NAME

Math::Fractal::Noisemaker - Visual noise generator

VERSION

This document is for version 0.100 of Math::Fractal::Noisemaker.

SYNOPSIS

use Math::Fractal::Noisemaker qw| :all |;

#
# use defaults
#
make();

#
# override defaults
#
make(type => 'gel',
  # ...
);

A wrapper script, make-noise, is included with this distribution.

#
# use defaults
#
make-noise

#
# override defaults
#
make-noise -type gel

#
# usage
#
make-noise -help

make-noise -help types

Noise sets are just 2D arrays, which may be generated directly using named functions.

use Math::Fractal::Noisemaker qw| :flavors |;

my $grid = square(%args);

#
# Look up a value, given X and Y coords
#
my $value = $grid->[$x]->[$y];

Imager can take care of further post-processing.

my $grid = perlin(%args);

my $img = img($grid,%args);

#
# Insert image manip methods here!
#

$img->write(file => "oot.png");

DESCRIPTION

Math::Fractal::Noisemaker provides a simple functional interface for generating 2D fractal (or non-fractal) noise.

If the specified side length is a power of the noise's frequency, this module will produce seamless tiles (with the exception of a few noise types). For example, a base frequency of 4 works for an image with a side length of 256 (256x256).

FUNCTION

• make(type => $type, out => $filename, %ARGS)

  #
  # Just make some noise:
  #
  make();
  
  #
  # Care slightly more:
  #
  my ( $grid, $img, $filename ) = make(
    #
    # Any MAKE ARGS or noise args here!
    #
  );

Creates the specified noise type (see NOISE TYPES), writing the resulting image to the received filename.

Unless seriously tinkering, make may be the only function you need. make-noise, included with this distribution, provides a CLI for this function.

Returns the resulting dataset, as well as the Imager object which was created from it and filename used.

MAKE ARGS

In addition to any argument appropriate to the type of noise being generated, make accepts the following args in hash key form:

• type => $noiseType

  The type of noise to generate, defaults to perlin. Specify any type.

  make(type => 'gel');

• sphere => $bool

  

  Generate a pseudo-spheremap from the resulting noise.

  When specifying sphere, the output image will be 50% of the len you asked for. This is done to avoid aliasing. Multiply the supplied len argument by 2 to work around this.

  See spheremap.

  make(sphere => 1);

• refract => $bool

  

  "Refracted" pixel values. Can be used to enhance the fractal appearance of the resulting noise. Often makes it look dirty.

  make(refract => 1);

• clut => $filename

  Use an input image as a color lookup table

  This feature is a work in progress.

  make(clut => $filename);

• clutdir => <0|1|2>

  0: Hypotenuse lookup (corner to corner, so it doesn't matter if the input table is oriented horizontally or vertically).

  

  This is the default. Best for seamless tiling.

  make(clut => $filename, clutdir => 0);

  1: Vertical lookup, good for generating maps which have ice caps at the poles and tropical looking colors at the equator.

  

  Output will have color seams at the poles unless viewed on a spheroid. This lookup method produces output which resembles a reflection map, if a photograph is used for the clut.

  make(clut => $filename, clutdir => 1);

  2: Fractal lookup, uses the same methodology as refract. Also good for seamless tiling.

  

  make(clut => $filename, clutdir => 2);

• limit => <0|1>

  0: Scale the pixel values of the noise set to image-friendly levels

  1: Clamp pixel values outside of a representable range

  make(limit => 1);

• quiet => <0|1>

  Don't spam console

  make(quiet => 1);

• out => $filename

  Output image filename. Defaults to the name of the noise type being generated.

  make(out => "oot.bmp");

• shadow => $float

  

  Amount of self-shadowing to apply, between 0 and 1.

• emboss => <0|1>

  

  Render lightmap only

NOISE TYPES

SINGLE-RES NOISE

Single-res noise types may be specified as a multi-res slice types (stype)

• white

  

  Each non-smoothed pixel contains a pseudo-random value.

  See SINGLE-RES ARGS for allowed arguments.

• wavelet

  

  Basis function for sharper multi-res slices

  See SINGLE-RES ARGS for allowed arguments.

• square

  

  Diamond-Square

  See SINGLE-RES ARGS for allowed arguments.

• gel

  

  Self-displaced white noise.

  See SINGLE-RES ARGS and GEL TYPES for allowed arguments.

• sgel

  

  Self-displaced Diamond-Square noise.

