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Paper details
Number 4 - December 2017
Volume 27 - 2017
Procedural generation of aesthetic patterns from dynamics and iteration processes
Krzysztof Gdawiec
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.
Keywords
dynamical system, dynamics, iteration process, aesthetic pattern