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The images you see to the right were all created with IFS Freestyle.* 
Click any image to see a larger view. Click here or click the logo above for a test drive! IFS Freestyle is free
software. Download it at Sourceforge! * The basic shapes were created with IFS Freestyle. The 3-d effects were added with the GIMP. Click here to learn more about processing IFS Freestyle images with the GIMP. |
 curly.fifs |
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 sierpinski2.fifs |
 tile.fifs |
Add an affine transformation to the design area by clicking the "Add Affine Transformation" button. You will see a highly decorated square appear. Your cool graphics are created by massaging at least two of these squares, but let's work with the one we have for now.
The decorations are actually tools for doing the massaging. After certain massages, the square may no longer be a square, so the following table refers to it as a quadrilateral. Don't be afraid of the long list of tools, or their definitions. Just grab one with your mouse, and drag to see what happens. Now is a good time to experiment a little. Massage your square with some of these tools. Even if you don't experiment with all the tools right now, make sure you DO use the translate tool to move the square so it's not right in the middle of the design area.
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Rotate
Tool Use this tool to spin the quadrilateral. |
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Translate
Tool Use this tool to move the quadrilateral. |
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Reflect
Tool Use this tool to make a mirror image of the quadrilateral. |
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Scale Tool Use this tool to change the size of the quadrilateral. |
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More
Scale Tools Use these tools to change the size of the quadrilateral in one direction, but not the other. |
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Shear
Tools Use these tools to turn the square into a diamond shape. |
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Delete
Tool Use this tool to delete the quadrilateral. |
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Add a second quadrilateral by clicking the "Add Affine Transformation" button again. As soon as the second transformation appears, an image should show in the preview area. This shows you the shape you have created so far. At this point, it's probably not too exciting, but just wait! Massage this quadrilateral and watch the preview change as you massage the new quadrilateral. Add a third, and perhaps a fourth, and see what you can come up with!
If you have any transformations in the design area, delete
them with their delete tools . Now
click the "Add Julia Transformation" button. You will see a circular
tool with a couple of decorations. Just as with the affine
transformations, your cool graphics are created by massaging at least
two of these circles. Here is what the tools do.
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Translate
Tool Use this tool to move the circle. |
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Plus/Minus
Toggle Use this tool to toggle the sign of this tool. |
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Delete
Tool Use this tool to delete the circle. |
Now is a good time to experiment a little. Massage your circle with one or both of the translate and plus/minus tools. Notice nothing happens in the preview area. Nothing will happen until you add a second transformation. Do it by clicking the "Add Julia Transformation" button again. Massage this circle and watch the preview change as you move it around.
When you like what you see in the preview area, you might want to click on the "Render Fractal" button. This will bring up a dialog box that allows you to create a larger, more colorful version of your fractal! Curly was rendered using the Random method; the fern was rendered with the single color method; the sierpinski triangle was rendered with the one color per map method; and the tile was rendered with the deterministic method. Feel free to try them all, but be careful with the deterministic method. It's not a mistake that the number of iterations is small. It takes a long time to do each iteration, and not very many are needed to create interesting renderings.
Even though the basic usage examples had you using only one or the other type of transformation, you can use both kinds at the same time! Here is a screenshot of the making of the curly graphic above. Notice the Julia transformation near the bottom left corner of the design area.
The fern is made with 4 affine transformations placed like so in the design area. Notice that the one in the bottom right has been reflected. The others have not. The fern was rendered in the single color green.
The .fifs files hold the mathematical description of your IFS fractal! It may or may not interest you, but this is how IFS Freestyle sees the shapes in the design area. Also, if you download the stand-alone version, you will get save and open buttons so you can save and retrieve your work. The .fifs file is what is saved and read during these operations. A line like
AffineBasics:7.624844e-01,9.264101e-01,8.226161e-02,-1.102754e-01,9.074441e-01,-3.107769e-01,-3.208020e-01,false
is the mathematical description for an affine transformation with
| horizontal scaling | 7.624844 x 10-1 |
| vertical scaling | 9.264101 x 10-1 |
| horizontal shearing (in radians) | 8.226161 x 10-2 |
| vertical shearing (in radians) | -1.102754 x 10-1 |
| rotation (in radians) | 9.074441 x 10-1 |
| reflected | false |
| horizontal translation | -3.107769 x 10-1 |
| vertical translation | -3.208020 x 10-1 |
applied in that order. A line like
Julia:-1.458647e+00,-1.408521e+00,false
is the mathematical description for the complex number mapping
where the plus or minus is chosen according to whether or not the last parameter is "true" or "false." True means positive and false means negative. Just click the "Show IFS Code" button to see what would be the contents of the .fifs file if you could save it.
