ppmforge(1)                                           ppmforge(1)

       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  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.

       -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

       -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

       -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-

       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
            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                        1