ppmforge - fractal forgeries of clouds, planets, and starry skies
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]
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-simi-
larity. The techniques used by ppmforge are essentially those given by Voss, particu-
larly the technique of spectral synthesis explained in more detail by Dietmar Saupe.
The program generates two varieties of pictures: planets and clouds, which are just dif-
ferent 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 in-
creased, 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 unmodi-
fied; 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; pow-
ers 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:
Clouds A colour map is created that ranges from pure blue to white by increasing admix-
ture (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 lati-
tude is modulated by the local elevation to generate polar ice caps--high alti-
tude 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 speci-
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 thou-
sands 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 pro-
duces better looking planets. ppmquant tends to create discrete colour bands, particular-
ly 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 -satura-
tion. 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 pic-
tures 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.
-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.
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.
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.
When generating a planet, hour is used as the ``hour angle at the central merid-
ian.'' If you specify -hour 12, for example, the planet will be fully illumi-
nated, 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 cres-
cents 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 cres-
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 promi-
nent 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.
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 tran-
sits the zenith at local noon. If 0, the planet is at equinox; the star is di-
rectly overhead at the equator. Positive values represent summer in the north-
ern 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 in-
clination angle is specified, a random value between -21.6 and 21.6 degrees is
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. In-
creasing 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
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 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 di-
mensions, may require a larger FFT mesh size and/or higher screen resolution to
Controls the degree of colour saturation of the stars that surround planet pic-
tures 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 percep-
tion 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 relation-
ship 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 gal-
axy, 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 par-
ticularly like at a higher resolution or with different viewing parameters.
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.
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.
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 in-
creased to equal the height.
All flags can be abbreviated to their shortest unique prefix.
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
pnmcut(1), pnmdepth(1), ppmdither(1), ppmquant(1), ppm(5)
 Voss, Richard F., ``Random Fractal Forgeries,'' in Earnshaw et. al., Fundamental Al-
gorithms for Computer Graphics, Berlin: Springer-Verlag, 1985.
 Peitgen, H.-O., and Saupe, D. eds., The Science Of Fractal Images, New York: Springer
Avenue des Champs-Montants 14b
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.
25 October 1991 ppmforge(1)