A BEGINNERS GUIDE TO CREATING BEAUTIFUL FRACTALS   by Leigh Murray  ¿? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿? INTRODUCTION Fractals are Easy Anyone can create beautiful fractal pictures. No understanding of maths is necessary nor is any artistic ability required. All you need is an Amiga, an interest in fractals, and patience while they draw. Of course, you can also get stuck into the maths, if you are that way inclined. There is abundant reading matter available on the subject, and most authors of fractal programs include some theory in their program doc files. This Beginners Guide consists mainly of practical notes aimed at providing extra help for beginners to get started in using these wonderful programs. The guide notes are supplementary to, and in no way replace, the documentation provided with each program. FracStarter and Fractal.Jigsaw To provide an inexpensive one-disk introduction to fractals, I prepared a disk for the MegaDisc Starter series, called FracStarter (START 6). It contains a selection of programs suitable for beginners, chosen to provide a cross-section of the main types of fractal programs. My favourite fractal programs are on the disk (FracGen and MandelMountains), along with other goodies in Biomorph, Lyapunovia, MandelPAUG, Scenery and Cloud. On this disk also are two excellent tutorial/review articles taken from earlier MegaDiscs: "Mandelbrots and Fractals in Depth" by Scott Campbell (from MD20), and "Making Mandelbrots" by Alan Jones (from MD21); both of the articles are also on MD.ArticlesII. The first article covers the theory of fractals, and the second has many hints; both contain descriptions and references to a wide range of fractal programs available in the public domain at the time the articles were written (a couple of years ago). Fractal.Jigsaw (MISC 173) is another disk I prepared recently for MegaDisc. It contains 28 fractal pictures created with four of the programs on FracStarter (FracGen, MandelMountains, Biomorph and Lyapunovia); the generated images were converted to 16-colour lo-res for use in the jigsaw puzzles. Despite the loss of some detail in the conversions, the pictures still look effective. Besides making interesting subjects for jigsaws, the pictures can be displayed in a slideshow simply by clicking on an icon. Pick a Program I suggest that you pick out a fractal program to try. Perhaps one of the programs on FracStarter may interest you. You may even have one already on a Fish disk or other MegaDisc PD disk. All of the programs on FracStarter, except Biomorph (which came from MD13), were originally distributed on Fish disks, and several also appear on MegaDisc's GR 97-99. Or if you have MD27, it contains another suitable program for beginners: Mandelbrot by David Taylor. I found this program easy to use, and I had a lot of fun with it while creating the fractals for the MD30 main icons. Scan, Run, Read Below are a few preliminary details on screen-swapping, reloading images, and copying prerequisite libraries; these are followed by notes about each of the programs on FracStarter. The notes, while quite specific to each program, should also contain a few clues for coping with similar situations in other programs. Because all of the FracStarter programs are easy to use, I suggest you just scan the relevant sections of these guide notes before giving a program a brief trial run (by loading a few of the supplied parameter files, or creating a fractal or two). Then when you have some basic familiarity with the functioning of the program, you should read the full program documentation (perhaps biting it off in small pieces to aid digestion!). I generally find it easier to understand and absorb documentation if I already have some idea of what the author is talking about when he describes the various program functions. The documentation supplied with some of these programs is excellent, and well worth studying in detail, as are the tutorials. Which Workbench All of the programs detailed below work fine on Workbench 1.3 and 2.0. There are other good fractal programs in the public domain that work only on Workbench 2 or higher, or only on accelerated Amigas; I have not covered these at all. WATCHING OR SWITCHING Watching the Pictures Unfold Most fractal images take a long time to render. I find it fascinating - almost mesmerising - to watch the pictures unfold, although sometimes I leave the longer-running ones to gurgle away unattended overnight, and have a wonderful fractal picture waiting for me when I wake. Working While You Wait On the other hand, it is quite feasible to run other Amiga applications while the pictures are rendering. The multitasking capability of the Amiga makes this easy to do. But the computations needed for fractals take up a lot of computer cycles, so response time with other applications may be slow and jerky. Switching Screens To change to another application, you need to be able to swap screens. This is easy when there are front/back gadgets for screen-swapping. However, some fractal programs do not have title bars on their rendering screens, and others make this an option. If there is no title bar and, therefore, no front/back gadget on a