This document is an attempt to summarize what I (Doug Houck)
have learned from creating and using FracGen.  This is a collection of
notes and observations to stimulate your mind.

	A fractal is an object with a non-integer dimension.  But how does
a person create a fractal from stock n-dimesional materials?  There are
two basic methods, which I will call Subtractive and Additive. 

SUBTRACTIVE METHOD

	A simple example of the Subtractive method is to take a sheet of
paper, which has two (2) dimensions, and punch holes in it a with a paper 
punch or shotgun.  If half (.5) of the paper were punched out (subtracted),
the remaining paper would have the fractal dimension (2 - .5), or 1.5.
The more paper you punch out, the more the fractal dimension approaches 1.

ADDITIVE METHOD

	An example of the Additive method is crumpling a piece of paper.
Flat paper has two (2) dimensions, length and width, but when crumpled it
adds a third dimension, density.  The fractal dimension would be 
(2 + density), where density ranges from 0 to 1.  Loosely crumpled 
paper might have a fractal dimension of 2.1, while tightly crumpled paper
might be 2.9. 

	Another example of the Additive method is scribbling on paper with a
pen.  A simple straight penstroke has one dimension, length.  Scribble all
over the sheet of paper, so that the paper is half covered with ink.
If the ink were to completely cover the paper, the ink would be
two-dimensional.  Since it only half-covers the paper, the fractal
dimension is (1 + .5), or 1.5.	FracGen uses the Additive method.  

TRUE FRACTALS

	As I understand them, fractals are self-avoiding.  Many of
the fractals on this disk are not truly fractals, since they lap over
themselves.  However, they do exhibit a striking degree of self-similarity,
which is a major part of the appeal of fractals.  

DOMINANT GENES

	Most of the fractals in Mandelbrot's book, "The Fractal Geometry
of Nature", have seeds in which the line segments are all the same
length.  A major premise of this program is to allow lines of different
length.  A prime example of this is MondoSpiral, in the Geometric 
drawer.  The longest line segment provides the basic character, the
spiral, while the shorter line segments provide body and embellishment.

	If the fractal seeds could be thought of in terms of DNA,
the longer line segments are dominant genes, while the shorter line
segments are the recessive genes.

DNA

	The strands of protein that make up your genes don't have 
enough bandwidth to directly encode such things as the precise shape
of your ear, or pointiness of your adam's apple.  However, by using
a scheme such as in FracGen, these things may be derived by repetitively
applying the seed to itself.  Thus, much information may be encoded in
a small space.

ENZYMES

	Enzymes have several levels of structure.  First the molecules
have certain angles.  Then molecules are combined to form amino acids, 
which are combined in certain angles to form proteins.  But not done
yet!  Another level of structure is added, analogous to shaping a wad
of string into an 'S' shape.  Look at 'S' in the Geometry drawer.

SIERPINSKI TRIANGLE

	Sierpinski formulated the famous Sierpinksi triangle, which looks
like a triangle with triangular holes.  (Look in the Sierpinski drawer.)
I stumbled upon three different ways to draw it, which supports the belief
that triangles are the strongest and most basic shapes known.

GEOMETRY OF NATURE

	Much of classic geometry deals with 'nice' angles, such as 45°
and 90°, and 'nice' proportions, such as 1/2 or 1/3.  However, the fractal
seeds that best describe natural objects have odd angles like 17.3°, and
odd proportions.  Indeed, it is these oddities that give rise to the
infinite variations that give an object a 'natural' look.