The QuasiTiler tiling generator is a part of the Geometry Center at the ScienceU web site. (See separate review of Geometry Center.) It provides an interactive exploration of quasitiling and crystal patterns -- Penrose tilings and their generalizations. There is a rather detailed explanation of how this occurs and the mathematics behind the scenes.
This is a simulation that allows you to change parameters by using the mouse or by entering numerical values. It will then redraw the Penrose tiling pattern. Explanations are available on related pages.
Recommended Uses:
QuasiTiler could be used just for fun, as a supplement to a linear algebra or geometry course, or as a tool in the serious investigation of quasitilings.
Technical Requirements:
The only requirement is a java-enabled browser.
Identify Major Learning Goals:
One possible use of this material is simply visual motivation to explore geometry. The extensive explanatory material could also be used to make the link to linear algebra and the use of higher dimensional spaces.
Target Student Population:
Any geometry students could explore the visual portion of this material. The related explanations are suitable for college level math students who have studied some linear algebra.
Prerequisite Knowledge or Skills:
The visual material itself requires no math background to enjoy. Some of the background explanations refer to linear algebra.
Content Quality
Rating:
Strengths:
The explanation of quasi-tiling generation by projection is excellent: clear and brief It provides a nice application of linear algebra applications, and demystifies the concept of ?higher dimensions?. Coupled with the quasi-tiler applet, this site provides an excellent introduction to quasi-tilings. Also provided is a good list of references for further study. There is an interesting paragraph of things that can go wrong when generating the patterns.
Concerns:
Some of the explanatory material is very dense and would benefit from several intermediate diagrams to better illustrate the text. The importance of the orthogonal projection is mentioned but not explained. It might be beyond the scope of this site, but perhaps a well-chosen example could shed some light here.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
As a tool to introduce quasi-tilings, this would be hard to beat. The eye-catching graphics could lead students to spend enough time with quasi-tilings to develop a good understanding of the concepts involved. Connections could be made to the works of M.C. Escher.
Concerns:
The explanations are too advanced for the casual visual user, and for the more advanced student the connection with the interactive portion is not immediately obvious. It would be easy to let a QuasiTiler session degenerate into playing around with pretty pictures. There?s nothing inherently wrong with this, but it doesn?t necessarily result in much mathematics being learned
Ease of Use for Both Students and Faculty
Rating:
Strengths:
If the goal were simply to produce a wide variety of beautiful quasi-tilings, QuasiTiler would rate a 5 on ease of use. To systematically change the offset and generating plane and observe the resulting changes by the point-and-click method is a little unpredictable, and the type-the-numbers method is a little tedious. It is,
however, worth the difficulty in use.
Concerns:
Sliders or some other method of changing the values that define the quasi-tiling would be nice, as well as a constant display of all of the coordinates of each defining vector. Also, while getting a feel for this in the three-dimensional case, a user-rotatable picture of the generating plane situated in a coordinate lattice would be nice.The interactive portion of this site has an annoying scale - the picture takes up the whole screen and the parameters are set below. This results in slow redraws every time a setting is changed and makes speedy experimentation difficult. More explanations of where and what to click would be useful.
Creative Commons:
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