Farn

Simple Iterations

Here we use an Iteration Machine with a single function. The calculation starts with a point P (x; y) of the two-dimensional plane. The next point is calculated with a simple formula in two variables x and y. After that, we take the result P' (x'; y') and use it for the following calculation. This iteration is repeated until the plotted points build the attractor of the process.

Iteration machine

Here is the first example. Look for another one at page 2.

Mira Attractor Applet

Use the Mira machine by changing the values in the edit fields at the bottom of the applet. Press the enter button and watch the new figure. The table below shows sample values. The figures depend sensitively on the numerals behind the decimal point. The color is changed every 1000 dots, until the 10 predefined colors are used, then the colors are repeated.

The Formula

Mira Formula

A

B

Dots

Scale

Name

0.29

1.0005

5000

5

Fort

-0.48

0.93

5000

10

Wing

-0.4

0.9999

9000

7

Amoeba

-0.2

1.000

8000

7

Carpet

Hints: Use -1 < A < 1 and B near 1

Quick-Links

Math&Art Gallery

3D-Galerie

Galerie Cosch

Ulliversum

© 2007 Ulrich Schwebinghaus