  See SINGLE-RES ARGS and GEL TYPES for allowed arguments.

• dla

  

  Diffusion-limited aggregation, seeded from multiple random points.

  See SINGLE-RES ARGS for allowed arguments.

  bias and amp currently have no effect.

• mandel

  

  Fractal type - Mandelbrot. Included as a demo.

  See SINGLE-RES ARGS and FRACTAL ARGS for allowed arguments.

  bias and amp currently have no effect.

  Example maxiter value: 256

• dmandel

  

  Fractal type - Deep Mandelbrot. Picks a random "interesting" location in the set (some point with a value which neither hovers near 0 nor flies off into infinity), and zooms in a random amount (unless an explicit zoom arg was provided).

  See SINGLE-RES ARGS and FRACTAL ARGS for allowed arguments.

  bias and amp currently have no effect.

  Example maxiter value: 256

• buddha

  

  Fractal type - "Buddhabrot" Mandelbrot variant. Shows the paths of slowly escaping points, density-mapped to escape time.

  See SINGLE-RES ARGS and FRACTAL ARGS for allowed arguments.

  bias and amp currently have no effect. This type does not zoom well, due to the diminished sample of escaping points.

  Example maxiter value: 4096

• julia

  

  Fractal type - Julia. Included as demo.

  See SINGLE-RES ARGS and FRACTAL ARGS for allowed arguments.

  bias and amp currently have no effect.

  zoom is not yet implemented for this type.

  Example maxiter value: 200

• djulia

  

  Fractal type - Deep Julia. Zoomed in to a random location, which might not even be in the Julia set at all. Not currently very smart, but pretty, and pretty slow. maxiter is very low by default.

  See SINGLE-RES ARGS and FRACTAL ARGS for allowed arguments.

  bias and amp currently have no effect.

  zoom is not yet implemented for this type.

  Example maxiter value: 200

• newton

  

  Fractal type - Newton. Included as demo.

  Currently, this function is ridiculously slow.

  See SINGLE-RES ARGS and FRACTAL ARGS for allowed arguments.

  bias and amp currently have no effect.

  zoom is not yet implemented for this type.

  Example maxiter value: 10

• fflame

  

  IFS type - "Fractal Flame". Work in progress. Slow but neat.

  See SINGLE-RES ARGS and FRACTAL ARGS for allowed arguments.

  bias and amp currently have no effect.

  Example maxiter value: 6553600

• fern

  

  IFS type - Barnsley's fern. Included as a demo.

• gasket

  

  IFS type - Sierpinski's triangle/gasket. Included as a demo.

• stars

  

  White noise generated with extreme gap, and smoothed

  See SINGLE-RES ARGS for allowed arguments.

  bias and amp currently have no effect.

• spirals

  

  Tiny logarithmic spirals

  See SINGLE-RES ARGS for allowed arguments.

  bias and amp currently have no effect.

• voronoi

  

  Ridged Voronoi cells.

  bias and amp currently have no effect.

• moire

  

  Interference pattern with blended image seams.

  Appearance of output is heavily influenced by the freq arg.

  bias and amp currently have no effect.

• textile

  

  Moire noise with a randomized and large freq arg.

  bias and amp currently have no effect.

• infile

  Import the brightness values from the file specified by the "in" or "-in" arg.

  my $grid = infile(
    in => "dirt.bmp"
  );

• intile

  

  Calls infile, and makes a seamless repeating tile from the image.

  my $grid = intile(
    in => "dirt.bmp"
  );

• sparkle

  

  Stylized starfield

  bias and amp currently have no effect.

• canvas

  

  Unsmoothed square noise with perpenticular linear blur

SINGLE-RES ARGS

Single-res noise types accept the following arguments in hash key form:

• amp => <0..1>

  Amplitude, or max variance from the bias value.

  For the purposes of this module, amplitude actually means semi- amplitude (peak-to-peak amp/2).

  make(amp => 1);

• freq => $int

  Frequency, or "density" of the noise produced.

