Mandelbrot- and Julia-like Rendering of Polynomiographs

Polynomiography is a method of visualization of complex polynomial root finding process. One of the applications of polynomiography is generation of aesthetic patterns. In this paper, we present two new algorithms for polynomiograph rendering that allow to obtain new diverse patterns. The algorithms are based on the ideas used to render the well known Mandelbrot and Julia sets. The results obtained with the proposed algorithms can enrich the functionality of the existing polynomiography software

Perturbation Mappings in Polynomiography

In the paper, a modification of rendering algorithm of polynomiograph is presented. Polynomiography is a method of visualization of complex polynomial root finding process and it has applications among other things in aesthetic pattern generation. The proposed modification is based on a perturbation mapping, which is added in the iteration process of the root finding method. The use of the perturbation mapping alters the shape of the polynomiograph, obtaining in this way new and diverse patterns. The results from the paper can further enrich the functionality of the existing polynomiography software

PSO-based Newton-like Method and Iteration Processes in the Generation of Artistic Patterns

In artistic pattern generation one can find many different approaches to the generation process. One of such approaches is the use of root finding methods. In this paper, we present a new method of generating artistic patterns with the use of root finding. We modify the classical Newton's method using a Particle Swarm Optimization approach. Moreover, we introduce various iteration processes instead of the standard Picard iteration used in the Newton's method. Presented examples show that using the proposed method we are able to obtain very interesting and diverse patterns that could have an artistic application, e.g., in texture generation, tapestry or textile design etc

Numerical simulation of investment casting of gold jewelry : experiments and validations

This paper proposes the numerical simulation of the investment casting of gold jewelry. It aims to study the behavior of fluid flow during mould filling and solidification and to optimize the process parameters, which lead to predict and control casting defects such as gas porosity and shrinkage porosity. A finite difference method, computer simulation software FLOW-3D was used to simulate the jewelry casting process. The simplified model was designed for both numerical simulation and real casting production. A set of sensor acquisitions were allocated on the different positions of the wax tree of the model to detect filling times, while a set of thermocouples were allocated to detect the temperature during casting and cooling. Those detected data were applied to validate the results of the numerical simulation to the results of the real casting. The resulting comparisons signify that the numerical simulation can be used as an effective tool in investment-casting-process optimization and casting-defect prediction