ppmforge(1) UNIX System V(25 October 1991) ppmforge(1)
NAME
ppmforge - fractal forgeries of clouds, planets, and starry skies
SYNOPSIS
ppmforge [-clouds] [-night] [-dimension dimen] [-hour hour] [-
inclination|-tilt angle] [-mesh size] [-power factor] [-glaciers
level] [-ice level] [-saturation sat] [-seed seed] [-stars
fraction] [-xsize|-width width] [-ysize|-height height]
DESCRIPTION
ppmforge generates three kinds of ``random fractal forgeries,'' the term
coined by Richard F. Voss of the IBM Thomas J. Watson Research Center for
seemingly realistic pictures of natural objects generated by simple
algorithms embodying randomness and fractal self-similarity. The
techniques used by ppmforge are essentially those given by Voss[1],
particularly the technique of spectral synthesis explained in more detail
by Dietmar Saupe[2].
The program generates two varieties of pictures: planets and clouds,
which are just different renderings of data generated in an identical
manner, illustrating the unity of the fractal structure of these very
different objects. A third type of picture, a starry sky, is synthesised
directly from pseudorandom numbers.
The generation of planets or clouds begins with the preparation of an
array of random data in the frequency domain. The size of this array,
the ``mesh size,'' can be set with the -mesh option; the larger the mesh
the more realistic the pictures but the calculation time and memory
requirement increases as the square of the mesh size. The fractal
dimension, which you can specify with the -dimension option, determines
the roughness of the terrain on the planet or the scale of detail in the
clouds. As the fractal dimension is increased, more high frequency
components are added into the random mesh.
Once the mesh is generated, an inverse two dimensional Fourier transform
is performed upon it. This converts the original random frequency domain
data into spatial amplitudes. We scale the real components that result
from the Fourier transform into numbers from 0 to 1 associated with each
point on the mesh. You can further modify this number by applying a
``power law scale'' to it with the -power option. Unity scale leaves
the numbers unmodified; a power scale of 0.5 takes the square root of the
numbers in the mesh, while a power scale of 3 replaces the numbers in the
mesh with their cubes. Power law scaling is best envisioned by thinking
of the data as representing the elevation of terrain; powers less than 1
yield landscapes with vertical scarps that look like glacially-carved
valleys; powers greater than one make fairy-castle spires (which require
large mesh sizes and high resolution for best results).
After these calculations, we have a array of the specified size
containing numbers that range from 0 to 1. The pixmaps are generated as
follows:
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Clouds A colour map is created that ranges from pure blue to white by
increasing admixture (desaturation) of blue with white.
Numbers less than 0.5 are coloured blue, numbers between 0.5
and 1.0 are coloured with corresponding levels of white, with
1.0 being pure white.
Planet The mesh is projected onto a sphere. Values less than 0.5 are
treated as water and values between 0.5 and 1.0 as land. The
water areas are coloured based upon the water depth, and land
based on its elevation. The random depth data are used to
create clouds over the oceans. An atmosphere approximately
like the Earth's is simulated; its light absorption is
calculated to create a blue cast around the limb of the planet.
A function that rises from 0 to 1 based on latitude is
modulated by the local elevation to generate polar ice caps--
high altitude terrain carries glaciers farther from the pole.
Based on the position of the star with respect to the observer,
the apparent colour of each pixel of the planet is calculated
by ray-tracing from the star to the planet to the observer and
applying a lighting model that sums ambient light and diffuse
reflection (for most planets ambient light is zero, as their
primary star is the only source of illumination). Additional
random data are used to generate stars around the planet.
Night A sequence of pseudorandom numbers is used to generate stars
with a user specified density.
Cloud pictures always contain 256 or fewer colours and may be displayed
on most colour mapped devices without further processing. Planet
pictures often contain tens of thousands of colours which must be
compressed with ppmquant or ppmdither before encoding in a colour mapped
format. If the display resolution is high enough, ppmdither generally
produces better looking planets. ppmquant tends to create discrete
colour bands, particularly in the oceans, which are unrealistic and
distracting. The number of colours in starry sky pictures generated with
the -night option depends on the value specified for -saturation. Small
values limit the colour temperature distribution of the stars and reduce
the number of colours in the image. If the -saturation is set to 0, none
of the stars will be coloured and the resulting image will never contain
more than 256 colours. Night sky pictures with many different star
colours often look best when colour compressed by pnmdepth rather than
ppmquant or ppmdither. Try newmaxval settings of 63, 31, or 15 with
pnmdepth to reduce the number of colours in the picture to 256 or fewer.