  For the purposes of this module, frequency represents the edge length of the starting noise grid.

  make(freq => 8);

• len => $int

  Side length of the output images, which are always square.

  make(len => 512);

• bias => <0..1>

  "Baseline" value for all pixels, .5 = 50%

  make(bias => .25);

• smooth => <0|1>

  Enable/disable noise smoothing. 1 is default/recommended

  make(smooth => 0);

• gap => <0..1>

  Larger values increase the chance for black pixels in white noise (which many noise types are derived from).

  make(type => "white", gap => .995);

FRACTAL ARGS

• zoom => $num

  Magnifaction factor.

  make(type => 'mandel', zoom => 2);

• maxiter => $int

  Iteration limit for determining infinite boundaries, larger values take longer but are more accurate/look nicer.

  make(type => 'mandel', maxiter => 2000);

MULTI-RES TYPES

Perlin (multi-res) noise combines the values from multiple 2D slices (octaves), which are generated using successively higher frequencies and lower amplitudes.

The slice type used for generating multi-res noise may be controlled with the stype argument. Any single-res type may be specified.

The default slice type is smoothed wavelet noise.

• perlin

  

  Multi-resolution noise.

  See MULTI-RES ARGS for allowed args.

  make(type => 'perlin', stype => '...');

• ridged

  

  Ridged multifractal.

  See MULTI-RES ARGS for allowed args.

  Provide zshift arg to specify a post-processing bias.

  make(type => 'ridged', stype => '...', zshift => .5 );

• block

  

  Unsmoothed multi-resolution.

  See MULTI-RES ARGS for allowed args.

  make(type => 'block', stype => ...);

• pgel

  

  Self-displaced multi-res noise.

  See MULTI-RES ARGS and GEL TYPES for allowed args.

  make(type => 'pgel', stype => ...);

• fur

  

  Fur-lin noise; traced paths of worms with multi-res input.

  See MULTI-RES ARGS for allowed args.

• tesla

  

  Long, fiberous worm paths with random skew.

  See MULTI-RES ARGS for allowed args.

• lumber

  

  Persistent noise with heavy banding.

  Looks vaguely wood-like with the right clut.

  See MULTI-RES ARGS for allowed args.

• wormhole

  

  Noise values displaced according to field flow rules, and plotted.

  amp controls displacement amount (eg 8).

  See MULTI-RES ARGS for allowed args.

• flux

  

  Noise values extruded in three dimensions, and plotted.

  amp controls extrusion amount (eg 8).

  See MULTI-RES ARGS for allowed args.

MULTI-RES ARGS

In addition to any of the args which may be used for single-res noise types, Perlin noise types accept the following arguments in hash key form:

• octaves => $int

  e.g. 1..8

  Octave (slice) count, increases the complexity of Perlin noise. Higher generally looks nicer.

  my $blurry = make(octaves => 3);
  
  my $sharp = make(octaves => 8);

• persist => $num

  Per-octave amplitude multiplicand (persistence). Traditional and default value is .5

  my $grid => make(persist => .25);

• stype => $simpleType

  Perlin slice type, defaults to wavelet. Any single-res type may be specified.

  my $grid = make(stype => 'gel');

DUAL NOISE

Dual noise contains two noise sets of the same type.

• delta

  

  Difference noise; output contains absolute values of subtracting two noise sets.

  make( type => "delta" );

  Use ltype to specify any single-res or perlin layer type. If specifying a perlin layer type, you may also specify stype to override the slice type.

  make(
    type => "delta",
    ltype => "gel"
  );

• chiral

  

  Twin noise; output contains the lightest values of two noise sets.

  make( type => "chiral" );

  Use ltype to specify any single-res or perlin layer type. If specifying a perlin layer type, you may also specify stype to override the slice type.

  make(
    type => "chiral",
    ltype => "tesla"
  );

• stereo

  

  Stereoscopic depth map.

  Use ltype to specify any single-res or perlin layer type. If specifying a perlin layer type, you may also specify stype to override the slice type.

COMPLEX NOISE

Complex noise is a homebrew noise recipe inspired by (but not using) libnoise.

• complex

  

  Complex layered noise

  make(type => "complex");

  This function generates a noise base and multiple noise layers. Each pixel in the resulting noise is blended towards the value in the noise layer which corresponds to the reference value in the noise base. Finally, the noise base itself is very slightly superimposed over the combined layers.

  my $grid = complex();

  Hundreds of noise variants (many of them quite interesting visually) may be generated through this function, by combining different base types, layer types, and slice types.

  my $grid = complex(
    lbase => <any noise type but complex>,
    ltype => <any noise type but complex>,
    stype => <any single-res type>,
    # ...
  );

In addition to all single-res and Perlin args, complex noise accepts the following args in hash key form:

• feather => $num

  e.g. 0..255

  Amount of blending between different regions of the noise.

  make(type => 'complex', feather => 50);

