Procedural generation of aesthetic patterns from dynamics and iteration processes. (English) Zbl 1396.49037
Summary: Aesthetic patterns are widely used nowadays, e.g., in jewellery design, carpet design, as textures and patterns on wallpapers, etc. Most of the work during the design stage is carried out by a designer manually. Therefore, it is highly useful to develop methods for aesthetic pattern generation. In this paper, we present methods for generating aesthetic patterns using the dynamics of a discrete dynamical system. The presented methods are based on the use of various iteration processes from fixed point theory, W. R. Mann [Proc. Am. Math. Soc. 4, 506–510 (1953; Zbl 0050.11603)], M. A. Noor [J. Math. Anal. Appl. 251, No. 1, 217–229 (2000; Zbl 0964.49007)], etc., and the application of an affine combination of these iterations. Moreover, we propose new convergence tests that enrich the obtained patterns. The proposed methods generate patterns in a procedural way and can be easily implemented on the GPU. The presented examples show that using the proposed methods we are able to obtain a variety of interesting patterns. Moreover, the numerical examples show that the use of the GPU implementation with shaders allows the generation of patterns in real time and the speed-up (compared with a CPU implementation) ranges from about 1000 to 2500 times.
MSC:
| 49N90 | Applications of optimal control and differential games |
| 47N70 | Applications of operator theory in systems, signals, circuits, and control theory |
| 49J40 | Variational inequalities |
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