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^C^13-D FRACTAL LANDSCAPES
^Cby
^CJoel Ellis Rea
^C(based on a program by M. van de Pane)

   Until just a few years ago, mathematicians could not really describe the
world around us.  The elegant formulas and precise geometric constructions of
traditional mathematics were great for exploring the abstract world
mathematicians like to inhabit, not so great for describing the jagged peaks of
a mountain range.  Nature isn't tidy.

   It was a daunting problem:  how do you translate a pine tree or a seacoast 
into a set of equations?  "Fractals," developed in the mid-Seventies by IBM 
mathematican Benoit Mandelbrot (now at Harvard), proved to be the answer. 

   Mandelbrot discovered that most objects -- clouds, river banks, and the like
-- exhibit a regular pattern, no matter how confused and irregular they first
appear.  That regular pattern is "self-symmetry."  In other words, a part of an
object resembles the entire object.

   A seacoast is an often used example.  Say that you are floating in a hot air
balloon over a small cove made in a rocky coastline.  A jagged line marks the
boundary between water and land.  Now imagine that you see the entire coast from
100 miles up -- the seacoast with its bays and peninsulas will resemble your
small cove.  In a fractal landscape, an enlargement of a small section of a
formation resembles the whole object.

   In order to classify these self-symmetrical fractals, Mandelbrot gave them
fractional dimensions.  While a line in Euclidian geometry has a dimension of
"1," a jagged fractal line can have a dimension between 1 and 2.  These two
characteristics of fractals -- self-symmetry and fractional dimensions -- open
very complex patterns to mathematical analysis.

   Unlike most branches of higher mathematics, fractal geometry has produced
immediate practical benefits.  Scientists are now using fractals to describe
everything from the toughness of particular metals to the distribution of
galaxies in the universe.  Fractals also promise to revolutionize computer
graphics.  Normally, a detailed computer reproduction of a landscape would
require storing millions of bits of data.  But by using fractals, computers can
now generate incredibly realistic pictures from relatively little information.

The Program
-----------
   No, ^13-D FRACTAL LANDSCAPES^0 does not produce realistic landscapes, but it does
generate some faScinating patterns.  [Most fractal-generating programs work by
drawing a basic shape (a triangle, for example) over and over again on different
scales.  Random variations are thrown in to make the drawing rougher and more
realistic.]

   Play around with the program and see what kinds of effects you can make.
Hopefully, ^13-D FRACTAL LANDSCAPES^0 will pique your interest and make you want to
learn more about this fascinating branch of mathematics.

   To run this program outside BIG BLUE DISK enter: ^13DFRCTLS^0.

DISK FILES THIS PROGRAM USES:
^F3DFRCTLS.EXE
^FBRUN30.EXE
^FRETURN30.EXE