OPTIONS
-clouds Generate clouds. A pixmap of fractal clouds is generated.
Selecting clouds sets the default for fractal dimension to 2.15
and power scale factor to 0.75.
-dimension dimen
Sets the fractal dimension to the specified dimen, which may be
any floating point value between 0 and 3. Higher fractal
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dimensions create more ``chaotic'' images, which require higher
resolution output and a larger FFT mesh size to look good. If
no dimension is specified, 2.4 is used when generating planets
and 2.15 for clouds.
-glaciers level
The floating point level setting controls the extent to which
terrain elevation causes ice to appear at lower latitudes. The
default value of 0.75 makes the polar caps extend toward the
equator across high terrain and forms glaciers in the highest
mountains, as on Earth. Higher values make ice sheets that
cover more and more of the land surface, simulating planets in
the midst of an ice age. Lower values tend to be boring,
resulting in unrealistic geometrically-precise ice cap
boundaries.
-hour hour
When generating a planet, hour is used as the ``hour angle at
the central meridian.'' If you specify -hour 12, for example,
the planet will be fully illuminated, corresponding to high
noon at the longitude at the centre of the screen. You can
specify any floating point value between 0 and 24 for hour, but
values which place most of the planet in darkness (0 to 4 and
20 to 24) result in crescents which, while pretty, don't give
you many illuminated pixels for the amount of computing that's
required. If no -hour option is specified, a random hour angle
is chosen, biased so that only 25% of the images generated will
be crescents.
-ice level
Sets the extent of the polar ice caps to the given floating
point level. The default level of 0.4 produces ice caps
similar to those of the Earth. Smaller values reduce the
amount of ice, while larger -ice settings create more prominent
ice caps. Sufficiently large values, such as 100 or more, in
conjunction with small settings for -glaciers (try 0.1) create
``ice balls'' like Europa.
-inclination|-tilt angle
The inclination angle of the planet with regard to its primary
star is set to angle, which can be any floating point value
from -90 to 90. The inclination angle can be thought of as
specifying, in degrees, the ``season'' the planet is presently
experiencing or, more precisely, the latitude at which the star
transits the zenith at local noon. If 0, the planet is at
equinox; the star is directly overhead at the equator.
Positive values represent summer in the northern hemisphere,
negative values summer in the southern hemisphere. The Earth's
inclination angle, for example, is about 23.5 at the June
solstice, 0 at the equinoxes in March and September, and -23.5
at the December solstice. If no inclination angle is
specified, a random value between -21.6 and 21.6 degrees is
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chosen.
-mesh size
A mesh of size by size will be used for the fast Fourier
transform (FFT). Note that memory requirements and computation
speed increase as the square of size; if you double the mesh
size, the program will use four times the memory and run four
times as long. The default mesh is 256x256, which produces
reasonably good looking pictures while using half a megabyte
for the 256x256 array of single precision complex numbers
required by the FFT. On machines with limited memory capacity,
you may have to reduce the mesh size to avoid running out of
RAM. Increasing the mesh size produces better looking
pictures; the difference becomes particularly noticeable when
generating high resolution images with relatively high fractal
dimensions (between 2.2 and 3).
-night A starry sky is generated. The stars are created by the same
algorithm used for the stars that surround planet pictures, but
the output consists exclusively of stars.
-power factor
Sets the ``power factor'' used to scale elevations synthesised
from the FFT to factor, which can be any floating point number
greater than zero. If no factor is specified a default of 1.2
is used if a planet is being generated, or 0.75 if clouds are
selected by the -clouds option. The result of the FFT image
synthesis is an array of elevation values between 0 and 1. A
non-unity power factor exponentiates each of these elevations
to the specified power. For example, a power factor of 2
squares each value, while a power factor of 0.5 replaces each
with its square root. (Note that exponentiating values between
0 and 1 yields values that remain within that range.) Power
factors less than 1 emphasise large-scale elevation changes at
the expense of small variations. Power factors greater than 1
increase the roughness of the terrain and, like high fractal
dimensions, may require a larger FFT mesh size and/or higher
screen resolution to look good.