screen, you can still usually swap to other screens by using one of the very handy Left-Amiga/n and Left-Amiga/m key combinations. By Left-Amiga/n combination, I mean that you hold down the left Amiga key and then press the n key; similarly for the Left-Amiga/m combination. These key combinations can be used to swap between all sorts of screens and Workbench. The Left-Amiga/n combination always swaps back to the Workbench screen. The Left-Amiga/m combination works differently on Workbench 1.3 systems and Workbench 2. On Workbench 1.3, it swaps you back to the screen you came from when you used the Left-Amiga/n combination, whereas on Workbench 2 systems, it can be used to swap to the next screen if you have a number of screens open at once, and you can keep cycling through those screens by continuing to use it. With the few AMOS programs I have tried, the Left-Amiga/n and m key combinations haven't worked. For these, I've found the Left-Amiga/a combination handy. By holding down the left Amiga key while pressing the a key, you can swap from an AMOS program to Workbench, and back from Workbench to the AMOS program. Whenever you swap screens, remember that to activate a screen you have swapped to, you must click anywhere on that screen with the left mouse button to select it. RELOADING IMAGES Under Development Most good fractal programs let you reload the parameters of previously saved fractal images created with that program, so that you can easily continue developing your fractal. For instance, you could zoom into different areas, modify the palette to another of the program's standard ones, or change the screen size or resolution before re-rendering. This is a very handy facility. IFFs and Buts To give a couple of examples, MandelMountains and FracGen both have this facility, but they implement it in different ways. MandelMountains has only one save, called Save Image, which always saves the file as an IFF. Normally, the IFF will be saved with an additional chunk containing the fractal parameters, so that MandelMountains can reload it. This IFF should also be loadable into a Paint program. (Optionally the file can be saved without the chunk, in case the Paint program can't handle it.) But note that ordinary IFFs created by Paint programs won't have this parameters chunk, so these IFFs can't be loaded into MandelMountains (nor can you reload MandelMountains images that have been modified in a Paint program). In FracGen, there are two menu items for saving images, one for saving the fractal parameters so that the image can be regenerated by FracGen (Save), and one for saving the image as an IFF so that it can be loaded into Paint programs (Save Pic). Save Early, Save Often When you are starting to use a fractal program for the first time, check out the menu items and doc to see how that program approaches reloading. Then try a save and reload fairly early on, so you know how the function works before you've done a great deal of work. And save often while you are working (say, each new set of parameters), so that you can easily back up a step or two when, for example, a zoom doesn't work well. LIBRARIES FIRST Prerequisite Libraries Many fractal-generating programs need special libraries. For instance, on the FracStarter disk, Scenery and Cloud require no special libraries to function, but all the others depend on having certain libraries in the libs: directory. (The libs: directory is the directory called libs in the root directory of the Workbench disk you have booted from.) Below I will describe the installation process for those FracStarter programs which have prerequisite libraries, as a general guide. Mathtrans.library and Mathieeedoubbas.library MandelMountains, FracgGen and Biomorph require mathtrans.library in libs:, and MandelMountains also requires mathieeedoubbas.library. These two libraries are normally present in libs:, but you may have removed them in tailoring your Workbench disk. ReqTools.library Lyapunovia uses ReqTools.library (by Nico Francois) for file requesters, information boxes etc. This library is not on a standard Workbench disk as distributed by Commodore. So before running Lyapunovia, Reqtools.library must be copied to your libs: directory if you have not already done so for some other program that uses this library (it is often used by programs in the public domain). Versions of ReqTools.library for Workbench 1.3/1.2 and Workbench 2 or higher are in the Lyapunovia drawer of FracStarter, along with Install scripts. Req.library MandelPAUG needs req.library in libs:. Req.library also is not standard Commodore fare, and must be copied to libs: (it is in the MandelPAUG drawer of FracStarter). Checking Libraries and Versions You can check which libraries you have in libs: by opening a Shell (double-click on the Shell icon to do this), and typing cd libs: dir You can use the Version command to check which version you have of any particular file (as long as version details have been recorded for it). For instance, you can check the version of Reqtools.library (and whether you even have it) by typing version reqtools.library If the library is present, the version will be listed If the library is not present, an error message