NAME
ppmforge  fractal forgeries of clouds, planets, and starry skies
SYNOPSIS
ppmforge
[clouds] [night] [dimension dimen] [hour hour] [inclinationtilt angle] [mesh size] [power factor] [glaciers level] [ice level] [saturation sat] [seed seed] [stars fraction] [{xsizewidth} width] [{ysizeheight} height]
DESCRIPTION
This program is part of Netpbm(1)
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 selfsimilarity. 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 glaciallycarved valleys; powers greater than one make fairycastle 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. ppmforge generates as follows:
The randomness in the image is limited before Netpbm 10.37 (December 2006)  if you run the program twice in the same second, you may get identical output.
Clouds  A color map is created that ranges from pure blue to white by
increasing admixture (desaturation) of blue with white. Numbers less
than 0.5 are colored blue, numbers between 0.5 and 1.0 are colored
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
colored 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 capshigh
altitude terrain carries glaciers farther from the pole. Based on the
position of the star with respect to the observer, the apparent color
of each pixel of the planet is calculated by raytracing 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.

OPTIONS
You can abbreviate any options to its shortest unique prefix.
clouds  
Generate clouds. An image 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 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
geometricallyprecise ice cap boundaries.
 
hour hour  
When generating a planet, ppmforge uses hour 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 center 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.
 
inclinationtilt 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
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
nonunity 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 largescale
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 color 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 color 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 color. 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 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
rerender 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.
 
xsizewidth 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 image,
make a square one with ppmforge, then use pamcut to
extract a portion of the shape and size you require.
 
ysizeheight 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.
 
LIMITATIONS
The algorithms require the output image 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 image if necessary.
You may have to reduce the FFT mesh size on machines with 16 bit integers and segmented pointer architectures.
SEE ALSO
pamcut(1) , pamdepth(1) , ppmdither(1) , pnmquant(1) , ppm(5)
[1]  Voss, Richard F., ‘‘Random Fractal Forgeries,’’ in Earnshaw
et. al., Fundamental Algorithms for Computer Graphics, Berlin:
SpringerVerlag, 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 ChampsMontants 14b CH2074 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 ChaosThe Software’’ for MSDOS, 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) 6882344 tollfree or, outside the U.S. (415) 3322344 Ext 4886. Fax: (415) 2894718. ‘‘ChaosThe Software’’ includes a more comprehensive fractal forgery generator which creates threedimensional 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.