Symmetry Generator

Date started: Fall 2019
Leads: Laura Taalman, Carolyn Yackel


The symmetry generator (SG) continues and expands an OpenSCAD project begun by Laura Taalman to a more robust Processing/Python design tool that enables knitters to create and envision knitting patterns featuring specific wallpaper symmetries. Somewhat in the spirit of iOrnament, this tool allows the user to select a symmetry type to apply to a given pattern region. Unlike continuous applications such as iOrnament, the SG interface is made for discrete settings such as hand knitting patterns and punch cards for knitting machines.

In its current form, the SG can be applied to a number of native tiles designed to help the user observe the distinctions between symmetry types. Buttons on the side allow users to change between wallpaper (symmetry) types, and many keyboard press buttons have also been enabled to allow users to cycle through symmetries, tiles, and number of tiles displayed on the board. Beyond its practical fiber arts use, the easy functionality of the SG can be used as an educational tool for exploring wallpaper/orbifold symmetries.

The generator has a design feel in addition to its mathematical element, meaning that for some symmetries both vertical and horizontal versions are generated from the original tiles, allowing the user to choose their preferred aesthetic. The Symmetry Generator functionality currently allows user input of square tile images, an interface for generating knitting punch card pattern bases, generation and enumeration of two-color symmetries.

Future goals include implmentation of parallellogram lattice designs and non-rectilinear translation vectores. An off-shoot of this project has been a separate project that involves approximating three- and six-fold symmetries on a square grid. The results of that project will eventually be absorbed into this project.


Symmetry Generator showing action of wallpaper symmetry pmg on a simple “smile tile” SVG image
Symmetry Generator showing action of wallpaper symmetry pmg on a reverse transpose “comma” SVG image, with visible glide, mirror, and reflection marks
Symmetry Generator showing action of a two-color variant of wallpaper symmetry pmg on an interactively generated “punch card” design
Punch cards for Brother KH-881 analog knitting machine, illustrating six different wallpaper symmetries
Two-color fair isle knitted fabric from punch card symmetry designs, with additional color applique