will be issued (eg Error: could not open reqtools.library) Copying Libraries via an Install Script, CLI Copy or Directory Utility If you need to copy mathtrans.library or mathieeedoubbas.library, you will find them in the libs directory on the standard Workbench disk distributed by Commodore for the release of Workbench that you are currently using. ReqTools.library (needed by Lyapunovia) and Req.library (for MandelPAUG) can be copied from their respective drawers on the FracStarter disk with a copy command such as copy FracStarter:Lyapunovia/install/libs13/reqtools.library to libs: or you could use the Install scripts provided; these will be simpler to use and less prone to typing errors. However, it is difficult to write scripts that work with all possible Amiga configurations, so if the install script doesn't work for you, use a CLI copy as described above, or (even easier) a directory utility to copy the libraries. (There are three good directory utilities on the Directory Utility Starter disk (START 2), and plenty of others available in the public domain or commercially.) FOLLOWING ON Having got through the preliminary stuff, guide notes (some quite lengthy) follow for the seven FracStarter programs. These are followed by brief notes on several other programs which I have found interesting and easy-to-use, and short descriptions of a few commercial programs. MANDEL MOUNTAINS MandelMountains produces exceptionally beautiful 3D fractals. The notes in this section apply to MandelMountains version 2.1 on FracStarter; this was distributed on Fish 383. An earlier (and very similar) version (2.0) comes on Fish 354 or GR 99. Both of these versions of MandelMountains worked fine for me. Starting Up There are two ways of starting MandelMountains from Workbench: . click on the MandelMountains icon (this will load the MandelMountains program but no image); or . click on the icon called Initial (this will start MandelMountains and load in the Mandelbrot picture called Initial). If you take the first approach, MandelMountains will open a small window on the Workbench screen, showing parameters which can be modified by typing in any field. The default parameters and settings are those for the Initial picture, with the screen option set to overscan interlace, and red-yellow colour range. If you click on the front/back gadget in the top right-hand corner of the Workbench screen, you will be switched to a blank black screen. This is MandelMountains' rendering screen, and it can be a bit disconcerting the first time you meet it. See below for how to exit this screen. If you take the second approach, MandelMountains will open the small window on the Workbench screen, load the Initial image and its parameters, and switch to the rendering screen to display the rendered image. The screen options for this image have been set to full-screen interlace, with a colour range of blue-cyan. If MandelMountains does not load OK from one of the icons, you may need to copy a couple of libraries to your Workbench boot disk (see the Libraries First section above). Exiting the Rendering Screen The standard way to exit the MandelMountains rendering screen, whether it is blank black, part-way through the process of rendering, or displaying a completed image, is to click once with the left mouse button (to select the screen) and once with the right mouse button to tell MandelMountains that you want to return to the Workbench screen. An alternative to this is to use one of the very handy Left-Amiga/n and Left-Amiga/m key combinations (see Swapping Screens above). Remember to click anywhere in the MandelMountains window to reactivate it after you have swapped back from another application. Things to Try Select Load Image from the menu. Experiment by changing the colours, or set the Mode to Julia instead of Mandelbrot. Select Suggest HZoom from Parameters menu. Or Zoom In, drag the mouse to outline the area (pushing the mouse away from you shrinks the zoom area, dragging it towards you expands it); press the right button to confirm the outlined area. Select Start Rendering. The screen will go black, and eventually the image will start to appear at the bottom of the screen area; it takes ages (faster for Small Screen option), so do something else while it works. To exit the picture screen, click anywhere on the screen with the left mouse button, and then with the right button; return to the screen via the Workbench front-back gadgets. To stop rendering at any time, click on STOP (bottom right corner of the window). Save Image (as an IFF) if you want to keep it. Leave the MMD1 header selected if you wish to be able to reload this fractal image into MandelMountains; you should only need to turn off this option if you wish to modify the picture in a Paint program that can't handle the MandelMountains chunk in the IFF (check that out). Loading Images/Parameters When you load the image called Initial, the completed picture is loaded and the screen swapped to display that image. When you load image parameters only (by loading one of the files from the Parameters or Extra.Parameters directories), the parameters are loaded and the display screen is blank black, but you have to