The computational generative patterns in Indonesian batik

The paper discusses the terminology behind batik crafting and showed the aspects of self-similarity in its ornaments. Even though a product of batik cannot be reduced merely into its decorative properties, it is shown that computation can capture some interesting aspects in the batik-making ornamentation. There are three methods that can be exploited to the generative batik, i.e.: using fractal as the main source of decorative patterns, the hybrid batik that is emerged from the acquisition of L-System Thue-Morse algorithm for the harmonization within the grand designs by using both fractal images and traditional batik patterns, and using the random image tessellation as well as previous tiling algorithms for generating batik designs. The latest can be delivered by using a broad sources of motifs and traditionally recognized graphics. The paper concludes with certain aspects that shows how the harmony of traditional crafting and modern computation could bring us a more creative aspects of the beautiful harmony inherited in the aesthetic aspects of batik crafting

Generalized Fractals for Computer Generated Art: Preliminary Results

This paper explores new types of fractals created by iteration of the functions xn+1 = f1(xn, yn) and yn+1 = f2(xn, yn) in a general plane, rather than in the complex plane. Iteration of such functions generates orbits with novel fractal patterns. Especially interesting are N-th order polynomials, raised to a positive or negative integer power, p. Such functions create novel fractal patterns, including budding, spiked, striped, dragon head, and bat-like forms. The present faculty working paper shows how to create a rich variety of complex and fascinating fractals using this generalized approach, which is accessible to students with high school level skills in mathematics and coding

Iteration of holomorphic functions and visualisation of fractals

Treballs Finals de Grau d'Enginyeria Informàtica, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Núria Fagella Rabionet Anna Puig Puig[en] When a holomorphic function is iterated, it generates a dynamical system on the complex plane. In this project we describe both the local and global theory of the different orbits of holomorphic functions, focusing on the polynomial families. We present the necessary results leading to two algorithms to draw both Julia sets and Mandelbrot (and Multibrot) set: the Escape Algorithm and Henriksen Algortihm. In addition, we present the development of an interactive application, made with Unity, that allows us to visualise fractals on the complex plane -rendered using the aforementioned algorithms- and a generalisation of them over a 3-dimensional space, directly on a website

Fractals with arbitrary segment lengths

Work in the area of fractal geometry has generally focused on a specific facet of the discipline at the expense of other interesting features. This approach often generates more questions than answers for the general audience due to the lack of unification across all views. It appears that a common thread to relate all aspects of fractal characteristics is missing. This paper addresses this question and presents some new and fascinating results. For example, in-depth mathematical analysis often defers to the intriguing and attractive graphical displays produced by mapping the complex plane to the pixel field on a CRT. Both area, mathematics and graphics, are generally developed or presented independently. the development of common attribute linkages is done separately or perhaps not at all. First, a completely modular survey of the state of the art concerning regular fractal geometry is given. In addition, a method for calculating the fractal dimension of asymmetric fractals is proposed, where a symmetric fractal is a special case of an asymmetric fractal --page iii

Fractals: A More Dynamic & Multidimensional Approach to Business Analytics

This paper has two parts. In the first part, I articulate the short but significant evolution of the study of fractals. In the second part, I discuss the application of fractals to business models and business analytics. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line (Mandelbrot, 1982, pg. 1). Thus began the study of fractals on a large scale. Fractals in their most common sense are nothing but interesting images. To scientists, however, they represent a fairly untrodden field in mathematics. Until the 1970s, fractals had been identified but not studied due to the lack of adequate technology. With the invention of the computer, however, fractals have been gaining increasing popularity among everyone from artists to businesspeople

Computational Batik Motif Generation: Innovation of Traditional Heritage by Fractal Computation\ud

Human-computer interaction has been the cause of the emerging innovations in many fields, including in design and art, architectural, technological artifacts, and even traditional heritage. In the case of Indonesian traditional heritages, the computation of fractal designs has been introduced to develop batik design – the genuine textile art and skill that becomes a symbol of Indonesian culture. The uniqueness of Batik, which depicted in the richness of its motifs, is regarded as one of interesting aspect to be researched and innovated using computational techniques. Recent studies of batik motifs have discovered conjecture to the existence of fractal geometry in batik designs. This finding has given some inspiration of implementing certain fractal concepts, such escape-time fractal (complex plane) and iterated function system to generate batik motifs. We develop motif generator based upon the Collage Theorem by using Java TM platform. This software is equipped by interface that can be used by user to generate basic patterns, which could be interpreted and painted as batik motif. Experimentally, we found that computationally generated fractal motifs are appropriated to be implemented as batik motif. However, human made batik motifs are less detail and some of them differ significantly with the computationally generated ones for tools used to draw batik and human aesthetic constraints