What is GeCla?

The program GeCla, short for Generator and Classifier1, allows the user to generate a pattern, a frieze or a rosette with a previously chosen kind of symmetry starting from an asymmetric motif. It also allows the classification (with or without help from the program) of the patterns, friezes, rosettes obtained in this manner. In the end, the program provides a report of the errors committed.

GeCla was designed to be attractive and accessible to students of various levels of education.

The generator writes encoded information about the existing symmetries in the jpg image file generated. Then the classifier reads and interprets this coded information, which allows it (according to the level of aid chosen) to give information about how the classification process is going, preventing wrong choices, or only indicating at the end whether the classification is correct and, if not, indicating the first mistake.

GeCla also includes a practice option that can be used via the Internet. In it, each player generates a pre-agreed number of images and then both exchange images and each classifies the other's images. All steps are managed by the program, which in the end provides a report on eventual mistakes.

Atractor intends to carry out online workshops about GeCla for students and also to promote competitions between schools2. If you are a teacher interested in participating with students in a workshop or in a student competition, please contact Atractor: atractor@atractor.pt.

1 GeCla is a program which is associated with the DVD Symmetry - the dynamical way, but whose use does not assume that one knows this DVD.

2 In the past, a competition was organized between Portuguese students of a school in Valadares and Italian students from a school in Besozzo. See references in the Gazeta de Matemática, X'la Tangente and in Educação e Matemática.