This paper presents an algorithm for creating Escher-like tiling patterns. Escher's print "Sky and Water I" contains a bird tile at the top, a fish tile at the bottom, and many intermediate tiles between them; from the top towards the bottom, the copies of the bird deform gradually, melting away into the background, while the fish gradually appears from the background. For any pair of tiles, the proposed algorithm creates this type of a tiling pattern automatically. The algorithm is a combination of three techniques: tiling, morphing, and figure-ground reversal. The algorithm is implemented as an interactive system, and its performance is also shown by examples. The algorithm will offer a new option to the menu of a computer-aided system for designers to create artistic patterns efficiently.

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The correspondence principle of linear viscoelasticity has been widely used to solve viscoelastic problems. Based on the correspondence principle, we can obtain the viscoelastic solution in the Laplace domain directly from the associated elastic solution only by replacing the elastic constants with their corresponding values. In order to obtain the viscoelastic solution in the time domain, however, we must perform the inverse Laplace transform, which usually requires very complicated calculation. In this paper, we show a few useful theorems concerning the completely relaxed viscoelastic solution based on the correspondence principle, the final-value theorem of the Laplace transform, and the hereditary integral. These theorems indicate that the completely relaxed viscoelastic solution due to a step force is proportional to the solution due to a force that increases linearly in a long term, and that the completely relaxed viscoelastic solution can be directly obtained from the associated elastic solution without complicated viscoelastic calculation.

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