Creating a fractal fern

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 |

© 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.