Computer Explorations of Fractals, Chaos,Complex Systems, and Adaptation

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 MANDEL Documentation

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```

NAME

```       mandel - make a plot the Mandelbrot set

```

SYNOPSIS

```       mandel -help
or
mandel [-width integer] [-height integer] [-maxit integer]
[-levels  integer]  [-bail  double]  [-ulx  double]
[-uly  double]  [-lly double] [-box integer] [-bulx
double] [-buly double] [-blly double] [-idiv  inte-
ger] [-rev] [-inv] [-mag integer] [-term string]

```

DESCRIPTION

```       The  Mandelbrot  set  is  drawn according to the specified
parameters.  The image is computed by iterating  the  com-
plex  equation  z(t) = (z(t-1))^2 + c, where c is the com-
plex point (x + yi) that corresponds to an (x,  y)  screen
coordinate and the initial value of z(0) = 0.  If the sys-
tem diverges at time k (i.e., |z(k)| > BAIL) then a  point
at  (x, y) is plotted with the grayscale color (k / IDIV +
(k % IDIV) * (LEVELS / IDIV)) % LEVELS), which reduces  to
(k % LEVELS) with an IDIV of 1.

```

OPTIONS

```       -width integer
Width of the plot in pixels.

-height integer
Height of the plot in pixels.

-maxit integer
Maximum number of iterations before automatic bail-
out.

-levels integer
Number of plot (gray) levels to use.

-bail double
Value of |z| to end iteration,  i.e.,  the  bailout
value.

-ulx double
Upper-left corner x-coordinate.

-uly double
Upper-left corner y-coordinate.

-lly double
Lower-left corner y-coordinate.

-box integer
Line width for a box.  If zero, no box is drawn.

-bulx double
Box's upper-left x-coordinate.

-buly double
Box's upper-left y-coordinate.

-blly double
Box's lower-left y-coordinate.

-idiv integer
Iteration  divisor.    When  greater than one, this
creates a banding effect.

-rev   Reverse all colors but first?

-inv   Invert all colors?

-mag integer
Magnification factor.

-term string
How to plot points.

```

COLORS

```       The four permutations of using or not using -rev and  -inv
will  yield  four  different coloring schemes.  Try it and
see.

```

MISCELLANY

```       The method for  choosing  the  viewable  region  may  seem
counter-intuitive  at  first, but it has some nice proper-
ties.  In particular, selecting the exact (x,  y)  coordi-
nates  for  the  upper-left  corner and only selecting the
lower right y coordinate forces both the x and y scales to
be  identical  since all scales are uniquely determined by
these values along with the plot width and height.  If you
then  change the width or height of the plot, the relative
scales will still match up.  The options for making a  box
work similarly.

```

BUGS

```       No  sanity  checks  are performed to make sure that any of
the options make sense.  In particular, the bounding  cor-
ners  can  be  screwed  up, and division by zero can occur
with a malicious setting of IDIV.

```

AUTHOR

```       Copyright (c) 1997, Gary William Flake.

Permission granted for any use according to  the  standard
GNU ``copyleft'' agreement provided that the author's com-
ments are neither modified nor removed.   No  warranty  is
given or implied.

```