Path: utzoo!news-server.csri.toronto.edu!rutgers!sun-barr!cs.utexas.edu!sdd.hp.com!caen!kuhub.cc.ukans.edu!zeus.unomaha.edu!ka013 From: ka013@zeus.unomaha.edu Newsgroups: comp.graphics Subject: Re: Fractals Message-ID: <10225.27d7b69b@zeus.unomaha.edu> Date: 8 Mar 91 22:06:51 GMT References: <586@cayne.UUCP> Followup-To: alt.fractals Lines: 54 In article <586@cayne.UUCP>, ron@cayne.UUCP (Ronald Cayne) writes: > Could some please explain what exactly are fractals and how they are > used in the imaging field. Pardon my ignorance. Thanks Ron I might be able to help you Ron. I have been doing a little study on the side about these fractals. They are graphic representations of an equation - much like the curves you learned in calculus -only these have special properties. They were brought into the open by a guy named Benoit Mandelbrot (so you can library search him) while at IBM. The most basic form (paradoxically?) is the one which bears his name - the Mandelbrot set. Say for instance you have the equation z = z^2. You start with any value 'z', square it and then run the equation again and again using the new 'z' each time. There are 3 potential outcomes- if initial z >1 then you will quickly zoom into infinity (or computer errors,at least). If z<1 then you will zoom into 0. In this case, the value of 1 becomes a boundary between the two infinities. Plotting this on a cartesian graph, you would have a circle of radius=1. The mandelbrot set simply takes this idea a step further. The equation is now z= z^2 + C, whereby a constant 'C' is introduced. This one little constant, introduces a universe of change into the circle. The edges of this set become fuzzy in a sense. Again, once outside the set, off to infinity- trapped inside the set, off to zero. The boundary takes on a new life here. You can magnify the set to huge proportions to look more closely at the edge, which takes on incredible variations of swirls, eddys, spikes, and so on. What is really neat is that these microstructures go on infinitly. The closer you look, the farther it goes. Folks have enlarged the magnification to beyond the orbit of mars, and it just keeps changing. You are only limited by the number of times you can interate the equation before you croak. Anyway, to make a long story short, Mr. Mandlebrot noticed how nature-like some of these structures could look, and began to relate formulas to nature. Lots of folks have taken this work even further and use their computers to generate fractal landscapes (mountains especially). For instance, the scene used in Star Trek II the 'Wrath of Khan' where they demo-ed the genisys device (a blazingly fast set of scenes in which you are whisked over the surface of a quickly forming planet) was created entirely by animating several frames of fractal generated landscapes. I've heard a rumor that a Florida company has announced the abililty to store approx. 2 min of video by representing the NTSC data by fractals. Hell of a compression when you can represent a photograhic quality picture with a formula a 6th grader could work! Anyway, if your still interested in fractals- there is a newsgroup called alt.fractals (with accompanying alt.fractals.pictures) you can subscribe to. I personally am a Mac head and generate color versions of these fractals on Macs but there are lots of programs out there for all machines, if you use something else. There are several excellent books available also- The Beauty of Fractals and The Fractal Nature of SomethingorOther (-sorry, it's been a long semester) There's one book that even has the algorythms to program your own, if you hack. I hope this has been of some benefit - It is probably better to ask a math major friend, but I tried! Happy Mac-ing! Mike ZA024@zeus.unomaha.edu