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-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 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 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
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 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 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 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 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.
- -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 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 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.
- -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 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 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 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
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 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 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 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 pointer architectures.
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 Graphics, Berlin: Springer-Verlag,
1985.
- [2]
- Peitgen, H.-O., and Saupe, D. eds., The Science Of Fractal Images, New
York: Springer Verlag, 1988.
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 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.