•Cabri 3.0.1 - Cabri Version 3.0.1 allows you to handle graphs as you would do it on paper, with all the facilities and power a microcomputer can bring. The main interest of CABRI (“Cahier de BRouillon Informatique”, i.e. “computerized notebook”) lies in its highly interactive behaviour. The objects manipulated by Cabri are sets of points together with edges interconnecting them. The incidence relation between points (also called vertices) and edges is the only mathematical structure involved, and geometrical aspects are ignored. Up to now, Cabri only considers graphs without loops or multiple edges - such graphs are called “simple”. Cabri consists essentially of a graph editor, associated with a toolkit allowing different computations, such as the evaluation of graph invariants or the performing of some classical transformations. Transformations upon graph drawing are also available. Finally, a random generator of graphs, satisfying a number of parametrizable properties, has been specially developed to allow the user (student, teacher or researcher in Graph Theory) to experiment with theorems. Thus, one may also invalidate a hasty conjecture, or on the contrary, bring some support to a more elaborate one.
•mac-to-midi-interface - This is a description of a small MIDI-interface for macintosh. It is a postscript document, use SendPS or Distill to print it. You are free to copy the PC board layout for personal use.
Education 91.02
•Parallaxis 1.01 - Parallaxis is a procedural programming language based on Modula-2, but extended for data parallel programming. It was developed at the Universitaet Stuttgart (Germany) and is now available as public domain software.
Education 91.03
•Griffeath’s Cyclic Automata - Here is a nifty implementation of the cyclic cellular automaton described in the August 1989 Scientific American. The purpose of this program is to make pretty colour pictures.
•MandelZot 3.0 - excellent Mandelbrot set drawing program
•MandleCrawl 1.01 - Application and C code for a fast Mandelbrot Algorithm called Contour Crawling, invented by Scott Sherman in 1986 while a math student at Western Washington Univ. The algorithm works by scanning across the Mandelbrot Set point by point, looking for regions of the same colour. Once a “Contour” is detected, the algorithm bounces back and forth along the boundary of the contour until it finds its way back to its starting point, and then fills the interior. Intuitively and in practice it is far more efficient than the normal pixel by pixel method or Mariani’s Method. The following code should demonstrate that it is also simple. Scott and I (John Gossman) have written an article about Contour Crawling that covers the theoretical aspects and such concerns as “Islands”, the connected nature of the level sets around the Mandelbrot Set, and the practical issues of Contour Crawling on a discrete lattice. I will post this article somewhere soon, and leave a note here about getting hold of it. The best argument is to code up a version of this program and look at the results. Another nice thing is that all the optimization tricks for calculating the count (assembly, fixed-point etc.) can still be applied to this method in order to further increase the speed.
•Tile - “Tile is a simple program I wrote for playing with some tilings of the plane and their duals. You can explore a small class of tilings with it, and also create some interesting patterns. Click on a cell to change its state; I’ll leave it to you to figure out how it works. “
•TimeLines 1.0 - an application which produces an “On this day…” reports
•Truchet - The “Computer Recreations” column of the July 1989 Scientific American mentions Truchet tiles. This program creates random tilings from Truchet tiles and from some variants, including some tiles created by my colleague Greg Turk. Fingerpaint with the mouse button.
Education 91.04
•GraphMu 4.06 & MacMul 3.01 - MacMul and GraphMu are two programs for multivariate data analysis and graphical display on Macintosh.
MacMul performs computations of three basic multivariate data analysis methods: PCA (principal component analysis) for quantitative variables, CA (correspondence analysis) for counts tables, and MCA (multiple correspondence analysis) for qualitative variables. The PCA part offers several options: centered, standardized, non centered, or general PCA with any diagonal metric. Use of the three methods have been unified from the point of view of input files, computations, and outputs. A complete set of interpretation helps is proposed: inertia analyses (absolute and relative contributions, for rows and columns), data reconstitution using one or more factors, additional elements (rows or columns). Particular options are also available: CA seen as canonical correlation analysis of two discrete variables, variables/factors correlation ratios for MCA. Graphical outputs may be drawn with GraphMu. Data tables may have less rows than columns, and computations are always performed in the lowest dimension space. Version 3.01 needs 4Mb of main memory. An older version is available from the author ; it needs only 800Kb, but is in French and has more limited possibilities (max. table size = 9000 rows and 200 columns).
GraphMu is designed to draw graphical outputs of data analysis methods (principal axes planes), as well as several types of graphics usefull for the analysis of multivariate data (scattergrams, line charts, bar charts, histograms, stepped curves, maps with circles and squares, ellipses, Gaussian curves). It is possible to superimpose graphics over digitized background maps. The main feature of GraphMu is the possibility to draw automatically *collections* of graphics. Each elementary graphic may correspond to one column of the data table (comparison of variables) and/or to one group of rows (comparison of sets of individuals). Drawings may be saved in files of type “PICT”, and are compatible with commercial drawing software of the Macintosh (e.g. MacDraw). Copy/paste operations on pictures are supported, making superimpositions easy.
•Mephem 4.21 - Mephem4.21 is a port to the Macintosh of Elwood Downey’s astronomical computation program, ephem version 4.21. It computes positions and rise/set times of planets, the moon, comets, and more. It also has functions to graphically display object positions and search for interesting astronomical events. A manual is included. Questions about the Mac version should go to Peter Newton (newton@cs.utexas.edu).
Education 91.05
•CoCoA 1.0c - CoCoA is a Macintosh system for doing Computations in Commutative Algebra. It runs on any Macintosh with at least 512K of RAM, but it takes advantage of any additional available memory; it runs also under MultiFinder (even though it is not yet capable of performing computations in the background). It is written in Pascal (apart from a few ‘glue routines’ in assembler); the release 1.0b of the system consists of about 24,000 lines of code. CoCoA has been designed for offering the maximum ease of use and flexibility to the mathematician with little or no knowledge of computers. It is capable of performing simple and sophisticated operations on multivariate polynomial rings and on various data connected with them (ideals, modules, matrices, rational functions); polynomials may have coefficients either in the field Q of rational numbers or in the residue ring Zp. A current limit of the system is that the numerator and denominator of the coefficients in Q must not exceed 231-1=2147483648, and the integer p for Zp must not exceed 215-1 = 32767.
•HSTMAP 3.4.0 - HSTMAP displays the ground track and instantaneous prbital position of the Hubble Space Telescope projected on a world map. Also shown are the terminator deliniating the day/night sides, the sub-solar and sub-vernal equinoctal points, the longitude at 0h siderial time, one of several SAA models, and the ZOE.
Education 91.06
•Gravitation Ltd 4.0 - a graphic, two dimensional orbital simulation. Users can enter custom designed solar systems or run previously created ones. Systems can be views at varying zoom levels, recorded and played back at high speed, and edited via the graphic solar system editor.
•MacSim 1.1 - MacSim is a MicroCode simulator that implements the arch. described in Andrew Tanenbaum’s _Structured Computer Organization_ on pages 126-147 in the 2nd edition of his book. (Don’t know the pages for 3rd edition, but it works with the one presented there as well.)
•MacWordSearch 1.2 - MacWordSearch is a freeware utility that creates a word search puzzle given a list of words in a text file. You use your favorite word processor to finalize and print the output. Happy Word Hunting!
•StarAtlas v0.06b1 - This program draws a map of a region of the sky. Unlike the preceding application StarChart (*), it conforms to the Apple standard menu system with reverted black menu bar.
