Affine Transformation Fractals

Affine Transformation Fractals are different fractals than the L-Systems. In fact they are constructed and represented in a total different way. in fact an ATF is represented using a matrix of 6 values: a, b, c, d, e, f.

 

Pressing the Set Button will open the below dialog box where one can enter the settings for the fractal.

 

Enter the parameters in the above dialog box and Load/Save as appropriate. More than 1 transformation are required for each fractal. The constants a, b, c, d, e, f are equivalent to those in the equations below:

x’ = ax + by + e
y’ = cx + dy + f

                      

Generating the Fractal

    Once that the parameters have been entered the fractal can be generated. Four different Coloring Algorithms exist and one of them must be selected. Pressing on the Draw button will start generating the fractal.

Coloring Algorithm Description
Coloring Algo 1 (Intensity) This coloring algorithm will use color 1 from the IFSPref and will use the fact that some pixels in fractal generation are hit more than once. Each time the same pixel is hit it will increase the brightness of the color.
Coloring Algo 2 (1 at a Time) This coloring algorithm requires a list of colors and will draw using one of the colors in sequence. Pixel 1 will get color 1, pixel 2 will get the 2nd and so on. When the end of the list is reached the colors starts off from 1 again
Coloring Algo 3 (Range) This coloring algorithm uses Color 1 and Color 2 from IFSPref and will range a palette of colors with those two at the far ends. It will then divide each color over a number of pixels.
Coloring Algo 4 (Sequence of Colors) This coloring algorithm requires a list of colors but is similar to the above. It will color a series of pixels using 1 color then move on to the next.

 

Color List Chooser

The color list chooser will allow you to select a number of colors. By double clicking on a particular color or else selecting a color and clicking the Add Color Button the color will be added to the list.

 

Drawing the Fractal

Pressing the Draw button will generate the fractal but if the fractal is too big or else it lies out of bounds then one can solve this by Stopping the fractal generation and modifying the scale/start position.

To modify the scale there is a numeric up down component which would initially be set to 100%

The start position is modified by a double click on the drawing canvas. The new values start XY coordinates are displayed near the scale marker.

 

Saving the Fractal Image

The fractal image can be saved to disk in a jpeg or gif file. When the Save Image Button is pressed then the Select Save Region window is displayed with the fractal. Once can choose the region and press the Save button.