------------------------------------------------------------------ FRACTAL.EXE ------------------------------------------------------------------ FRACTAL.EXE can generate three different types of fractals: Mandelbrot, Julia, and Lyapunov. FRACTAL.EXE is not meant as general fractal exploration devices. It was written as a means of generating landscape for use with VistaPro. You can control several of the parameters of the fractals. After saving them they can be further manipulated by VistaPro. All three types of fractals are mathematical objects. They have infinite complexity (although the calculating precision of computers limits the amount of complexity that can be rendered) and can make for interesting and unusual landscapes. These fractal landscapes use a different method of generation than VistaPro does. VistaPro's fractal landscapes are intended to mimic real landscapes but FRACTAL.EXE's are just "pictures" of the three mathematical objects. FRACTAL.EXE uses the same type of graphical user interface as VistaPro. It also uses the same file requestor. You can refer to the VistaPro manual for general instructions on how menus, buttons, and gadgets work. FRACTAL.EXE requires a VGA graphics card and a Microsoft compatible mouse. This document makes no attempt to explain what these fractals are or the mathematics behind them. You should be able to find many books at your local bookstore which describe fractals and iterated functions. ------------------------------------------------------------------ PROJECT MENU ------------------------------------------------------------------ Project --> Spawn DOS --------------------- This menu item allows you to start a DOS command line while keeping FRACTAL.EXE in memory. When you return to FRACTAL.EXE all your settings will be intact. This function allows you to perform any DOS functions without quitting FRACTAL.EXE. For instance, you could format a new diskette for saving your landscapes. To exit from the DOS and return to FRACTAL.EXE you should type EXIT at the DOS prompt. Project --> Save DEM -------------------- This item saves the current landscape as a VistaPro DEM file. You will be allowed to select the directory and filename of the file using the file requestor. Project --> Quit ---------------- Select this item when you are done exploring and wish to quit the program. ------------------------------------------------------------------ FRACTAL MENU ------------------------------------------------------------------ Fractal --> Lyapunov -------------------- This item selects the Lyapunov type landscape. It also resets many the settings on the control panel to the defaults for this type of landscape. Fractal --> Mandelbrot ---------------------- This item selects the Mandelbrot type landscape. It also resets many of the settings on the control panel to the defaults for this type of landscape. Fractal --> Julia ----------------- This item selects the Julia type landscape. It also resets many of the settings on the control panel to the defaults for this type of landscape. ------------------------------------------------------------------ HEIGHT MENU ------------------------------------------------------------------ Height --> Linear ----------------- This menu item selects linear heights in the landscape. Calculated values are used exactly as is in the landscape. For example, a mandelbrot escape time of 10 becomes 10 meters, 20 becomes 20 meters etc. Height --> Sqrt --------------- This menu item selects square root heights in the landscape. The sqare root of calculated values are used in the landscape. For example, a mandelbrot escape time of 9 becomes 3 meters, 16 becomes 4 meters etc. Use this altitude type if you want to compress a wide range of altitudes into a smaller range. Height --> Log -------------- This menu item selects logrithmic heights in the landscape. The log (base 10) of calculated values are used in the landscape. For example, a mandelbrot escape time of 10 becomes 1 meter, 100 becomes 2 meters etc. Use this altitude type if you want to compress a very wide range of altitudes into a smaller range. ------------------------------------------------------------------ CONTROL PANEL ------------------------------------------------------------------ Lyapunov Control String ----------------------- This is the control string which determines which of the two lyapunov equations is executed for each iteration. Only the least sinificant bit of each character is acually used so the letter "a" is the same as the letter "c" is the same as the letter "e" etc.... and "b" = "d" = "f" etc.... All you really need to know is that changing this character string will change the landscape -- different control strings will lead to different landscapes. We allow you to use all letters of the alphabet so you can generate landscapes based on your name or any text that you want. This string is only used in the generation of lyapunov landscapes. Start X ------- The topographic map area is a window onto the two dimesional mathmatical plane. Start X is the coordinate of the horizontal coordinate of the left edge of the topographic window. You can reposition the window by typing a new value into this gadget. Gererally, all the intersting parts of all three fractal types fall within the range of -2 to +2 on both the X and Y axis. Start Y ------- The topographic map area is a window onto the two dimesional mathmatical plane. Start Y is the coordinate of the vertical coordinate of the bottom edge of the topographic window. You can reposition the window by typing a new value into this gadget. Gererally, all the intersting parts of all three fractal types fall within the range of -2 to +2 on both the X and Y axis. Size ---- This value controls the range (on the X and Y axis) that the topographic window covers. For example, a value of 2.0 means that the window will cover a range of 2.0 accross the X and Y axis of the topographic map. If the Start X value is 1.0 then the window will cover the range from 1.0 to 3.0 on the horizontal axis. Julia X ------- This represents the coordinate on the Mandelbrot set for which the gernerated Julia set is based. This is the "real" part of the coordinate. As with the Start X value, most of the interesting values will range from -2 to +2. This value is only used in generating Julia landscapes. Julia Y ------- This represents the coordinate on the Mandelbrot set for which the gernerated Julia set is based. This is the "imaginary" part of the coordinate. As with the Start Y value, most of the interesting values will range from -2 to +2. This value is only used in generating Julia landscapes. Seed ---- This is starting value used to generate Lyapunov landscapes. It should be set between 0 and 1. It's value becomes less and less critical as the interation count is raised. Iteratns -------- This controls the maximum number of iterations allowed before "timing out" on calculations of all three objects. The larger you make this value the longer calculations will take -- but larger values will also bring out additional detail. VScale ------ This controls the vertical scale of the landscape. Large values will result in landscapes with tall features, smaller values will result in flatter landscapes. This setting is used for all three fractal types. "Good" values range from 1000 to 5000 but you are free to enter small or larger values. Zoom Var -------- This is the variable zoom function. It allows you to zoom into or out of a section of the fractal object. After selecting the button you must mark a box on the topomap to zoom in to. Use the mouse (position and click the left mouse button) to select both corners of the area of interest. If you mark an area smaller than the topographic map you will zoom in to that area. If you mark an area larger than the topographic area you will zoom out to that area. Zooming in or out changes the Start X, Start Y, and Size variables. Generation of the new area will start automatically. Zoom +2x -------- This button allows you to zoom in two fold onto the fractal object. After selecting the button you must select the area to zoom into by moving the visible box over the area of interest and pressing the left mouse button. Zooming in or out changes the Start X, Start Y, and Size variables. Generation of the new area will start automatically. Zoom -2x -------- This button allows you to zoom out two fold onto the fractal object. You have no further choise of area, the window is simply expanded two fold around the current center of the topographic window. Zooming in or out changes the Start X, Start Y, and Size variables. Generation of the new area will start automatically. Generate -------- This initiates the generation of a new fractal landscape using the current settings. Generation is not automatic when you change some of the settings since it is assumed that you might also want to change some of the other settings. In these cases you will need to use the Generate button to start calculating a new landscape. Escape ------ You can press the escape key to terminate the generation of the current landscape. When the program is done with the current horizontal line it will stop calculating and you will be able to change other settings or quit.