The 892 unique ways to partition a 3 x 4 grid

dubberly.com reports: [edited]

For many years, designers have used grids to unify diverse sets of content in books, magazines, screens, and other environments. The 3 × 4 grid is a common example. Yet even in this simple case, generating all the options has — until now — been almost impossible.

Patch Kessler designed algorithms to generate all the possible variations, identify unique ones, and sort them—not only for 3 × 4 grids but also for any n × m grid. He instantiated the algorithms in a MATLAB program, which output PDFs, which Thomas Gaskin imported into Adobe Illustrator to design the poster.
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