedural planet and location name generator that wasn't entirely horrible ;)

    Like I said- you get into this sort of thing and totally forget that it's NOT FUN for anybody else, unless there's a plot. I'd suggest that the author of this more recent work, if he seriously expects to earn money off it, should treat it very much like selling an art object: 'here's a viewer through which you can explore millions of worlds much like Bryce, only with less interaction', and not be too haughty about the price, either. This isn't a set of libs that will be useful for anyone creating a game, period. For one thing, you can get the same thing cheaper from elsewhere- it's NOT a unique idea.

    1. Re:Hmph (proprietaryware seller!) by Fixer · · Score: 1
      I think everybody has the ideas you've outlined at one point or another. Heck, I just read an article at Gamasutra a few days ago about procedural worlds. So of course I'm thinking procedural universe.

      But such a universe is empty and dead. As you say, not fun for anybody else.

      So now I'm thinking about aspects of alien civilizations that could be mapped to various math functions. Color schemes and habitation layouts seem like an obvious mapping. Entire classes of names and gibberish seem like another (as you've done already). Certain game-dependant things, like types and levels of technology, could work too.

      But the biggest problem with the whole scheme, is how to keep it realistic when someone decides to play Captain Kirk and goes galavanting to hell and gone, pissess off a few civilizations, destroys a bunch of bases and ships.. then returns a month later to find out it all reset. No good. Gotta find a resonable way to store events, or more properly, to instantiate a given set of fractal points as persistant, malleble data, without occupying terrabytes.

      --
      "Avast! Prepare for the rodgering!" THWACK! "Arrr.. me nards.."
    2. Re:Hmph (proprietaryware seller!) by Chris+Johnson · · Score: 2
      Well, it's not just trying to have persistent data: 20 billion planets is not fun! Games are _constrained_. Especially with a plot. Look at how constrained even some MMORGs are: it's 'camp out by monster X's spawn point' and all that.

      Here's what I'd gotten to, in case it's useful in any way: I figured, the universe was divided neatly into 8 quadrants. Center of the universe is too hot with radiation to survive in, so you're going around the edges. Two corners are occupied by opposite races: one, a race of pacifist avian creatures, and two, a race of basically Daleks ;) robot things that only want to take over everything else and exterminate everyone. That is an immediate overriding plotline: these bad guys, with a home turf, making attacks. You could also have certain resources only exist within the baddies' territory. It's all about forcing mechanisms- you don't give a player a choice. If you play chess it's not to perform interpretive dance with knight movements, it's to take pieces and win and beat the other player. In a vast universe game like we're talking about there has to be a vast universe-sized plot-line, and the most direct one is an attacker.

      That said, look to Star Wars for an object lesson in the scale of conflict. In theory it's about the decline and return of the Jedi etc etc, but in practice, in the film, it's Luke in hand to hand combat with his father Darth Vader. In 'A New Hope', even the cinematography is more upfront and immediate- things are in your face, whizzing through the frame, it's not about pulling back and getting a broad view. (PM does that sometimes, and it sucks ;) )

      So, in making your massive universe, in what ways can it be made so that a player's IMMEDIATE location is compellingly interesting? Then there can be billions of such locations- but people will be interested in just the one they're in.

  43. "The Galaxy is on Orion's Belt" by No+Such+Agency · · Score: 2

    (MIB)

    :-)

    --
    Freedom: "I won't!"
  44. 90k worlds? Pah! Elite had 8 galaxies in 48 bytes! by evilandi · · Score: 4, Interesting
    Elite (1980's 8-bit wireframe space trading game) used only 48 bytes to carry names, descriptions, positions and trading data on hundreds of star systems spread across 8 galaxies (see Elite Faq question 13).

    Elite used Fibonacci Numbers with a eight 6-byte seeds, plus a few dozen bytes of look-up tables, to achive this. The principle was very similar to MojoWorld's use of fractals, but Fibonacci series are considerably quicker to process, particularly on an early 80's home computer.

