These are 32-bit Windows programs compiled with Borland C++ 5.0. They should continue to work in current 64-bit Windows versions, and, depending on the emulator, in various versions of LINUX and Mac systems.

EZFract: This program renders classic Mandelbrot and Julia fractals. It utilizes many different coloring methods, but in addition to the esthetic nature of these fractals, it explores a number of their mathematical properties, including binary decomposition, orbital paths, periodicity and buds, equipotential lines, external rays, distance estimation and triangle inequality averaging.

FractFloat: In contrast with EZFract, this program renders a collection of virtually all the fractal and other mathematically-oriented formulae that I've found to be interesting since the 1990's. Because the program uses floating point, rather than integer, calculations, I've named it "FractFloat" in respectful acknowledgement of one of its major inspirations, the classic DOS program "FractInt".

QS Attractor: This is a collection of various chaotic attractors and related mathematical images. Some are well-known, such as the Lorenz and Rossler attractors, and others are more esoteric.

QS DLA: A simulation of "diffusion limited aggregation", a process in which particles moving randomly adhere on contact to either a central "seed" or an enclosing circle, and subsequently to each other. This results in branching patterns that grow gradually over time. An associated screen saver is included.

QS Flame: "Cosmic recursive fractal flames" are a form of chaotic attractor which first were created by Scott Draves in 1992. Their popularity has made them ubiquitous throughout the digital world. This program was written in 1999 for Windows 95, and as far as Draves knew at the time, it was the first port of his UNIX code to Windows. Since then, numerous versions of flame software have appeared for most platforms, even including PhotoShop plug-ins. An associated screen saver is included.

QS Ganymede: This program uses the four attractor formulae described in the book "Chaos in Wonderland" by Clifford Pickover. These formulae generate striking images of chaotic attractors. The book's premise is that alien beings called "Latoocarfians" inhabit Jupiter's moon Ganymede. They visualize the attractors in their dreams. The book describes Latoocarfian civilization in detail, and presents the account of a human visitor and his companion. Within this science fiction are descriptions of chaotic attractors and related mathematical concepts, sample programming code, games and references to mathematical history. The original program was written in 1994 for DOS. A third dimensional factor was added which allows images to be rotated around each of the three axes.

QS Pig: The classic dice game. Play against the computer or another human.

QS Roulette: This program plots roulettes of circles and ellipses rolling around fixed circles, and related rhodonea curves - a digital version of the popular Spirograph toy. Roulettes are curves described by a point attached to a moving curve as that curve rolls along a second fixed curve. A companion program, "QS Roulette 3", simulates situations with 2 moving circles and 1 fixed circle. An associated screen saver is included.

QS SymXaos: This program uses the five attractor formulae described in the book "Symmetry in Chaos", by Michael Field and Martin Golubitsky. These formulae generate striking symmetric icons, and tiling patterns which the authors refer to as "quilts". The program was written in 1997 for Windows 95, with tweaks in 2000 and 2018. A companion program, "QS SymXaos 3D", is included. It adds a third dimensional factor to the Icons 1 and Icons 2 formulae from the book. The images can be rotated around each of the three axes.

MAP file collection: Most of these programs on this page use Fractint 256-color MAP files for their color palettes. They are text files containing RGB triplets, which are easy to create or edit. This ZIP archive contains a small collection. There are hundreds if not thousands of these files available on the Web. The programs allow you to select MAP files from their GUI menus, and usually show a preview of their color spectra.

MAPView: This is a stand-alone program that displays the color spectrum of any selected MAP file.

Palette editing collection: This ZIP archive contains two programs that can create smooth gradient color palettes, using sine curves, circular arcs, lines, Bezier curves and B-splines. The palettes can be saved as MAP files (described above) containing 256 colors. In addition, QS BSpline appends the 768-color palettes from which the 256-color versions are derived. 2 PDF files contain descriptions of Bezier and B-Spline curves.

QS Domain Coloring: Graphically representing equations in complex variables requires 4 dimensions. One method of approaching this objective is domain coloring, in which points in the 2-dimensional plane of the domain are assigned colors based on the position of the results of the calculations in a color map plane. Typically, variations of HSV gradients are used, which leads to brightly colored images.

Latest revision 4 May 2020

Michael Sargent

msargent@uvm.edu