step 0
step 1
The process used to create a very realistic image of a fern is
similar to the process used for the Serpinski Cheese, and is very
simple.
It consists of iterating a large number of times the transformation
represented below : each rectangle is replaced by three smaller
rectangles (w2,w3 and w4) and a last rectangle reduced to a segment
of line (w1), placed as indicated on the second picture.
step 0
step 1
The parameters needed to definite this process are only a few. Here is a set of values that specify the construction of a fern.
w
a
b
c
d
e
f
p
1
0
0
0
0.16
0
0
0.01
2
0.85
0.04
-0.04
0.85
0
1.6
0.85
3
0.2
-0.26
0.23
0.22
0
1.6
0.07
4
-0.15
0.28
0.26
0.24
0
0.44
0.07
These parameters can be used as input in the public domain program FRACTINT (see below) which draws the associated fractal. To know what these parameters stand for or where fractint can be found, examine the links given further on in the main page.
| Fractals |
The Center for Polymer Studies, a scientific visualisation research center in the Physics department at Boston University.
Fractint:
A public domain software package which enables you to specify
an iterative process and then draws the corresponding fractal.
It also draws fractals constructed by other methods than iterative
processes and provides the possibility of magnifying every detail
of the constructed fractal.
Fractamina:
A link to an iteractive program which draws the Sierpinski Gasket
by playing dice.
There is a great deal of information about fractals available
through a net search.
© Mathematics and Knots/Edition Limitee 1996 - 2002
This material may be used freely for educational, artistic and
scientific purposes, but may not be used for commercial purposes,
for profit or in texts without the permission of the publishers.