    --
    Andrew Oakley - www.aoakley.com
  45. Check out 'The Science of Fractal Images' by webbunny · · Score: 1

    If anyone would like to see what Musgrave and Mandelbrot were up to in the late 70's/early 80's with all this stuff (and yes, that makes Musgrave the 'daddy' of fractal landscapes! Loren Carpenter, eat ya heart out :^), you should check out the book they contributed to:
    The Science of Fractal Images, edited by Heinz Otto Peitgen.
    This book can be considered 'Fractals 101', and when I was doing a fractal related final year university project about 8 years ago, it came it VERY handy :)
    However, the images on Musgrave's website don't look much better than the colour plates in that book, so other peoples comments, like 'Big Deal' etc, do hold. I was expecting him to have at least produced better looking images than my team at Uni did :^)
    But whatever, the guy still gets major respect from me, he is a true computing pioneer.

    Andy

  46. Multi-user interactive worlds by betaray · · Score: 1

    I work for a game company, and one of our next projects is going to be a multiplayer interplanetary action/advententure style game. I have been looking into ways to fractally generated planets quite a bit. While this software does look cool (especially the textures), it still has the one problem that hurts it's usablity in multi-user worlds, it changes shape dramaticly between certian levels of detail. If I think I'm hiding behind a hill, I should be hiding behind a hill on everyone else's front-ends no matter how far away they are.

    I wish I had known about this interview before hand so I could pose this problem to Dr. Musgrave himself, since he seems eager to use this in multi-user worlds.

  47. Starflight by Jace+of+Fuse! · · Score: 2

    Starflight had an entire Galaxy on two 5.25" floppy disks! :P

    --

    "Everything you know is wrong. (And stupid.)"

    Moderation Totals: Wrong=2, Stupid=3, Total=5.
  48. Great Advertising Campaign by BigJimSlade · · Score: 1
    Behold... the power of math.

    If they can just get that guy from the cheese comercial, I think it'll really sell.

  49. Bah! by kirkb · · Score: 1

    I can fit the whole universe in one byte: 42

    --
    Slashdot: come for the pedantry, stay for the condescension.
    1. Re:Bah! by Mr.+Piccolo · · Score: 1

      HA! I only need 6 bits:

      101010b = 42d

      --
      Glückwünsche, haben Sie Slashdot ermordet, indem Sie zum korporativen Druck beugten und Subskriptionen einlei
  50. powerMATH by Satai · · Score: 2

    ...it uses the power of math..."

    POWERmath is a system of high performance
    algorithms engineered to meet your
    planet creation and design
    needs head on. Want to know more?
    Follow the equals...

  51. Starflight was magnificent... by Anonymous Coward · · Score: 1

    ...wonderful plot, funny and alarming aliens, a horrific moral dilemma and a great mix of travel, adventure and exploration. And all in 720K. Where is a game as good as Starflight?

  52. This is old news. by netsplit · · Score: 1

    I remember a 26k executable file, from the same people nearly two years ago or so. It rendered an island. I remember a PR saying they had a pay-version on CD which contained a fractile of earth -- fairly complete which took up a 1 or 2 cd set. What ever happened to this?

  53. Not if they want to make the big money... by bugg · · Score: 3, Interesting
    Touch, taste and smell are "immediate" sensors--they must be in contact with what they're sensing. Fooling them will be much harder. But are they necessary to a perception of "reality?" Probably not.

    Not if they want to do well in the adult entertainment business. And don't think I'm kidding: the sex-starved portion of the population is willing to pay billions to see something like this developed.

    --
    -bugg
  54. Realtime vs. non-realtime arguments aside... by cr0sh · · Score: 2

    I have to agree with you AC, that Terragen is very impressive.

    Want to know what is more impressive about it?

    It is written mostly in Visual Basic (don't believe me? Email the author. I found out after having a conversation with him about using VB for 3D stuff like this a few years ago, because I noticed it installing the VB runtime during setup).

