packing problems

PACKING A SUCCESSION OF L'S IN A SQUARE CONTAINER
http://www2.stetson.edu/~efriedma/packing.html.

PACKING SYSTEMS. Packing systems are one of the very few alternatives to tessellating systems that have emerged in the last ten or fifteen years of architectural discourse. One aspect of the systems will be to define the concept of packing as it relates to certain rather pregnant case studies, to the program of housing, to a somewhat obscure branch of mathematics called packing problems and to analogous processes found in nature. Because of its novelty, the definition of packing systems will be fluid and changing due to what we may discover about packing and what we ultimately produce here. Because it is relatively new, it will be necessary to spend more time and creative energy on packing problems to bring them up to speed. To start, I would like to reference the mathematical problem of packing as well as a few case studies.

According to Wikipedia, packing problems are a class of optimization problems in recreational mathematics that involve attempting to pack objects together (often inside a container), as densely as possible. The source of many puzzles and games, these problems can also be related to real life storage and transportation issues. With a little expertise, we may find that they have a practical relation to architecture as well. In a packing problem, you are given two components: containers (usually a single two or three-dimensional convex region, or infinite space) and goods (usually a single type of shape, some or all of which must be packed into this container). Usually the packing must be without overlaps between goods and other goods or the container walls. The aim is to find the configuration with the maximum density. In some variants the overlapping (of goods with each other and/or with the boundary of the container) is allowed but should be minimized.