Farn

Fractal Typewriter

With my FracType applet you can create fractal words by simply writing into an edit field. Type in a word using the letters from a to z or the ciphers 0 - 9. In addition you may use the characters "!", "−" and "?". Press return or click the draw button to start the calculation and the drawing process. After a few seconds you'll get the fractal graph.

Based on a description in Herfort/Klotz, Ornamente und Fraktale, Vieweg

Get the source code

The FracType Algorithm

IFS for R

Fig. 1: IFS for the charakter R

The applet contains 40 predefined characters, formed of a puzzle of up to 7 rectangles or otherparallelograms. All characters in principle fill the same basic rectangle, defined by the points P, Q and R (watch fig. 1). If you choose a word with n letters, the applet's image plane (the word plane) is devided into n rectangles of the same width and height, called character fields, defined by the corners P'(i), Q'(i) and R'(i), i = 0 to n-1.

The second step is to calculate a linear transformation for every character field, which transformates the points P, Q, R of the basic rectangle into the corners P'(i), Q'(i), R'(i) of each character field. These transformations are used to bring the letter puzzles from the basic field into the according character field.

IFS for FOUR

Fig. 2: Puzzle-Set for the word FOUR

In a third step the before transformed letter puzzle pieces are seen as transformation results of the whole word rectangle and one transformation for every piece of the letters is therefor calculated.

Finally the resulting transformations (up to 7n) form an IFS (watch sections IFS I-III) and the chaos game method produces the wanted fractal word (watch fig. 2).

Use of the applet

You may type up to ten characters a-z or 0 - 9 into the edit field. Confirm with the return key or use the draw button. With the checkbox you decide wether the fixed points of the transformations are visible or not. The circles representing the fixed points are moveable for fine adjusting the figure. The "spacing" edit field is used to take influence on the space width between the characters. A value of 0.15 means 15% of the character width.

Quick-Links

Math&Art Gallery

3D-Galerie

Galerie Cosch

Ulliversum

© 2007 Ulrich Schwebinghaus