Club Amiga de Montreal - CAM/CAM_CD_1.iso/files/376.lha/HPFrac_v1.0/HPFrac.DOC

Text File | 1990-04-01 | 9KB | 176 lines

                             Documentation for
                               HPFrac  v 1.0
                                     by
                               Alex Takessian


   Yet another fractal program!  Yes, but this time it plots the
Mandelbrot set at up to 300 dpi on a LaserJet or DeskJet printer.  Thats
3000 x 2400 dots!  It can also do it at 75, 100, and 150 dpi.


    This program is freely distributable as long as you don't make ANY cash
profit from it (you can trade it though.)

                Send any constructive comments by EMAIL to:
                 Alex Takessian     Compuserve [75655,223]


     I tired of printing the typical 640 x 400 plots on my Deskjet.  I
wanted full resolution plots so I wrote this program.  I hope you find it
fun too.  It easily produces publication-quality Mandelbrot images
especially if the distance-estimation plotting method is used.

     The program works only from the CLI because I wanted to write portable
code that could be compiled and run on other computer types.  I easily
ported it to PC-DOS and compiled it with Microsoft C v 5.0.  Interestingly,
the DOS version running on a COMPAQ 386 Deskpro (16MHz 80386, 80287) runs
about 7 times slower than the AMIGA version running on an A2000/A2630.

     Note that HPFrac only works with a LaserJet or DeskJet -- no other
printers are supported.  Sorry.  The program will either generate a file
which can be copied to the PAR: device or it can directly write to the PAR:
device.  If you generate to a file, be aware that your file device (RAM,
FLOPPY, HARD, etc.) must be capable of storing about 10 * dpi * dpi bytes.
That is over 900K for a 300 dpi plot.  To write directly to the PAR: device
you just specify PAR: when the program asks for a filename.  When you write
directly to the PAR: device, the storage requirements are very low, but it
ties up your printer for a long time.  I prefer to write to a file because
the file can be archived and saved for re-printing at a later time.
Anything less than a 300 dpi plot can easily be written to a floppy file.
So, if you've got enough RAM, then its best to generate to a RAM file.
Otherwise, generate to a HARD disk file or Floppy file or directly to the
PAR: device (in that order.)

     This program (actually HPFrac_6888x) is really meant for the power
users because it eats up CPU cycles like crazy.  If you've got an
accelerator board (Imtronics, Hurricane, GVP, CSA, A2620, A2630, etc.) this
program is for you.  It'll really give your accelerator something to sink
its teeth into.  It's written in optimized Lattice C V5.04.  It could be
made faster through assembly programming and fixed-point math, but I felt
that would limit its scope and portability too much.  Since the math is
carried out in floating-point, any portion of the Mandelbrot set can be
plotted without the quantization errors common in the fixed-point programs.
The quantization problem would be extremely severe in the distance-
estimation mode where the dynamic range of the numbers is very large.

     The 6888x and the IEEE versions use double-precision math while the
FFP version uses single-precision math.  The IEEE and FFP versions were
included because I didn't want to leave anyone out.  So even if you don't
have any kind of accelerator, you can still produce exceptional fractal
plots -- you just have to wait longer.  Waiting is not too bad if you run
HPFrac as a background task with a priority of -1 and just leave your
machine on all the time.  You should use the version which is fastest on
your hardware configuration.  The IEEE version is great for those of you
who have a 68881/2 installed as a peripheral processor (such as in the
Processor Accelerator board.)  The 6888x version only works if you have a
68010, 68020, or 68030 processor with a 68881/2 as a coprocessor.  The FFP
version is good if you have no accelerator or if your do have one but it
doesn't have math coprocessor or peripheral math processor installed yet.

     In addition to the standard worn-out iteration limit and iteration
modulus plotting, this program offers magnitude modulus, binary phase,
quaternary phase, phase modulus, and distance estimation.  Orbit cycle
detection is used throughout to speed-up the calculations when inside the
Mandelbrot set.

