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
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,
particularly the technique of spectral synthesis explained in more de‐
tail by Dietmar Saupe.
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 synthe‐
sised 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 memo‐
ry 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 trans‐
form 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 ap‐
plying 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 re‐
places 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 con‐
taining numbers that range from 0 to 1. The pixmaps are generated as
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 approximate‐
ly 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 illumi‐
nation). 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 pic‐
tures often contain tens of thousands of colours which must be com‐
pressed 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 dif‐
ferent 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 gener‐
ating 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, simulat‐
ing planets in the midst of an ice age. Lower values tend to
be boring, resulting in unrealistic geometrically-precise ice
When generating a planet, hour is used as the “hour angle at
the central meridian.” If you specify -hour 12, for exam‐
ple, 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 pret‐
ty, 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.
Sets the extent of the polar ice caps to the given floating
point level. The default level of 0.4 produces ice caps sim‐
ilar 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) cre‐
ate “ice balls” like Europa.
The inclination angle of the planet with regard to its prima‐
ry star is set to angle, which can be any floating point val‐
ue 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 hemi‐
sphere. 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 incli‐
nation angle is specified, a random value between -21.6 and
21.6 degrees is chosen.
A mesh of size by size will be used for the fast Fourier
transform (FFT). Note that memory requirements and computa‐
tion 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 256×256, which pro‐
duces reasonably good looking pictures while using half a
megabyte for the 256×256 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 run‐
ning out of RAM. Increasing the mesh size produces better
looking pictures; the difference becomes particularly notice‐
able 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.
Sets the “power factor” used to scale elevations synthe‐
sised from the FFT to factor, which can be any floating point
number greater than zero. If no factor is specified a de‐
fault 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 be‐
tween 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 exponen‐
tiating 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 varia‐
tions. 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
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 sky‐
glow, 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 re‐
flected in the skies created by ppmforge. Dim, low mass
stars live much longer than bright massive stars, consequent‐
ly 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.
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 speci‐
fied, 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
Sets the height of the generated image to height pixels. The
default height is 256 pixels. If the height specified ex‐
ceeds the width, the width will be increased to equal the
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 con‐
straints are enforced by increasing the size of the requested pixmap if
You may have to reduce the FFT mesh size on machines with 16 bit inte‐
gers and segmented pointer architectures.
 Voss, Richard F., “Random Fractal Forgeries,” in Earnshaw et.
al., Fundamental Algorithms for Computer Graphics, Berlin:
 Peitgen, H.-O., and Saupe, D. eds., The Science Of Fractal Images,
New York: Springer Verlag, 1988.
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, with‐
out 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: Sci‐
ence 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 compre‐
hensive fractal forgery generator which creates three-dimensional land‐
scapes as well as clouds and planets, plus five more modules which ex‐
plore 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