create the image yourself with those parameters, by Start Rendering (choose the screen options you want first). These parameter files are actually IFFs that have been saved before any rendering has taken place; this is a nifty way of saving the parameters of any interesting MandelMountains pictures because the parameter IFFs take less than 3K, whereas a fully-rendered picture might take 100K. Varying the Colours Cycle through the colour variations by pressing F1 repeatedly, or use F2 to backtrack. This can be done at any time during the rendering process or after picture completion, and is the easiest way to choose the most effective colour scheme for any given picture. Correcting Faults Say, you do a zoom and the rendered result is a flat 2-dimensional picture with large uninteresting areas of colour. . Select small screen to save time while testing parameter changes. Generally, it is better to try one change at a time. You need only let each rendering process run long enough to see the effect of that change. . To get a more 3-D mountainous effect, increase HZoom (if it's 4.8, try 5.8 for example). . To reduce the area of colour, increase ColorMin (eg, from 32 to 38). . To get more colour variation, reduce ColorDiv (say, from 100 to 50); by this I mean that if ColorDiv is too high, most of the coloured areas will look the same colour. . To eliminate coloured contour lines as edging to all the coloured areas (which sometimes happens when you increase HZoom), increase HSmooth (say, from 100 to 150). Or if the coloured areas are large, reduce the area of colour by increasing ColorMin - this sometimes eliminates the unsightly coloured contour lines. . To remove vertical stripes from the image (usually at very high magnifications), choose double precision from the menu; this is much slower to render than single precision, and is not normally necessary. . Stop rendering (by clicking on the STOP gadget in the bottom right-hand corner of the MandelMountains window) before the picture is completed if black areas are filled with white near the end of the rendering process - this sometimes happens, and it can ruin the appearance of a masterpiece! Comment in Fractals Tutorial re DPaint In the "Mandelbrots and Fractals in Depth" tutorial on FracStarter or MD20, the author comments that he had trouble loading images created and saved with MandelMountains and FracGen into DeluxePaint (the version of DPaint is not stated) and couldn't display them with Display. I have had no trouble at all in loading IFFs saved from MandelMountains or FracGen (or from any of the other programs on FracStarter) into DeluxePaintIII or DeluxePhotoLab Paint and Colors. However, if you do have such problems, then you could (as suggested in the tutorial) save the screen image with a screensaver - I like PicSaver or ScreenX for such tasks. FRACGEN FracGen draws fractal images from `seeds'. It has a moderately primitive interface (it's an old program now) but it is very powerful, and quite easy to use once you get used to it. It needs mathtrans.library in libs:, as detailed above in Libraries First. It comes on FracStarter, Fish 188 or MegaDisc's GR 97. Starting and Swapping When FracGen is started, it briefly displays a `seed' diagram. It then swaps to the rendering screen and draws the fractal. To exit that screen and return to the main FracGen screen, you could use the same technique as in MandelMountains: click once with the left mouse button to select the screen, and then once with the right to swap screens. Or you could press F1 to flip between screens. You can also swap back to the rendering screen via the front/back gadget on the FracGen title bar, or swap to the Workbench screen via the Left-Amiga/n or m key combinations. From the rendering screen you can swap to Workbench by clicking near the top right hand corner, on an invisible front/back gadget. Parameter Files FracGen comes with a large number of parameter files, in the directory called Formulas. If you load any of these files, FracGen will go through the same process described for startup: it will display the seed then render the fractal. Many of these fractals are absolute wows; I particularly like a lot of the fractals in the ManMade directory, such as Curlicue, Slinky and Say Cheese! (and String Art is fascinating, but set aside a lot of time for this one). Palettes FracGen has 4 standard palettes which can be loaded from the Palettes directory (which is within the Formulas directory) via the Load menu item. After loading a palette, select Draw to redraw the fractal in the new colours. Things to Try Load all the parameter files - many of the fractals generated from them are superb. After making any changes, select Draw from the Fractal menu to render the new fractal. If you don't like the result, select Undo from the Project menu; this will undo all changes since the last Draw. Or you can stop plotting by hitting the Esc key. Select Detail or Depth from the Fractal menu, and change the value by moving the slider, then Draw. Load a different palette (see above). Select Move from the Edit menu, and drag one of the portions of the seed to left or right. Or select Add to let you add to the seed. If the fractal