-saturation sat
Controls the degree of colour saturation of the stars that
surround planet pictures and fill starry skies created with the
-night option. The default value of 125 creates stars which
resemble the sky as seen by the human eye from Earth's surface.
Stars are dim; only the brightest activate the cones in the
human retina, causing colour to be perceived. Higher values of
sat approximate the appearance of stars from Earth orbit, where
better dark adaptation, absence of skyglow, and the
concentration of light from a given star onto a smaller area of
the retina thanks to the lack of atmospheric turbulence
enhances the perception of colour. Values greater than 250
create ``science fiction'' skies that, while pretty, don't
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occur in this universe.
Thanks to the inverse square law combined with Nature's love of
mediocrity, there are many, many dim stars for every bright
one. This population relationship is accurately reflected in
the skies created by ppmforge. Dim, low mass stars live much
longer than bright massive stars, consequently there are many
reddish stars for every blue giant. This relationship is
preserved by ppmforge. You can reverse the proportion,
simulating the sky as seen in a starburst galaxy, by specifying
a negative sat value.
-seed num Sets the seed for the random number generator to the integer
num. The seed used to create each picture is displayed on
standard output (unless suppressed with the -quiet option).
Pictures generated with the same seed will be identical. If no
-seed is specified, a random seed derived from the date and
time will be chosen. Specifying an explicit seed allows you to
re-render a picture you particularly like at a higher
resolution or with different viewing parameters.
-stars fraction
Specifies the percentage of pixels, in tenths of a percent,
which will appear as stars, either surrounding a planet or
filling the entire frame if -night is specified. The default
fraction is 100.
-xsize|-width width
Sets the width of the generated image to width pixels. The
default width is 256 pixels. Images must be at least as wide
as they are high; if a width less than the height is specified,
it will be increased to equal the height. If you must have a
long skinny pixmap, make a square one with ppmforge, then use
pnmcut to extract a portion of the shape and size you require.
-ysize|-height height
Sets the height of the generated image to height pixels. The
default height is 256 pixels. If the height specified exceeds
the width, the width will be increased to equal the height.
All flags can be abbreviated to their shortest unique prefix.
BUGS
The algorithms require the output pixmap to be at least as wide as it is
high, and the width to be an even number of pixels. These constraints
are enforced by increasing the size of the requested pixmap if necessary.
You may have to reduce the FFT mesh size on machines with 16 bit integers
and segmented pointer architectures.
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SEE ALSO
pnmcut(1), pnmdepth(1), ppmdither(1), ppmquant(1), ppm(5)
[1] Voss, Richard F., ``Random Fractal Forgeries,'' in Earnshaw et. al.,
Fundamental Algorithms for Computer Graphics, Berlin: Springer-
Verlag, 1985.
[2] Peitgen, H.-O., and Saupe, D. eds., The Science Of Fractal Images,
New York: Springer Verlag, 1988.
AUTHOR
John Walker
Autodesk SA
Avenue des Champs-Montants 14b
CH-2074 MARIN
Suisse/Schweiz/Svizzera/Svizra/Switzerland
Usenet: kelvin@Autodesk.com
Fax: 038/33 88 15
Voice: 038/33 76 33
Permission to use, copy, modify, and distribute this software and its
documentation for any purpose and without fee is hereby granted, without
any conditions or restrictions. This software is provided ``as is''
without express or implied warranty.
PLUGWARE! If you like this kind of stuff, you may also enjoy ``James
Gleick's Chaos--The Software'' for MS-DOS, available for $59.95 from your
local software store or directly from Autodesk, Inc., Attn: Science
Series, 2320 Marinship Way, Sausalito, CA 94965, USA. Telephone: (800)
688-2344 toll-free or, outside the U.S. (415) 332-2344 Ext 4886. Fax:
(415) 289-4718. ``Chaos--The Software'' includes a more comprehensive
fractal forgery generator which creates three-dimensional landscapes as
well as clouds and planets, plus five more modules which explore other
aspects of Chaos. The user guide of more than 200 pages includes an
introduction by James Gleick and detailed explanations by Rudy Rucker of
the mathematics and algorithms used by each program.
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