Index
I.F.S. Fractals Setup

Use this dialog box to change the settings for the I.F.S. Fractals  screen saver. This screen saver computes, and then displays, an I.F.S.  Fractal, consisting of a number of dots. After a certain time interval,  which you can specify, a new I.F.S. fractal will be computed. The dots  will move, in a number of steps which you can specify, from their positions  in the old to their positions in the new I.F.S. fractal.

Choose one of the following buttons for information about the dialog  box:

What are I.F.S. Fractals?

Options

Fractal Options

Animation Options

Password Options

Bug Reports

Legal Stuff


Fractal Options

Here you can specify a number of options of the I.F.S. fractal:

 	The number of points in the I.F.S. fractal.

 	The color in which the fractal will be drawn. This color can be specified, or  can be choosen randomly.

 	Whether random mutations will be performed to the I.F.S. fractal matrix,  allways choosen randomly from a list of 50 standard matrices.


Animation Options

Use these options to set the number of steps in the animation of the old  fractal into the new one, and the number of seconds which a fractal will  stay on the screen.


Password Options

Use these to use a password with the screen saver.

 	Select the Password Protected check box to turn on password protection. When password protection is turned on, you cannot return to Windows from  the screen saver until you type the password.

 	To assign a password to the screen saver, press the Set Password button,  and then complete the Change Password dialog box.


What are I.F.S. Fractals?

I.F.S. (Iterated Function Systems) fractals are figures in a n-dimensional  space generated by transforming points, using a matrix multiplication  followed by a vector multiplication, into a new point. The old an the new  point are then plotted or connected with lines. In the I.F.S. fractals  screen saver, the points are two-dimensional. I.F.S. fractals were first explored by Michael Barnsley and his co-workers  at the Georgia Institute of Technology.

A two-dimensional I.F.S. fractal is defined by a (6 x n) matrix. For example:  The world-famous fern fractal is defined by the following (6 x 4) matrix:

 0.00	 0.00	 0.00	 0.16	 0.00	 0.00

 0.20	-0.26	 0.23	 0.22	 0.00	 1.60

-0.15	 0.28	 0.26	 0.24	 0.00	 0.44

 0.85	 0.04	-0.04	 0.85	 0.00	 1.60

The values on each line define a (2 x 2) matrix, and a (1 x 2) vector. If  we define a (6 x 1) I.F.S. matrix as:

a  b  c  d  e  f,

then the (2 x 2) matix, and the (2 x 1) vector are:

matrix         vector

a  b               e

c  d                f

A (1 x 2) point in the I.F.S. fractal is transformed into a new one by  taking its vector product with the (2 x 2) matrix, and the (2 x 1) vector.

Each of the n lines in the (6 x n) matrix has a relative probability  corresponding to the determinant of its (2 x 2) matrix of being used to  transform the old fractal point into a new one.

In the I.F.S. fractals screen saver, a (6 x n) matrix, with n between 3  and 5, is chosen randomly from a list of 50 default values. Optionally,  it is possible to replace a randomly chosen matrix element with a random  number.


Bug Reports

If you find any bugs in this program, or have any suggestions or questions  about the program or any other matter (life in general, the universe, etc.)  please contact me and I will give you a response as soon as possible.

You can contact the author at the following address:

Mario van den Ancker

Potvisstraat 30

NL-1035 HK  Amsterdam

The Netherlands

E-mail: mario@astro.uva.nl


Legal Stuff

You are free to use, copy and distribute the I.F.S. Fractals screen saver  program.

This program is being made available on an "as is" basis, and carries no warranties, expressed or implied.  The author shall in no way be held liable for any damages resulting from the use of this program or the media on which it is distributed, including, without limitation, loss of business profits, interruption of business, loss of information, damage to equipment, or any other incidental or consequential damages.

If you cannot accept these terms, please do not use this program. By using this program, you indicate you agree with these terms and will abide by their restrictions.