Mathaquilta is designed to help mathematicians visualize interesting patterns that arise in quilts, and to let quilters play around with those patterns before committing. Inspiration for this app comes from studying a quilt block known as Drunkard’s Path: a square with a quarter circle in a contrasting color in one corner. In studying the patterns possible from the Drunkard’s Path block, a related block is mentioned, Snake’s Trail. It has two quarter circle “stripes” in opposing corners.
Quilts using both kinds of tiles can be created in whatever size you would like, and foreground/background colors can be changed as necessary. When a Snakes Trail tile is tapped on, it toggles its orientation, so users can while away the hours making interesting patterns/mazes. The user can make an entire quilt with the same orientation, or randomly choose between a "northwest" and "southeast" orientation. In addition, once the quilt has been created, tiles can be edited in place, saved, printed, etc.
The same idea applies to the Quarter Circle patterns, except that since they are in a 4x4 pattern, that changing any tile in the visualization window automatically updates the entire quilt.
Both quilt types are fully editable once created -- so you can resize, recolor, reorient as you see fit. Naturally these can be saved and printed for further study.
This app allows you to play/experiment with each of these types of square blocks—for the purposes of designing quilts or merely whiling away a few hours having fun exploring these patterns.