The inverse problem for IFS (finding the transformations to generate a given image) usually is introduced with fairly simple mathematical fractals. We did this in Finding IFS for Fractal Images, where the basic IFS parameters are introduced. More complicated examples are presented in Spiral Fractals from IFS.
Still, the often stated ability of fractals to make convincing forgeries of natural objects is satisfied only in part with abstract ferns, trees, and Queen Anne's lace. To see a more direct example, we take the outline of a real leaf and use scaled copies of the outline to find IFS rules for generating an approximation of the leaf. That a leaf is just approximately fractal, and that over only a few levels, adds a complication to the method of finding IFS rules for exact mathematical fractals. However, we shall see that the familiar methd can be modified to a successive approximation approach that seems to work reasonably well.
Return to A Fractal Leaf by IFS.