C.A.B. Smith (CABS)
Colossus reconstructed
W. T. Tutte
Giovanni Resta's Perfect Rectangles The dissection of rectangles, cylinders, tori and Mobius strips into squares ; S J Chapman (subscription only)
John Shier's work on fractal space-filling with squares, (In fact with any shape). John's interesting discovery is that one can fill all space by placing ever-smaller shapes at random without overlap (the areas of the shapes must follow a prescribed sequence). In the limit where one places an infinite number of shapes, they completely fill the space in fractal fashion. The evidence is that any shape will work. It may seem surprising, but all of these varied images are examples of the same algorithm. The rules only apply to the shapes -- the color scheme can be chosen arbitrarily.
Links to further work and examples from John Shier are here.
Related work by Paul Bourke is here
Squaring Game
addresses a special kind of tiling puzzles or, more appropriately, tiling quilts, and is based on a well-known mathematical problem called "square packing" or, seen from a different perspective, "square (or rectangle) dissection".When a game starts, a square (or a rectangle) is divided into smaller squares of various sizes, each with its own color. Rearranging these squares into the original square (or rectangle) is the purpose of the game. Please note that each tiling has one, and only one, solution.
Since squares have even edges and do not stick together, each of them has to be positioned in its exact place on stage A in order to solve the game. Although squares are automatically snapped along a preset grid, their precise rearrangement is your own task.
Updated on ... June 2 2012
