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ppmforge(1) General Commands Manual 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 embody-
ing 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 gen-
erated 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 num-
ber 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 eleva-
tion 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 re-
sults).
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:
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 corre-
sponding 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 plan-
et. 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 pp-
mdither 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 de-
pends 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 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 ter-
rain 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 speci-
fied, 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 set-
tings 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 south-
ern 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 speci-
fied, a random value between -21.6 and 21.6 degrees is 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 be-
comes particularly noticeable when generating high resolution images with relatively high fractal dimen-
sions (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 synthe-
sis 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 fac-
tor 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 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 ppm-
forge. 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 ex-
tract 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.
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 Graph-
ics, 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 AT 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 as-
pects of Chaos. The user guide of more than 200 pages includes an introduction by James Gleick and detailed explana-
tions by Rudy Rucker of the mathematics and algorithms used by each program.
25 October 1991 ppmforge(1)
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