An Auto-Drawing Method Of General M-J Set Based On Design Case

In the past few decades, great important progress has been made both in fractal application and theory. People are shocked by the complex patterns and wonderful colors of images drawn with fractal theory. General M-J set images have been widely used in the design of product package and security logo. However, graphical features of the general M-J sets are affected by many parameters. As a result, phenomenon such as blind spots, aesthetic fatigue appeared during the design process. Thus, a computer-aided method is needed to reduce designers'workload and improve the efficiency on the premise of high quality.Design case is the designer's previous and successful case, which contains all the parameters in the whole process and the designer's experience, concepts and personal preferences. Design is a process which aims to solve complex problems and find the best solution step by step. In the computer-aided design system, the design system can be effectively improved by the design knowledge learned from design cases. Therefore, design case can provide great help for the later design.In this paper, automatic drawing method of the general M-J set is researched. First, drawing parameters and image feathers are analyzed, and then evolutionary computation method is used to draw general M-J set images, which have the specific style. This method can eliminate designer's blind spot. During the process, a method of calculating the similarity between design cases is proposed according to the feathers of the general M-J set images, and based on the similarity of case base, a fitness function is established to guide the evolution. This method can make design more automatic and reduce the designers'workload. Research details of this paper are as follows:(1) Analysis of drawing parameters of image feathersGeneral M-J set images are effected by lots of drawing parameters, including iterative formula, color scheme, image type, drawing method, etc. Different parameters have different effects. Meanwhile, image complexity and satisfaction of general M-J set are defined, the former refers to the complexity of the structure, expressed by its contour number and the latter is given by the designer, represents designer's subjective preferences.(2)Storage and similarity of the design caseDesign case records all the information in the whole process of fractal image design, containing the designer's personal preference and design style. Excellent design case has reference value and guidance to the new design. In this paper, after analyzing the general M-J set, methods are proposed for representing and storing the design case, as well as calculating their similarity.(3) General M-J set auto-drawing with evolutionary calculation methodIn this paper, iterative formula and color scheme of the general M-J set are encoded as genetic factors with different encoding ways, and images are drawn automatically with GA. In the process, fitness function based on the similarity between individual case and case base is established to guide the evolution, so as to shorten the cycle and success rate of the design.This research is drawn from our researching project: Independent Innovation Special Projects of Shandong Province"Product packaging and anti-imitation brand innovative design base on Fractal technology, 2006ZZ10". This method was applied in the FDS (Fractal Design System), developed by the project, and got good results.