ppmforge(1)ppmforge(1)NAMEppmforge - fractal forgeries of clouds, planets, and
starry skies
SYNOPSISppmforge [-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]
DESCRIPTIONppmforge generates three kinds of ``random fractal forg
eries,'' 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 di
rectly from pseudorandom numbers.
The generation of planets or clouds begins with the prepa
ration 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 require
ment increases as the square of the mesh size. The frac
tal 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 frac
tal 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 ampli
tudes. 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 -pow
er 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 en
visioned by thinking of the data as representing the ele
vation of terrain; powers less than 1 yield landscapes
with vertical scarps that look like glacially-carved val
leys; 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:
Clouds A colour map is created that ranges from pure
blue to white by increasing admixture (desatura
tion) 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 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 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
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 val
ues 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 pn
mdepth rather than ppmquant or ppmdither. Try newmaxval
settings of 63, 31, or 15 with pnmdepth to reduce the num
ber 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 di_
men, which may be any floating point value be
tween 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 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 op
tion is specified, a random hour angle is cho
sen, biased so that only 25% of the images gen
erated 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 specify
ing, 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 inclina
tion 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 re
quirements 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 num
bers required by the FFT. On machines with lim
ited memory capacity, you may have to reduce the
mesh size to avoid running out of RAM. Increas
ing the mesh size produces better looking pic
tures; the difference becomes particularly no
ticeable when generating high resolution images
with relatively high fractal dimensions (between
2.2 and 3).
-night A starry sky is generated. The stars are creat
ed by the same algorithm used for the stars that
surround planet pictures, but the output con
sists exclusively of stars.
-power factor
Sets the ``power factor'' used to scale eleva
tions 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 op
tion. 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 val
ues 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 re
semble the sky as seen by the human eye from
Earth's surface. Stars are dim; only the
brightest activate the cones in the human reti
na, causing colour to be perceived. Higher val
ues 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 fic
tion'' 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 popu
lation 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 pre
served by ppmforge. You can reverse the propor
tion, 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. Specify
ing an explicit seed allows you to re-render a
picture you particularly like at a higher reso
lution 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. Im
ages 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 pre
fix.
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 ALSOpnmcut(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 soft
ware 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 im
plied 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 di
rectly 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'' in
cludes 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 de
tailed explanations by Rudy Rucker of the mathematics and
algorithms used by each program.
25 October 1991 ppmforge(1)