image is not centred on the screen when rendered, move the seed with the cursor keys and re-render. Saving You can save the parameters by selecting Save from the Project menu, or save the image as an IFF by selecting Save Pic. The requesters are primitive, and do not list hard drives in the volumes list. But hard drives can be accessed by typing the device address (such as dh0:) or drive name (such as BigDisk:) in the Drawer field of the requester. The requester then behaves in a normal Amiga fashion, displaying the list of directories on that disk, and allowing you to click down the levels. Enter the filename in the File gadget, and click on OK to save (or CANCEL to exit). LYAPUNOVIA Lyapunovia renders an unusual fractal set, with very striking images. The ones I like best look reminiscent of metal. On FracStarter, Lyapunovia (v1.0) has been dearchived from Fish 784 and is ready to use, except that you must have Reqtools.library in your libs: directory, as detailed above in the Libraries First section. General Usage When Lyapunovia is started, it immediately loads an image (the parameters of this image are in the Coordinates directory, called Startup Coordinates) on a lo-res non-interlaced 16-colour screen with Palette 1. When you change the coordinates (for instance, when you zoom to enclose an area and click on OK in the zoom requester), rendering will start automatically. Rendering in Lyapunovia always starts from the top of the screen, so if you have the Title bar across the top, you won't see anything happening until the rendered picture shows below that bar (but you can deselect Title bar to see it earlier if you wish). For easier swapping to Workbench, select Title bar from the Screen menu (or use Left-Amiga/n). Select Save IFF from the Program menu to save a picture, or select Save from the Image menu to save only the coordinates. Stop rendering at any time by selecting Stop from the Program menu. Things to Try Change the palette (see below) for dramatically different effects. Load an existing picture (such as Metal in the Lyapunovia drawer) by selecting Load IFF from the Program menu. Modify the coordinates from the Image menu: . select Coordinates and type figures directly into the coordinates fields, or . select a Zoom submenu item, hold down the left mouse button and drag the mouse to enclose an area, or . select Load to load a new set of coordinates from the Coordinates directory (there are many sets of coordinates in this directory). Palettes You can modify the palette, from the Screen menu. When you load a picture or set of coordinates, the rendered image uses the current screen palette. There are 4 preset palettes available; these are easy to use - just select the one you want from the menu. Or you can modify one of these palettes to any other colours via the Palette Edit menu item. The palette can be changed before loading a picture or changing coordinates; it can also be changed during rendering, but the process will temporarily halt while you are changing the palette. Another option is to load one of the palettes from the Palettes directory in the Lyapunovia drawer; there are many interesting colour combinations. Some are 16-colour palettes, and some are 32. If you load a palette of the same number of colours as the current palette, the image will immediately be displayed with the new palette. But if you change from a 16-colour palette to 32-colour or vice versa, the picture will be redrawn (after a warning message is issued), and the resolution may be changed first (there is a maximum of 16 colours in hi-res). Good Reading Read the sections in the Lyapunovia Doc file called Getting Started and Tips & Tricks; these contain many helpful suggestions for making best use of the program. SCENERY Scenery, a random scenery generator, is probably the easiest program on FracStarter to use (it was originally distributed on Fish 155, and also comes on MegaDisc's GR 97). It needs no prerequisite libraries - just click on its icon and away you go. Note that it opens an NTSC screen. Program documentation is sparse; there is no separate documentation file - all the doc is displayed from the About menu item. But the program is so straightforward to use that documentation is not really necessary. Things to Try Scenery opens with a random seed, an integer between 1 and 99999. To draw the picture related to that seed, select the menu item called Generate Scene - Use Same Seed. To use a different seed, select Generate Scene - Use New Seed. You can vary height, lighting position, water and view by selecting the appropriate menu items. A few interesting seed values to try (with, say, height 2000, water med, lighting behind right shoulder) are: 2813, 283, and 46875. Saving Pictures Pictures can be saved as IFFs. When you select Save, a requester pops up with a string gadget that allows a maximum of 19 characters for the full pathname. If you want to save the file with a longer pathname, it could first be saved temporarily as, say, ram:scenery1, and then that file could be copied (via CLI or directory utility) to floppy or hard disk. CLOUD Cloud comes on FracStarter, Fish 216, or GR 97, with very detailed documentation. It generates fractal