     The program is accompanied by a file called HPFrac.DAT.  This .DAT
file contains several interesting locations of the Mandelbrot set and is
the main input to the program.  When you run HPFrac, you are asked which of
the locations in the .DAT file you want to plot.  The locations have names.
To see them, just TYPE the file out (ie TYPE HPFrac.DAT.)  The .DAT file is
easily edited with the ED editor, so you can add your own favorite
locations or modify the current ones.  Actually, I first find an
interesting place with one of the many excellent graphical Mandelbrot
graphers (I prefer MandFXP by CygnusSoft), then I enter those coordinates
into the HPFrac.DAT file and run HPFrac to generate the plot.  The format
of the .DAT file is:

Imaginary range, Real range, Iteration limit, NAME

The Imaginary range is the narrow width of the plot on the paper.  This
corresponds to the vertical direction on the screen for the graphical
Mandelbrot programs.  The Real range is the long direction of the paper
plot and corresponds to the horizontal direction on the screen.  The
iteration limit is the same as on the graphical programs.  It specifies the
maximum number of iterations spent on each point to determine if it lies in
the Mandelbrot set.  The name is there as a descriptive label.  You can
make up your own names.  Descriptions of the various plotting modes follow.

Iteration Limit
This mode plots a dot only when the iteration limit limit is reached for
that value of C represented by the dot.

Iteration Modulus
This plots a point if (iterations / divisor) mod 2 is equal to 1.  Where
iterations is the number of times the Mandelbrot equation can be iterated
before the iteration limit is reached or before the iteration becomes
unstable.  This creates a contour map of iteration values.  The divisor
determines the width of each contour band.  This is the mode most graphical
Mandelbrot programs work in.  They plot the contour bands in different
colors and the colors repeat over and over.

Magnitude Modulus
The Mandelbrot set is those points in C which satisfy Z(n+1) = Z(n)^2 + C
for the number of iterations specified by the iteration limit.  This
selection plots a point if (100 * |Z| / divisor) mod 2 is equal to 1.  The
symbol, |Z| is the complex magnitude of Z at the maximum number of stable
iterations.  This looks best for macro features of the set such as in the
"WholeSet" selection in HPFrac.DAT.  It makes a contour plot of the
magnitude of Z with the contour band width given by the divisor.

Binary Phase
This plots a point if phase(Z) at the maximum number of stable iterations
is either in quadrants I & II or in quadrants II & III.  The choice is made
at the beginning of the program.  This makes interesting plots of the
phase.

Quaternary Phase
This plots a point if phase(Z) at the maximum number of stable iterations
is either in quadrants I & III or in quadrants II & IV.  The choice is made
at the start of the program.  This is typically called the Binary Phase
Decomposition of the Mandelbrot set and makes very interesting plots.

Phase Modulus
This plots a point if (100 * phase(z) / divisor) mod 2 is equal to 1.  This
gives a plot of the phase just like the Magnitude Modulus give the plot of
the magnitude at the maximum number of stable iterations.  This is good for
macro features.

Distance Estimation
This is similar to the Iteration Limit mode except that a threshold value
is specified which allows the plot to reveal much more intricate detail.
This method generates the best plots I've ever seen.  This method is also
the slowest because it does a lot more calculation to determine if a given
point is close enough to the Mandelbrot set to be considered a part of it.
A small threshold will find fewer points.  A threshold of zero is exactly
like the Iteration Limit mode.  A large threshold finds more points.  I
find a value of 0.000001 works well most of the time for plots with
iteration limits > 500.  For Iteration Limits < 500, the suggested 0.00001
works well.  Also, for this mode, increasing the iteration limit improves
the resolution of the plot.  This is unlike the plain Iteration Limit mode
where increasing the limit will eliminate peripheral Mandelbrot points.  It
is those peripheral points which reveal the infinite beauty of this set.

     The program will also ask if you want aspect restoration.  It is a
good idea to answer yes unless you want distorted aspect for a special
effect.  Aspect restoration guarantees that there will be no aspect
distortion in the generated plot even if the ranges specified in HPFrac.DAT
have distorted aspect.  Note that the ranges I've specified in HPFrac.DAT
do have some distortion in them.

     To get acquainted with the program, run it on "WholeSet."  This will
plot the entire Mandelbrot set.  Try the different plotting modes at 75 dpi
to get a rough idea of what they do.  You should get plots rather quickly
at 75 dpi.


Enjoy!
Alex Takessian
CIS [75655,223]