%GENERAL INFORMATION % % FRACTORY is an interactive visally-oriented tool %designed to help the user create fractal images. The %fractals are generated by the method of Iterated Function %Systems (for a complete description, see Chap 5, Sect ? of %"Invitation to Dynamical Systems" by Ed Scheinerman). An %Iterated Function System (IFS) consists of several linear %transformations which map the unit square to a subset of %itself. In this program, such a 2-dimensional transfor- %mation (referred to herein as a "square" or a "function") %is represented by the image of the unit square under it, %which appears in the form of a parallelagram, possibly a %rectangle or square. % An IFS consists of at least two (usually more) such %transformations. In this program, these functions are %represented (and uniquely determined) by where the points %X=(0,1), Y=(0,0), and Z=(1,0) are mapped to (i.e. their %image under the function). Note that the standard %mathematical representation of such a function is the %2-dimensional linear transformation Ax+b. % The fractal is drawn using a randomized algorithm (also %described in the aforementioned text). This algorithm %takes a point, randomly chooses a function from the IFS, %applies that function to the point, and then repeats the %process on the resulting point. After the first few such %points, all resulting points are (at least to within the %precision of a computer screen) in the fractal. The %fractal is drawn by plotting all but the first few of %these points. % FRACTORY consists of a CONTROL PANEL with numerous %controls (see individual HELP topics) and a GRAPHICS %WINDOW (see separate HELP listing). Most modifications %to the functions are made on the Control Panel, although %some manipulation is also possible from the Graphics %Window.