surfaces that look like clouds. With the preset palettes available, these images can be made to look instead like pictures of water, or thermal diagrams, or land maps, and all of these palettes can be reversed easily by clicking on the REVERSE gadget in the control panel. The clouds are very realistic depictions of thin high cloud (the author calls them fracto-cumulus). Things to Try Some easy variations with this program include changing the palette by clicking on EARTH, WATER etc (the changes are displayed instantly), or changing the percentage from say 80% to 70% (delete the value first, then type in the new value) and clicking on GEN to generate the new image. Saving Screens The Save function is not operational, so to save images as IFFs you will need to use something like PicSaver or ScreenX. The images are in lo-res non-interlaced 320 x 200 size (including the control panel), and the clouds could be useful as scenic background in landscape pictures. BIOMORPH Biomorph (on FracStarter or MegaDisc 13), generates beautiful images with a biological theme. This program has a rather basic interface, but it is quite easy to use. It needs mathtrans.library in libs: (see the Libraries First section above). Starting Up When the program is started, it opens a small Biomorph input window on the Workbench screen and asks you to type in a value of 1 to 5. Enter the number (say, 4) and hit Return. You will then be asked for the next parameter: type a value, say, 4 (the decimal point doesn't matter) and hit Return. Similarly with the third and fourth values (eg, .5 and 0). The screen will be swapped to the rendering screen, and the image rendered. Rendering There is no title bar on the rendering screen, so to swap to Workbench while rendering is in progress you will need to use the Left-Amiga/n key combination. Rendering can be stopped early by clicking anywhere on the rendering screen with the left mouse button. When rendering is complete, the program will wait for you to click anywhere on the rendering screen with the left mouse button. It will then swap you to the next screen (which will probably be Workbench unless you have other applications running - if so, keep swapping screens until you get back to Workbench). Saving Pictures Biomorph will display a message in the Biomorph input window asking you whether you want to save the image. Click in the Biomorph window with the left mouse button to select that window, then type y if you want to save, n (or any other letter) if you don't. You will be asked to type in the full pathname of the file. Long pathnames will wrap on to the next line, but will be accepted, although the maximimum total pathname length is 28 characters and any longer names will be truncated. If the pathname is not valid (for example, if you misspell a directory name), then the image will not be saved and Biomorph will exit, so you'll lose the image. If you are unsure of the full pathname, the safest way would be to save the file in ram: with a very simple name (say, ram:bio1) and then copy the file to its final home straight afterwards via the CLI or a directory utility. Automatic Exit Biomorph will exit at the end of these processes. If you want to try another set of values, you will have to start Biomorph again. MANDELPAUG MandelPAUG (on FracStarter or Fish 452) is a fast, straightforward fractal program with many features. It has an excellent user interface and full online help files so I will say little about this program and leave you to explore it yourself. As noted above in the Libraries First section, MandelPAUG needs Req.library in libs: before running the program. The online help is initiated via the Info menu or the Help key; then, while the Help screen is on display, select the menu item you want explained. MandelPAUG operates only as an NTSC screen. The Title bar is optional. Try Color Cycling via the Project menu, Zoom In from the Location menu, or change the Iterations value or Fractal Type in the Calculations menu; each of these changes will produce dramatic changes in the image. OTHER INTERESTING FRACTAL PROGRAMS There are many excellent fractal programs other than those on FracStarter. Check out the two tutorial articles on FracStarter or MD20 and 21 for guidance on programs in the public domain, such as MandelVroom; below are short notes on a few of the more recent ones, and brief details of several commercial fractal programs. MandelVroom MandelVroom is one of the best fractal programs around. But it took almost an entire disk in its original distribution, and I think it is suited to more experienced Amiga users rather than beginners. So I didn't attempt to fit it on the FracStarter disk. However, once you have gained experience in using fractal programs, I recommend you try this superb program. It comes on Fish 215, with voluminous documentation and many presets. TreeGrow TreeGrow (on Fish 814) is a program which generates quasifractal trees or plants, and it comes with a small `library' of parameter sets with names such as Colorful, Cornflower etc. Although TreeGrow is easy to use, it did take me a bit to figure it out initially, so I thought I'd add a few notes about it here. It needs four libraries in