Farn

Fractal Branches

In the Applet: Use the button "random" to create a new fractal branch with random parameters. After you've clicked the button "mouse", click and drag the paint area to draw the basic figure yourself (select 2, 3 or 4 branches). The fractal image construction will follow immediately. With "colorset" you are able to change the colors of the existing branches, 8 sets are available. The button "base figure" opens a new window showing the basic branch construction. The choice element allows to decide about the number of branches (2, 3 or 4) for the next construction process.

Construction of Fractal Branches

The fork construction starts with 2, 3 or 4 branches, growing from one common point. Direction and length of every branch is chosen at random (random mode), according to a given variation width. In "mouse mode" you are able to draw the basic fork yourself. The fork ends are the start points for smaller forks constructed similar, but only having a length of 70% from the basic branch length. The construction is continued that way until the minimal length is reached.

The branches are colored in 3 steps, depending on the actual length. Coloring like this creates aesthetic looking plants. Because drawing runs recursively, every branch is drawn with all his smaller twigs before the next branch appears. A test routine automatically varies some of the drawing parameters in order to use the paint window completely.

People can hardly imagine how such simple principles are able to form this wonderful colored trees and spirals.

Astfrak Prinzip

Construction of fractal branches

Thanks

Thanks to Peter Kraus for the original version of the source code of his fractal applet. Here is the modified source code Astfraktale to download. You'll find more interactive applets in several fractal sections.

Quick-Links

Math&Art Gallery

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© 2007 Ulrich Schwebinghaus