| The Julia set and Mandelbrot set (shortened form is J-M sets) are the typical delegate of iterated fractal-sets, fc(z) = z2+c is their iterated function, while the general J-M sets are the extension of J-M sets whose iterated function is changed to fω,c(z) = zω+ c. The general J-M fractal images which are generated by iteration according to the definitions of general J-M sets are the researching objects of this paper.The property of general J-M fractal images is studied by the method of experimental math in this paper. First of all, the escape time algorithm which is the generated algorithm of general J-M fractal images is analyzed seriously, using the knowledge of complex analysis, and the basic steps of generated algorithm are given. Then, on the basis of studying the property of iterated function, some controlling variables (such as: Rmax, B) are made certain whenω∈R,ω> 1, and therefore the above-mentioned algorithm is optimized consequently. At last, in term of the before-mentioned basic steps of generated algorithm, the computer conformation of general J-M fractal images is realized using the Visual C++ programming, and large numbers of fractal images are obtained. According to these images, some characteristics of general J-M fractal images can be abstracted, and they can be proved.Because the general J-M fractal images are constructed by the iterated function fω,c(z) = zω+ c, their property is researched by analyzing the relationship between general J-M fractal images and iterated function. In this paper, the relationship between general J fractal images andω, c is researched, and the relationship between general M fractal images andωis researched too. In fact, A few people study the connection of general J fractal images and c which is analyzed in this paper tentatively and successfully. |
