With my FracType machine 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 "?". Lower case letters will automatically be converted into their upper case equivalents. 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

The Javascript source codes are if.js, chaosgame.js and typewriter.js.

Watch the HTML source code of this page, too.

The FracType Algorithm

Fig. 1: IFS for the charakter R

The machine contains 42 predefined characters, formed of a puzzle of up to 7 rectangles or other parallelograms, called frames. 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.

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 constructed fractal word (watch fig. 2).

Use of the machine

You may type up to eleven characters a-z, 0 - 9 or the symbols "!", "+", "−", "=" and "?" into the **edit field**. Undefined characters are replaced with a "?". Confirm with the return key or use the draw button. With the **checkbox** you decide wether the fixed points, represented by **white circles**, and the puzzle frames of the transformations are visible or not. The **"spacing" slider** is used to take influence on the space width between the characters. A value of 0.15 means 15% of the character width.

© 2007 Ulrich Schwebinghaus