Software Reviews

ADOBE ILLUSTRATOR Applications Product Division of Adobe Systems, Mountain View, CA, U.S.A., 1987. $595.00. THE GEOMETER'S SKETCHPAD by NickolasJackiw, Visual Geometry Project. Key Curriculum Press, Berkeley, CA, U.S.A., 1991. $169.95. CABRI GEOMETRE by YvesBaulac, Franck Bellcmain and Jean-Marie Laborde. Brooks/Cole, Pacific Grove, CA, U.S.A., 1992. $95.00. CRYSTAL PAINT by DennisJohnson. Great Wave Software , Scotts Valley, CA, U.S.A., 1987. $49.95. ESCHER-SKETCH by Terry Flaherty. Intellimation, Santa Barbara, CA, U.S.A., 1991. $35.95. MATHEMATICA by Stephan Wolfram. Wolfram Research , Champaign, IL, U.S.A., 1988. $595.00. MOSEDIT byJanos]. Baracs and Nicolas Chourot. Broderbund Software, San Rafael, CA, U.S.A., 1992. SYMMETRY STUDIO by Timothy Binkley andJohn Simon. Van Nostrand Reinhold, New York, NY, U.S.A., 1992. $64.95. The program is packaged with a text: Symmetry Studio: Creative ComputerResourcesfor Twa-Dimensional Design. Reviewed by Dorisj. Schauschneider, Momvian College, Bethlehem, PA 18018-6650, U.S.A. There is a variety of computer software available to assist in the design of tilings. For relatively simple tilings, one can use one of the many powerful design programs for desktop publishing , such as Adobe Illustrator. (In fact, this program was used to produce all of the tilings shown in Britton and Seymour's Introduction to Tessellations [1]). But for more precise geometric control and automatic generation of tilings, several other programs are useful. 392 Current Media ill. Software Reviews The Geometer's Sketchpad and a similar program called Cabri Geometre aUow precise constructions (as well as freehand drawings) of polygonal tiles that can be dynamicaUy manipulated to change shape and size. Both programs can perform all of the Euclidean isometries (translation, rotation , reflection, glide-reflection) on constructed objects so as to create tilings . They can also record 'scripts' (or macros) that can be 'played' on specified objects (such as tiles) to produce tilings with desired properties. To produce tilings, the user must have some knowledge of the geometric transformations, of how they interact to produce tilings and of how the shape of tiles is influenced by the transformations that will produce certain tilings. Powerful multipurpose mathematical software such as Mathematica can be used to program routines that can draw Penrose and other aperiodic tilings [2]. There are four programs for the Macintosh computer that are dedicated to the automatic production of periodic patterns and tilings designed by the user. However, the degree of control by the user, the geometric knowledge required of the user to make the best use of the programs, and the range of capabilities of the programs vary widely. Crystal Paint is the simplest and also the most limited of the Macintoshcompatible programs. The user chooses one of 17 plane-symmetry types from a menu (a design with an 'F' motif displays the symmetry) and then draws a motifwith the mouse. Simultaneously, many images of the drawn motif are automaticaUy generated by the program, according to the symmetry type selected. BasicaUy, the program makes the computer act like a kind of kaleidoscope that repeats images of a drawing to fill the screen with a periodic pattern. The number of repeats viewed on the screen is controlled by an adjustable zoom feature. The program is good for the beginner to learn about the different symmetry types through experimentation and to make quick, rough patterns and tilings, but the user cannot adjust individual parameters of the 'repeat' (the underlying lattice), nor easily adjust the shape of tiles once a tiling is drawn. In the brief manual that accompanies the program, there is no attempt to explain the geometry that produces the patterns. Escher-Sketch produces periodic patterns and tilings much the same way that Crystal Paint does, but it provides more geometric clues for the user, including a translation unit with a generating region and a schematic diagram showing where (in a translation unit) the rotation centers and reflection and glide-reflection axes lie [3]. The program also aUowsrough adjustment of the shape oflattice units, modification of tile outlines after the tiling has been drawn, and 'filling ' (shading) of portions of a tile and its copies. The user can also store a motif that...