This is the first beta version of FracPPC, which I hope to eventually develop into a full-featured fractal program. Even though some essential features are still missing, I wanted to make this available as soon as possible so that fractal fans with Power Macs can get a taste of the fractal exploration capabilities of the new machines.
This program has some significant limitations, the main ones being that the color palette cannot be edited (although random palettes may be generated), it does not generate any fractals other than the Mandelbrot set, and the plots cannot be copied to the clipboard nor saved as PICT files. All of these features will be added in future versions. On the other hand, plots of any size, limited only by the memory allocated to the program, may be generated, and plots may be printed directly to color printers.
Here is a brief rundown of the features and how to use the program:
New windows start out at 200 X 200 pixels. This may be changed by the user. Every window starts out displaying the entire Mandelbrot set.
To zoom into the picture, click at any point of the picture and the fractal will be regenerated with the point clicked on as the new center, at double the vertical and horizontal resolution. Holding down the option and/or command keys will modify this behavior as follows:
click — zoom in at double h & v res.
command-click — zoom in at 4 X h& v res.
option-click — zoom out at 1/2 h & v res.
command-option-click — zoom out at 1/4 h & v res.
Eventually you will want to change at least the dwell limit as you zoom in. In the parameter dialog box the following parameters are displayed:
Dwell Limit
Map Factor
Pixels (h & v)
Center (real & imag)
Resolution
Any of these may be changed. The Map Factor also appears in the Color Map dialog box, explanation appears below. The horizontal and vertical pixels must be changed if you want to change the size of the fractal picture. The Center and Resolution determine what portion of the complex plane is being displayed. Normally you don't have to mess with these, but you can set them if you know the coordinates that you want to look at. The resolution is the area of the complex plane being displayed (therefore it is reduced by 1/4 every time you click in the fractal window and it is reduced by 1/16 every time you command-click). If you need to zoom in or out slightly (by less than the factor acheivable by clicking) you can do so by tweaking the resolution value.
The Color Map dialog box allows you to set parameters associated with the color map.
The Mapping Exponent is the same as the Map Factor in the Parameters dialog box. It allows you to change the way the dwells are mapped to the color palette. However, it is possible to change this factor directly via the cursor keys without bringing up the dialog box — this is almost always preferable because you can step through map factors rapidly and see the effect on the fractal picture.
Dwells are mapped to color values according to a power law. Initially a linear table is generated so that each dwell d is mapped to a color c(d). If the map factor is f and the maximum dwell is dmax, then the color assigned to d is:
c(dmax*(d/dmax)^f)
f > 1 maps dwells to higher values and f < 1 maps them to lower values.
The left and right arrow cursor keys reduces and increases the map factor respectively by about 5%. Holding down the modifier keys modifies the increment as follows:
no modifier: 5%
control: 10%
option: 2.5%
control-option: 1%
Holding down the cursor key will cause the map factor to change continuously. This somtimes causes a kaleidescopic effect similar to palette animation (try this on file "Sample 8," for example).
The up arrow cursor key will return the map factor to one.
The Map Limits pop-up menu controls how the minimum and maximum dwell values mapped by the color map are determined:
"Auto" means that the minimum and maximum dwell values will be automatically remapped to the minimum & maximum value seen in the last fractal generated.
"Fixed" requires the user to set the minimum and maximum values manually. Any dwell below the minimum will be mapped to the minimum value, any dwell above the maximum will be mapped to the maximum value.
"Wrap" is like "Fixed" except that any dwell value above the maximum is folded back into the minimum/maximum range (in other words, the color map will repeat itself).
In order to explain the other settings in the Color Map dialog box, we need to understand how the color map is constructed. Between the dwell minimum and maximum there can be an abitrary number of dwell breakpoints, or "breaks" for short. The minimum and maximum dwell value are themselves considered to be breaks. There is a color assigned to each break. For any dwell between two breaks, the color is detemined by calculating the gradient between the two bracketing breaks.
The random palette functions generates a random number of breaks, and assigns a random color to each break. The Color Map dialog box allows you to set the maximum number of breaks to be generated randomly (the maximum allowed for this value is 32). Also, "Randomize Color Breakpoints" randomizes the distrubution of breakpoints; if this is not set, the breakpoints are distributed uniformly between the minimum and maximum dwells.
Preferences lets you choose to save generated dwell values along with the other parameters. This allows you to open fractals pretty much instantaneously, but it can eat up disk space. You will find that the fractals generate rapidly enough that you may not want to sacrifice the disk space to save the dwells. This option will move to the Save file dialog in some future version.
The Fractal Generation Time slice determines how much time (in milliseconds) will be devoted to generating the fractal before yielding time to other processes. The default is 50 milliseconds, which leaves FracPPC perfectly responsive to clicks on menus, etc. You will note, however, in the statistics window that the elapsed time (the time that elapsed while the fractal was generated) is usually about twice as long as the CPU time (the time actually spent in calculation). You can reduce the elapsed time by increasing the time slice, at the expense of responsiveness. You can set this to any value from 10 milliseconds to 2000 milliseconds (2 seconds).
Preferences are not saved when you quit the application. This will change in a future release.
The Palette menu contains a few palettes, and the Randomize function, which can also be invoked via Command-R. Ususally, you will hit Command-R until you see an appealing palette, followed by tweaking the power law factor with the left and right arrow keys.
Printing: multiple pages are not currently printed. Don't specify a picture to be printed that is bigger than your page size unless you intend to use reduction in the Page Setup box.
Pictures smaller than the printed page are centered on the page horizontally and vertically. On some printers like the HP good results can be obtained by generating a very large fractal picture and then printing at 50% reduction. This is also highly recomended for monochrome pictures. Make sure to allocate enough memory for FracPPC if you intend to do this.
As far as saving files goes, the file format is bound to change significantly in the future, but I will do what I can about using files generated by 1.0b1 with future versions. The actual internal structure of a color map is likely to change significantly in future versions, so this may limit my ability to read in color maps saved with a fractal image.
The following features are going to appear in future versions, along with better documentation. I list them in the appoximate order of priority.
• Full color editing of the fractal's color palette.
• Speed-up algorithms (Contour crawling, etc. These don't seem as necessary with the speed the PowerPC can knock fractals out with, but it would still be useful for the large files one might want to generate for printing.
• Support for 16 and 32 bit screen depths. Also probably more options for rendering 8 bit images (for instance, generating a 16 or 32 bit off-screen image and using this to generate an 8 bit dithered image, or generating a high-res off-screen image and producing an anti-aliased image on-screen).
• Extendibility (so the user can add new fractals).
Being a beta version, the current version is bound to have bugs, so be careful. I haven't had any crashes with it lately, but prudence would dictate that you should not run it while you have other apps running with documents open that are not backed up.
