.t General
                     General Information on the Explorer

This Mandelbrot Set Explorer computes and plots functions defined on the
complex plane.  The functions are computed by repeatedly evaluating a
complex polynomial until the magnitude of the value exceeds 2.0 or a maximum
of 1000 iterations have been performed.  The number of iterations required
to exceed the limit is the value that is plotted. Three different functions
may be plotted. (See the "Function" menu item.) 

The Explorer translates the iteration count into a color and plots a pixel of
that color at the point in the image that represents the point in the complex
plane where the polynomial was evaluated.  Using the mouse you can select the
region of the complex plane to be plotted and the size of the window to dis-
play it in.  (See help on "Navigation".)  

Other options allow you to vary the mapping between iteration counts and
plotted colors (See help on "Coloring", "Rainbows", and "Scaling".), the
display mode, the whether a 2- or 3-dimensional view is plotted.
.t Actions
                             The "Actions" Menu

Help    - Displays help text such as this.
Load    - Loads a previously saved image from disk.
Save    - Saves the current image to disk as an ILBM file.  This file may be
          read by a paint program such as DPaint. Partially plotted images 
          may be saved. Plotting will be resumed when the image is reloaded.
Print   - Prints the current image.  (Currently ignores preferences)
Colors  
  Load     - Loads the color pallette from any ILBM file, such as the image
             and color files generated by the Explorer.
  Save     - Saves the current color palette.
  Display  - Opens a window on the screen that shows the current color
             palette.  Selecting this item again, turns the window off.
Reset
  Window   - Resets the plotting area to the full screen.
  Region   - Resets the plotted region to enclose the entire set.
  Both     - Resets the window and the region.
Banner  - Toggles the screen banner, which shows the plotting region.
Quit    - Exits the Explorer.  There is no failsafe on this selection.
.t Options
                             Other Menu Options

Function  - Selects which function is to be plotted by the Explorer.

Screen    - Selects between high and low resolution and interlaced and
            non-interlaced display modes.

Scale     - The Explorer uses a logrithmic function to map iteration counts
            into the color to be plotted. With the scaling at /1, values
            over 300 are assigned the color white, those over 1000 are 
            assigned the color black, the rest use approximately two cycles
            of the color palette. As you explore regions very close to the
            set, the plots will get very "busy" unless you increase the
            scale factor, which has the effect of assigning more counts to
            the same color.

View      - Selects between a 2-dimensional or a 3-dimensional plot.

Plotting restarts after a Function, Screen, Scale, or View item is selected.
The Window and Region are not affected.
.t Navigation
                          Navigating the Set

A <region> of the selected set is plotted in a <window> in the center of
the screen. The region is defined in the banner [toggled by Right-Amiga-B].
The screen outside the window is white.

You change the region and/or the size of the window by drawing a <rectangle>
on the screen with the mouse:

 - Move the cursor to a corner of the rectangle and press the left button.
 - While pressing the left button, drag the cursor to the opposite corner.
 - Release the left button and a small "What's New" requester appears:
   o Clicking <Window> causes the current region to be replotted the size of
     the drawn rectangle.
   o Clicking <Region> causes the region covered by the rectangle to be
     redrawn in the current window.
   o Clicking <Both> causes the region defined by the rectangle to be 
     redrawn in the current window.

If the window and region have different aspect ratios, the region is 
enlarged so that it has the same aspect ratio as the window.
.t Coloring
                          Coloring the Set

Scaled counts over 300 are always plotted in white. Counts over 1000 are
always plotted in black.  The remaining counts are plotted from a palette
of 29 (13 in hires) other colors, which you may redefine.

The palette of colors used to plot each set is controlled by keys on the
keyboard. These are always active, so you can get instant feedback on the
color settings.  The coloring of each set is very important in bringing
out desired detail. (See also scaling.)

The palette is constructed by varying the intensity of the red, green, and
blue portions of the color accross the color numbers according to a family
of sine waves.  You can control the relative phasing of the red, green, and
blue components, as well as the steepness of the curves.

You can also shift and permute the mapping between counts and colors.

The best way to learn how the keys work, is to bring up the "Colors" window
using Right-Amiga-C and watch the changes as you press the keys.
.t Rainbows
                        Controling The Rainbow

The following keys control coloring

NKP-7,-4    Moves the point of highest Red intensity up and down in the
            color map.
NKP-8,-5    Moves the point of highest Green intensity up and down in the
            color map.
NKP-9,-6    Moves the point of highest Blue intensity up and down in the
            color map.

(NKP stands for "Numeric Key Pad")

Left Arrow  Decreases the rate at which the intensity of the colors
            diminishes as they get farther away from the point of highest
            intensity.
Right Arrow Increases the rate of change in intensity.

Up Arrow    Cycles the color map one position.
Down Arrow  Cycles the color map one position in the opposite direction.

Space Bar   Permutes the color map.
.t Scaling
                               Scaling

/n means that the iteration count is divided by n before looking it up in
the color map.

As a rule of thumb, the scaling should be set so that on the first pass of
the plot, most of the pixels are colored.
.t Hints
                                Hints

   -  To find a region you'd like to plot, start from the title image and
      draw a rectangle around the region you'd like to see.  Select the
      Region option on the What's New requester.  The screen will clear and
      selected region will be plotted.  

   -  To see if it's the region you wanted, draw a small rectangle on the
      screen and select the Window option on the What's New requester. The
      selected region will now be drawn in the small window.

   -  If the region isn't centered properly, draw another rectangle that
      covers the region you really want and select a new region.  This 
      rectangle can overlap the borders of the window so it's possible to 
      shift the plotted region in any direction.  If the rectangle is smaller
      than the window, the new region will be enlarged, if it's larger,
      the new region will be reduced.

   -  When you have the region you want, use the "Screen" menu to set the
      display resolution, and then use the "Reset Window" item in the 
      "Actions" menu to start a full screen plot.
      
