Assign positive frequencies p i to the mappings F i . In practical terms, to depict an approximation of A F on a computer, the points of the sequence are displayed starting with a reasonably large index. The inverse problem is solved approximately by the Collage Theorem . The applet below was inspired by Barnsley's celebrated depiction of the Black Spleenwort fern. Three parallelograms almost covering a fourth and bigger parallelogram seemed to be naturally associated with the fern and each of its smaller branches.
Parallelograms lead to affine transformations, which map parallel lines onto parallel lines.
Affine transformations can be uniquely determined from images of any three distinct points - in particular, three consecutive vertices of a parallelogram. The applet consists of two parts. The first is the display area with several controls. First of all, there are several predefined IFSs to select from. The applet attempts to optimally exploit the visual estate.