Making mosaics from Tetris®tiles

This paper addresses the problem of reproducing greyscale images using mosaics composed of tetromino tiles, the building blocks of the well-known puzzle game Tetris®. An integer linear optimization model is proposed to minimize the discrepancy between the target image and the resulting mosaic. Three colouring schemes for assigning greyscale shades to the tetrominoes, together with three solution methods to manage the computational complexity of the model, are developed and assessed. Computational experiments on four images evaluate the proposed methods, combining image-similarity metrics with a user study gathering human preference judgements. The results identify the solution method that offers the best trade-off between mosaic quality and computational effort, while showing that the most suitable colouring scheme depends on the target image. Overall, the methodology provides a computationally efficient framework for generating visually coherent tetromino-based mosaics, even for images of realistic size and complexity.