Research On Generation Of Extended Fractal Patterns Based On Rules

Fractal theory, known as geometry of nature, is a new branch of modern mathematics, and its essence is a new world outlook and methodology. It recognized that partial of the world, under certain conditions or processes, may show self-similarity of the part and the whole in some respect (shape, structure, information, features, time, energy, etc.). Patterns obtained by fractal theory which are complicated, colorful and ever changing, give a strong heartshock to people. Fractal patterns which are not only a mathematics carrier, but also an expression of the art achieve the perfect combination of mathematics and the art.A large number of sophisticated patterns found in the fractal research, which not only make us think about pure and perfect structure in Plato's world, but also guide us to think about the complex and ever changing structure in the real world, have broad application prospects. Fractal patterns have infinitely delicate structure and some local lines, with the support of some color scheme, will show strong layering and have the feature of anti-copying, thus fractal patterns can be used in security design. Because fractal patterns have so many potential applications, studies of fractal composition processes, exploring new methods of composition in order to construct more fractal patterns, is very meaningful.This paper proposes the concept of extended fractal patterns, including traditional patterns and non-traditional ones. Traditional patterns refer to fractal patterns which are generated by traditional fractal algorithms; non-traditional patterns refer to fractal-derived patterns which are generated by the way of adding new rules to traditional fractal algorithms and have the shadows of classic fractal patterns, but are different from traditional ones. It is non-traditional patterns that enrich fractal pattern categories.In the drawing process of fractal patterns, thanks to theirs complex and ever changing characteristics, the patterns finally drawn are often unpredictable and uncontrollable. Therefore, the concept of composition rule is introduced into the process of fractal composition, considers the procedure of fractal composition from the perspective of rules, and controls the procedure of fractal composition with rules. Although patterns obtained are still complex, such kinds of patterns have rules to follow, abide by some contraints, and can be divided into different categories. Because the rules are man-made, fractal patterns designed can reflect people's aesthetic preferences and subjective needs. The rules of fractal composition can be divided into three categories including algorithm rules, layout rules and coloring rules, and intensive studies are carried out respectively from the three aspects.Algorithm rules influence the drawing results through algorithms, including traditional fractal algorithms and a number of adjustments or changes based on the traditional fractal algorithms. This paper introduces random, Boolean, stripes and other specific algorithm rules, gives corresponding composition formulas and patterns and these rules fundamentally change the structures of the patterns.Layout rules control the macro-structures of the patterns in the composition process, so that target patterns will present the specified structures. This paper introduces the symmetry, shape, composition and other specific layout rules, gives the corresponding composition formulas and patterns, and these rules make the pattern show in specified appearance.Coloring rules refer to different coloring methods for patterns, used to control the colors of the patterns. This paper introduces double color, transition, fusion and other specific coloring rules. Adopting different coloring rules, patterns with the same structure will produce different artistic effects.This paper is committed to the research of fractal composition rules, aiming at exploring better composition rules and combinations of rules. We carry out research on three types of rules respectively, but don't seperate one from another. We study both specific composition rules and combinations of different rules. Combining a variety of compositions rules, using flexibly, in the process of fractal compositon, is the real pursose of our research.