<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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 (Mann, S, Noor, 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.</p></abstract>

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 (Mann, S, Noor, 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.

Procedural generation of aesthetic patterns from dynamics and iteration processes

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

Procedural generation of aesthetic patterns from dynamics and iteration processes

Published Online: Jan 13, 2018

Page range: 827 - 837

Received: Apr 20, 2017

Accepted: Sep 01, 2017

DOI: https://doi.org/10.1515/amcs-2017-0058

Keywords
dynamical system, dynamics, iteration process, aesthetic pattern

© by Krzysztof Gdawiec

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Procedural generation of aesthetic patterns from dynamics and iteration processes

Published Online: Jan 13, 2018

Page range: 827 - 837

Received: Apr 20, 2017

Accepted: Sep 01, 2017

DOI: https://doi.org/10.1515/amcs-2017-0058

Keywordsdynamical system, dynamics, iteration process, aesthetic pattern

© by Krzysztof Gdawiec

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
dynamical system, dynamics, iteration process, aesthetic pattern