*** BIOMORPH ***
     By Terry Newton

Biomorphs were invented when IBM researcher Clifford Pickover had a bug in a
fractal program that resulted in strange radial spikes eminating out of a
fractal body. His strange new discoveries were covered by A.K.Dewdney in the
July 1989 issue of Scientific American. A perfect opportutity to write a
program to explore this new Biomorph universe.

Biomorphs are generated in a mannor similar to plotting Julia sets.
Points are iterated through a formula and the size of the iterate is used to
determine each pixel color. The formula takes the form of Z=something(Z)+C
with Z and C being complex numbers. C is held constant to a specific point
and the starting value of Z sweeps through the range to plot, usually within
+-5 real and imaginary. Each pixel is iterated until either the real or
imaginary component of Z exceeds absolute 10 or the absolute size of Z
exceeds 10 (or whatever other number) or the iteration limit is reached.
Pixels that both the real and imaginary components exceed 10 are plotted.
In color mode color 0 is for both components less than 10, color 1 for real
less than 10, color 2 for imaginary less than 10 and color three for
both components over 10.

Something(Z)+C can be almost any formula imaginable. Pickover used complex
sines and powers to generate some of his more exotic images. In this program
I stick to integer powers in the form of Z^2+C, Z^3+C, Z^4+C and Z^5+C.
These produce some pretty bizarre images and being not an expert on complex
math I haven't tried complex sines and other way-over-my-head methods.
I just like the pictures.

After loading BIOMORPH (with BASIC off) you will see the main menu with the
following selections: New, Continue, Save, Load, Magnify, View, Parameters,
Files, Alter colors and DOS. The first letter engages the function.

The variables that control the plot are Real Center, Imaginary Center,
Plot Range, Formula #, Iteration Limit, Size Limit and Resolution Low or High.
New parameters can be manually entered with New or displayed with Parameters.
Continue starts plotting the image from the last point plotted. Just press
[C] after loading to make a sample image. During the plotting process you can
speed things up by pressing [F] for screen off fast mode. Press [S] to restore
the screen. Press [ESC] to return to the menu.

After making a plot or partial plot use the Save function to put it on disk.
Enter a filename of up to 8 characters. The drive number defaults to D1: or the
drive specified in the Files function. The extension defaults to .PIC
if none specified.

The Load function retrieves saved image files from disk after getting a
file name. If the plot is not done you can use Continue.

View simply displays the image without the menu window.

To zoom in on areas of interest use the Magnify function. Crosshairs will
appear on the image you can move with the cursor keys. After placing on the
area of interest press RETURN to get the magnify menu. The coordinates will
be shown with the choices Magnify, Find again, Set or Return to Menu. After
selecting Magnify enter a number to enlarge by. After returning to the menu
select Continue to plot the image or New to modify the parameters. Press
RETURN to keep the value of any variable. The Set option converts a point
from a SCOPE file into a new plot. After loading in a Mandelbrot file from
SCOPE the variables will be wrong except for real, imag and range.
Go to Magnify to choose an image point then use Set to fix the variables
to produce a Biomorph plot.

Files displays a list of .PIC files after selecting drive 1 to 8, which
becomes the default drive.

Alter Colors displays a color menu to change the plotting colors. [C] changes
the color register, [H] changes the hue value and [L] changes the luminance.
[S] saves the colors internally to use as defaults. [R] restores the defaults.
Press any other key for the main menu.

DOS returns control to the operating system after confirming. Under SpartaDos
the graphics is kept intact so you can re-enter the program by using the
RUN command.