• layers => $int

  Number of complex layers to generate

  make(type => 'complex', layers => 4);

• lbase => $noiseType

  Complex layer base - defaults to "perlin". Any type except for complex may be used.

  make(type => 'complex', lbase => 'gel');

• ltype => $noiseType

  Complex layer type - defaults to "perlin". Any type except for complex may be used.

  make(type => 'complex', ltype => 'gel');

GEL TYPES

The single-res and Perlin "gel" types (gel, sgel, pgel) accept the following additional arguments:

• displace => $float

  Amount of self-displacement to apply to gel noise

  make(type => 'gel', displace => .125);

MORE FUNCTIONS

• img($grid,%args)

  my $grid = perlin();
  
  my $img = img($grid,%args);
  
  #
  # Insert Imager image manip stuff here!
  #
  
  $img->write(file => "oot.png");

  Returns an Imager object from the received two-dimensional grid.

• clamp($value)

  Limits the received value to between 0 and 255. If the received value is less than 0, returns 0; more than 255, returns 255; otherwise returns the same value which was received.

  my $clamped = clamp($num);

• noise($grid, $x, $y)

  The so-called "noise function" required to generate coherent noise. Returns the same "random" value each time it is called with the same arguments (makes it more like a key hashing function a la memcached doesn't it? Not very random, if you ask me).

  Math::Fractal::Noisemaker diverges from most Perlin implementations in that its noise function simply utilizes a lookup table. The lookup table contains pre-populated random values. Turns out, this works fine.

• lerp($a, $b, $x)

  Linear interpolate from $a to $b, by $x percent. $x is between 0 and 1.

• coslerp($a, $b, $x)

  Cosine interpolate from $a to $b, by $x percent. $x is between 0 and 1.

• smooth($grid, %args)

  #
  # Unsmoothed noise source
  #
  my $grid = white(smooth => 0);
  
  my $smooth = smooth($grid,%args);

  Perform smoothing of the values contained in the received two-dimensional grid. Returns a new grid.

  Smoothing is on by default.

• spheremap($grid, %args)

  Generates a fake (but convincing) spheremap from the received 2D noise grid, by embellishing the polar regions.

  Re-maps the pixel values along the north and south edges of the source image using polar coordinates, slowly blending back into original pixel values towards the middle.

  Returns a new 2D grid of pixel values.

  my $grid = perlin(%args);
  
  my $spheremap = spheremap($grid,%args);

  See MAKE ARGS

• refract($grid,%args)

  Return a new grid, replacing the color values in the received grid with one-dimensional indexed noise values from itself. This can enhance the "fractal" appearance of noise.

  my $grid = perlin(%args);
  
  my $refracted = refract($grid);

  See MAKE ARGS

• displace($grid,%args)

  Use the received grid as its own displacement map; returns a new grid.

  The amount of displacement is controlled by the displace arg.

  See GEL TYPES

SEE ALSO

Imager, Math::Trig

Math::Fractal::Noisemaker is on GitHub: http://github.com/aayars/noisemaker

Noisemaker borrows inspiration and/or pseudocode from these notable sources.

- http://freespace.virgin.net/hugo.elias/models/m_perlin.htm
  Perlin

- http://gameprogrammer.com/fractal.html
  Diamond-Square

- http://graphics.pixar.com/library/WaveletNoise/paper.pdf
  Wavelet (Pixar)

- http://www.complang.tuwien.ac.at/schani/mathmap/stills.html
  Moire (MathMap)

- http://libnoise.sourceforge.net/
  Libnoise is pro

- http://flam3.com/flame.pdf
  Fractal Flame

- http://en.wikipedia.org/wiki/File:Demj.jpg
  C<julia> and C<jdist> functions ported from "Julia set using
  DEM/J" by Adam Majewski

- http://vlab.infotech.monash.edu.au/simulations/fractals/
  C<newton> function ported from "Fractals on the Complex Plane"

... and a host of others.

AUTHOR

Alex Ayars <pause@nodekit.org>

COPYRIGHT

 File: Math/Fractal/Noisemaker.pm

 Copyright (C) 2009, Alex Ayars <pause@nodekit.org>

 This program is free software; you can redistribute it and/or modify
 it under the same terms as Perl 5.10.0 or later. See:
 http://dev.perl.org/licenses/

cpanm Math::Fractal::Noisemaker

perl -MCPAN -e shell
install Math::Fractal::Noisemaker