[

[

This program is part of

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

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 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 the more realistic the pictures but the calculation time and mem-

ory requirement increases as the square of the mesh size. The fractal

dimension, which you can specify with the

mines 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 fre-

quency domain data into spatial amplitudes. We scale the real compo-

nents 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

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 eleva-

tion 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.

lows:

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.

Cloud pictures always contain 256 or fewer colors and may be displayed

on most color mapped devices without further processing. Planet pic-

tures often contain tens of thousands of colors which must be com-

pressed with

format. If the display resolution is high enough,

produces better looking planets.

color bands, particularly in the oceans, which are unrealistic and

distracting. The number of colors in starry sky pictures generated

with the

Small values limit the color temperature distribution of the stars and

reduce the number of colors in the image. If the

to 0, none of the stars will be colored and the resulting image will

never contain more than 256 colors. Night sky pictures with many dif-

ferent star colors often look best when color compressed by

rather than

or 15 with

256 or fewer.

You can abbreviate any options to its shortest unique prefix.

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 con-

straints 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 inte-

gers and segmented pointer architectures.

[1] Voss, Richard F., ''Random Fractal Forgeries,'' in Earnshaw et.

[2] Peitgen, H.-O., and Saupe, D. eds., The Science Of Fractal

John Walker

Autodesk SA

Avenue des Champs-Montants 14b

CH-2074 MARIN

Suisse/Schweiz/Svizzera/Svizra/Switzerland

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.

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.

netpbm documentation 25 October 1991 Ppmforge User Manual(0)