Fractal Generator for Complex Iterative Systems

Downloads - Please read the associated instructions for your download.

Windows Instructions... Download the fracgen.exe install program using the link above this instruction box. Using Windows Explorer, double-click the file you just downloaded. A small dialog box will appear asking you to select several options. Simply click Extract to extract the files. A message box will appear notifying you that the extraction was successful. Click OK, and close the extraction dialog box. Using Windows Explorer, double-click the file setup.exe. This will begin the installation process. Follow the directions on the screen to install the software.

Screen Shots

Program Features

The Fractal Generator for Complex Iterative Systems program combines and extends two older programs I wrote several years ago. It has been completely rewritten for Windows. This program will graph fractals produced by a dynamical system of a single complex function.

• The user can create 5 types of fractal images:
  • The Mandelbrot Set and relatives of the set. That is, dynamical systems produced by Zⁿ+C, for an integer n between 2 and 1000.
  • Julia sets produced by Mandelbrot type systems. That is, dynamical systems produced by Zⁿ+C, for an integer n between 2 and 1000 and C fixed.
  • General Iterative Functions, where the user can create their own function for use in the dynamical system.
  • Julia sets produced by general iterative functions.
  • Basins of Attraction on a convergence plane. The user has the ability to insert their own function for convergence iteration. This form is usually used for Newton's method fractals.
• Each fractal type can be drawn in one of 6 different styles.
  • Simply graphing the fractal on the complex plane. This uses the standard pixel method, coloring by escape iteration.
  • Graphing the fractal on the inverse complex plane. This uses the standard pixel method, coloring by escape iteration, but inverts the plane.
  • Binary decomposition on the complex plane. This uses the standard pixel method, coloring by the half-plane position of the argument upon escape.
  • Binary decomposition on the inverse complex plane. This uses the standard pixel method, coloring by the half-plane position of the argument upon escape, and inverting the plane.
  • Angular decompositions on the complex plane. This uses the standard pixel method, coloring by the argument upon escape.
  • Angular decompositions on the inverse complex plane. This uses the standard pixel method, coloring by the argument upon escape, and inverting the plane.
• All types and styles can be graphed on the complex plane or the Riemann Sphere. The complex plane graphing utility also has tools for easy zooming and position manipulation.
• The program also includes utilities for mathematical exploration. These tools include: a quick image viewer for associated Julia sets of the Mandelbrot Set and its relatives, associated Julia set creation using a visual interface, and an orbit generator that calculates and displays periods.
• There are also full file saving and retrieving facilities which allow the user to save partially complete images and continue generating them at a later date. The program can save all images as bitmap graphics files. There is also a built-in slideshow viewer.
• The program offers a versatile fractal palette creator where the user can set the background, outline and set colors as well as a sequence of up to 5000 fill colors for the escape iteration bands. The palette construction facility also offers file transfer utilities and manipulation tools, including special scheme creation, panning, and automatic scheme resizing.