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          IFS Lab description and screenshots

    IFS Lab is a tool for creating and visualizing the class of fractals known as Iterated Function Systems (IFS) using the Collage Theorem and Random Iteration Algorithm. These mathematical terms may sound intimidating, but IFS Lab works around that by presenting its user with a friendly and intuitive visual interface, keeping the math firmly behind the scenes.
    The program focuses on enabling direct manipulation by the user of the Collage underlying a desired IFS fractal (which is more fun than it sounds!) It provides for the convenient sketching of approximate fractal outlines by a paint-program-like user interface, and for definition of IFS Codes by a mouse-driven Collage Editor that allows the user to move, stretch and distort copies of the Outline to create the Collage. The attractor of the resultant IFS Code can be rendered in black and white ("Preview") or in grayscale. The program can read IFS Code files generated by many other IFS programs, thus allowing them to be converted to a collage and manipulated further.

    IFS Lab has three modes, which are usually used in succession, as illustrated below for the creation of the classic "fern" fractal:

Outline Editor mode:

This mode allows you to draw the approximate outline of the desired fractal with the mouse, using the provided Freehand draw, Line draw, Area Fill and Erase functions.

In the screenshot at right, a rough sketch of a fern leaf has been drawn.

Outline Editor screenshot

Collage Editor mode:

This mode enables the mouse-driven sizing, distortion and positioning of the transformed images of the outline that are tiled onto the full-sized outline to form the collage, from which the IFS transformation coefficients are computed by the program.

In the screenshot at right, the white outline is covered by four such "pieces", of which the one currently being manipulated appears in red and the others in green.

Collage Editor screenshot
Once the outline is more or less fully covered by the pieces, you can use the  Optimize function to generate a precise collage from the actual attractor of the IFS you've defined.

In the screenshot at right, the Optimize function  has generated the same collage seen above, but now it uses an accurate outline that is fully covered by the green and red pieces. Now you can tweak the collage to correct any deviations from the fractal you were trying to create.

Optimized Collage screenshot

Rendering mode:

In this mode you create the  attractor of the current IFS, which is rendered using the Random Iteration Algorithm.

As you see in the screenshot at right, this  attractor is a higher-resolution, sixteen- gray-level version of the optimized collage shown above.

A lovely fern - and not a single math formula in sight!...

Attractor screenshot

For more details, refer to the user documentation file, which is included in the download package. You should also check the Quick Start guide, Demo and Examples under the program's Help menu.

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Copyright 2005 N. Zeldes. All rights reserved.