.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 of the selected set is plotted in a 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 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 causes the current region to be replotted the size of the drawn rectangle. o Clicking causes the region covered by the rectangle to be redrawn in the current window. o Clicking 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.