    --
    Reason is the Path to God - Anon
    1. Re:Realtime vs. non-realtime arguments aside... by Anonymous Coward · · Score: 0

      Actually, most of the stuff that does the work is written in C++, VB is pretty much only used for the UI these days. All of the speed critical stuff that used to be in VB inside the app has been moved out to C++ in the lib, and it goes a lot faster. I'm working on a port to the Mac, and had to go through and translate ( or rewrite ) all that VB code in C++ :-).

      Jo Meder -> not really an AC but can't find my login just now

    2. Re:Realtime vs. non-realtime arguments aside... by cr0sh · · Score: 2

      I might have to check it out again, then.

      I stopped playing with it a couple of years back. The things I keep waiting for is:

      Trees
      Sunlight thru clouds

      One other thing I would love to see (any possibility of?) is a Linux/X port. Basically, since you have the C++ stuff taken care of, most of it would be a UI interface, right (using GTK or some similar lib for that would work)?

      --
      Reason is the Path to God - Anon
  55. Generating fractal landscapes... by cr0sh · · Score: 4, Interesting

    Generating a simple fractal landscape is both an easy and a difficult process. The algorithm is relatively easy - it is the implementation that can be difficult.

    It is possible to implement a fractal landscape generation system on using only 2D graphics, which produce an image that looks amazingly 3D in scope, but isn't. Of course, it is possible to do the same algorithm in a 3D coordinate system.

    I came across the 2D method first in an old Creative Computing article from around 1983 (the issue was the "graphics" issue, and in addition to the fractal mountain code done in BASIC for a couple of systems, there was an article that detailed making photo masks and combining computer graphics and real photo techniques to produce cool effects for the time - today, photoshop works wonders). The BASIC code was for a PCjr (IIRC) and an Apple IIe, but I converted it to my TRS-80 Color Computer - and it ran fine (though very slowly).

    Essentially, the process is:

    1. Select three random (X,Y) points on the screen - these form the "base" triangle.
    2. Find the midpoints of each side of the base triangle. Split each side in half (subdivide it), and move the midpoint up/down by a small random amount (in the Y direction on screen), and join the points - the deformed triangle should now be composed of 4 sub-triangles.
    3. Repeat the process on each of the resulting sub-triangles n-times.

    Of course, n tends to be a small number - around 7-10, depending on the resolution of your output device. There is also a way to add "water" by deciding on an certain "Y" level to disallow drawing of "land", instead showing "water" (where "land" is green, brown, or grey, and "water" is blue).

    That's the basic algorithm, and the hard part is keeping all the sub-triangle's vertices joined, so that when one is shifted up, the adjoining triangle's vertex shifts up as well. In the Creative Computing article, this was accomplished with arrays and really complex code that wasn't explained too well. Today, you would probably use a combination of linked-lists of objects (where each object represents a vertex), and of course a recursive function system. It would end up being more of a memory hog, but it would be easier to code as well.

    Taking the algorithm into the 3rd dimension would be easy, since you would plot the base triangle on the X/Z (or X/Y) plane, then as you went through the subdivision process, you would simply change the height of each vertex in the Y (or Z) plane respectively.

    --
    Reason is the Path to God - Anon
    1. Re:Generating fractal landscapes... by pegacat · · Score: 1

      ...in fact the 3D version is simpler to implement than the 2D version - you just plot your triangles on a 2D grid, with the value at each grid position being the terrain height. Because the X,Y positions of your points are intrinsic in the 2D grid, you don't have to faff around trying to keep linked-list objects or anything.

      e.g.
      5 0 0 0 3
      0 0 0 0
      0 0 0
      0 0
      1
      =>
      5 0 7 0 3
      0 0 0 0
      2 0 2
      0 0
      1
      =>
      5 5 7 4 3
      3 2 6 3
      2 1 2
      1 3
      1

      (of course, for efficiency, you actually do it in squares, two triangles at a time.

      --
      Wer mit Ungeheuern kämpft, mag zusehn, dass er nicht dabei zum Ungeheuer wird.
    2. Re:Generating fractal landscapes... by cr0sh · · Score: 2

      Very true...

      --
      Reason is the Path to God - Anon