libs: before it will run. When TreeGrow is started, it opens a small window on the Workbench screen. Near the bottom of that window are two arrow gadgets and a list of names of parameter sets stored in a file called TreeGrow.lib. One of these parameter sets will be highlighted (on starting up, Colorful will be highlighted). If you click on the arrow gadgets, the list will be scrolled, and different names will be highlighted one by one. If you click on the Use gadget, the name of the highlighted parameter set will be placed into the Name field, and its values will be entered into the various calculating fields above (in Size, Angle etc). Click on Start to generate the tree. A hi-res interlaced screen will be opened and the tree will be drawn. Press the right mouse button if you want to interrupt the drawing. When the drawing is completed, press the left mouse button to return to the main window. If you want to save the image as an IFF, click on the large Save button under the Start button. A requester will pop up - just click on the gadgets to specify path details, and add the filename. There is also a smaller Save button below the Name field - this is for saving parameter sets into the TreeGrow.lib file. Scene Generator Demo This is a self-running demo of an upgraded (commercial) version of Scenery. The new version produces much more realistic effects, including clouds, shading of the sky, and snowcaps on the mountains. It comes on Fish 299. Just click on its icon to initiate it; the demo runs for about 25 minutes, and can be terminated early by pressing either mouse button. Landscape Landscape (on Fish 554) is a fractal scenery generator written in AMOS and compiled so that it can be run from Workbench. It has many user adjustable parameters such as height, sea, tree and snow levels, beaches, lighting angles, and palette, with 2D (contour map) and 3D rendering. Some example sets of parameters are provided. This program does not have a very elegant interface but its results are quite impressive. Although it didn't seem to be documented, you can swap back and forth to Workbench by using the Left-Amiga/a key combination (instead of the more usual Left-Amiga/n or m). When you start Landscape, try out the program the easiest way by selecting Load Data from the Pictures menu, to load in one of the supplied data files. Select Calculate from the Data Points menu, and when it has finished calculating, select Render 3D from the Pictures menu. If you want to try entering your own parameters, select Parameters from the Data Points menu, type in the new values, and click on Quit to exit that routine with the new parameters. Then Calculate and Render 3D, as before. IFSgen This is by the same author as Landscape (and comes on Fish 554 too); it has similar interface deficiencies, and you can only swap to Workbench with the Left-Amiga/a combination. It is an Iterated Function System generator which generates pictures of ferns, trees, galaxies, snowflakes etc. For an initial tryout, select one of the presets (such as Fern) from the menu, and then select Generate from the Picture menu. Fractal Universe CD An excellent introduction to the world of fractals is provided by the Fractal Universe CD, available commercially for about $70. It contains 400 pre-generated fractal images (set up so that they can be displayed in slideshows), plus spoken tutorials covering the theory of fractals. Fractal Universe also contains several fractal-generating programs. Images created with these programs can be saved as IFFs, but as you can't reload any of these fractals for further modification, the CD could hardly be considered a serious fractal-creation tool. It is mainly a slideshow and tutorial, and it performs these functions well. MathVision MathVision is a top-class commercial fractal program by the author of FracGen, Doug Houck. I haven't seen this package, but it has received rave reviews, including a lengthy and enthusiastic review in MegaDisc23 (now also in MD.ReviewsIII) by Bob Eason. MathVision is rather pricey, but it seems to be regarded as an excellent tool for fractal-creation which gives value for money. A recent review of it in Amiga User International summed it up as "serious software that feels like a game", and said that "educators will also find it invaluable for injecting some fun into mathematics and encouraging pupils to want to learn". Other Commercial Programs Fractuality is another commercial fractal program which has received good reviews in British magazines, and it seems relatively inexpensive there at £25. It may not offer the scope of MathVision, and I don't know whether it is available in Australia. Scenery Animator and VistaPro are highly-praised fractal landscape generators, and both are available locally for about $130. FINALLY Well, that feels like enough nitty-gritty for one article. I do hope you enjoy trying out some of the excellent fractal programs now available. All sorts of people have, often to their surprise, discovered that fractals can be unbelievably addictive. I've certainly found this to be so. Fractals are fascinating. © Leigh Murray Queanbeyan NSW July 1993  ¿? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿*? 35 ¿?