``````NAME
Math::Fractal::Julia - Calculate points in the Julia set

VERSION
version 0.000003

SYNOPSIS
use Math::Fractal::Julia;

# Procedural usage:
Math::Fractal::Julia->set_max_iter(\$iters);
Math::Fractal::Julia->set_limit(\$limit);
Math::Fractal::Julia->set_bounds( \$x1, \$y1, \$x2, \$y2, \$w, \$h );
Math::Fractal::Julia->set_constant( \$cx, \$cy );
for my \$y ( 0 .. \$h - 1 ) {
for my \$x ( 0 .. \$w - 1 ) {
my \$iter = Math::Fractal::Julia->point( \$x, \$y );
}
}

# Object Oriented usage:
my \$julia = Math::Fractal::Julia->new(%options);
\$julia->set_max_iter(\$iters);
\$julia->set_limit(\$limit);
\$julia->set_bounds( \$x1, \$y1, \$x2, \$y2, \$w, \$h );
\$julia->set_constant( \$cx, \$cy );
for my \$y ( 0 .. \$h - 1 ) {
for my \$x ( 0 .. \$w - 1 ) {
my \$iter = \$julia->point( \$x, \$y );
}
}

DESCRIPTION
Calculates points in the set named after the French mathematician Gaston
Julia.

The procedural interface is based on that provided by
Math::Fractal::Mandelbrot.

METHODS
new
Arguments: %options?
Return value: A Math::Fractal::Julia object

Creates a new Math::Fractal::Object. If no options are provided, the
default values will be used.

options
The "options" hash may contain any or all of the following:

max_iter => \$iters

limit => \$limit

bounds => [ \$x1, \$x2, \$y1, \$y2, \$width, \$height ]

constant => [ \$cx, \$cy ]

The default maximum number of iterations is 600. The default limit is 5.
The default bounds is [-2.2, -1.1, 1.0, 1.1, 640, 480]. The default
constant is [0.0, 0.0].

my \$julia = Math::Fractal::Julia->new();

my \$julia = Math::Fractal::Julia->new(%options);

my \$julia = Math::Fractal::Julia->new(
max_iter => \$iters,
limit    => \$limit,
bounds   => [ \$x1, \$x2, \$y1, \$y2, \$width, \$height ],
constant => [ \$cx, \$cy ],
);

set_max_iter
Arguments: \$max
Return value: undefined

Set the maximum number of iterations. The default value is 600.

Math::Fractal::Julia->set_max_iter(\$max);

\$julia->set_max_iter(\$max);

set_limit
Arguments: \$limit
Return value: undefined

The default value is 5.

Math::Fractal::Julia->set_limit(\$limit);

\$julia->set_limit(\$limit);

set_bounds
Arguments: \$x1, \$y1, \$x2, \$y2, \$width, \$height
Return value: undefined

Set the bounds of the set. The first four values (\$x1, \$y1, \$x2, \$y2)
define a rectangle. The remaining two (\$width, \$height) define a
viewport.

The default values are (-2.2, -1.1, 1.0, 1.1, 640, 480).

Math::Fractal::Julia->set_bounds( \$x1, \$y1, \$x2, \$y2, \$width, \$height );

\$julia->set_bounds( \$x1, \$x2, \$y1, \$y2, \$width, \$height );

set_constant
Arguments: \$cx, \$cy
Return value: undefined

The default values are (0.0, 0.0).

Math::Fractal::Julia->set_constant( \$cx, \$cy );

\$julia->set_constant( \$cx, \$cy );

point
Arguments: \$x, \$y
Return value: The number of iterations needed to exceed the limit or 0
if the the limit is not exceeded.

This function translates the coordinates using the bounds and then
iterates.

\$iters = Math::Fractal::Julia->point( \$x, \$y );

\$iters = \$julia->point( \$x, \$y );

CAVEATS
*   This module is not thread-safe.

*   Any packages derived from "Math::Fractal::Julia" will share the same
internal state when the procedural interface is used.

*   Math::Fractal::Mandelbrot

*   Julia set <http://en.wikipedia.org/wiki/Julia_set>

AUTHOR
Jeffrey T. Palmer <jtpalmer@cpan.org>