Maciej Klimek

Iteration of analytic multifunctions

It is shown that iteration of analytic set-valued functions can be used to generate composite Julia sets in C-N. Then it is shown that the composite Julia sets generated by a finite family of regular polynomial mappings of degree at least 2 in C-N, depend

Discovering Curves and Surfaces with Maple

From the Publisher: Despite the fact that Maple V has become one of the most popular computer algebra systems on the market, surprisingly few users realize its potential in the field of scientific visualization. The purpose of this book is to equip the reader with a variety of graphics tools needed on the voyage of discovery into the complex and often beautiful world of curves and surfaces. A comprehensive treatment of Maples graphics commands and structures is combined with an introduction to the main aspects of visual perception. Top priority is given to the use of light, color, perspective, and geometric transformations. Numerous examples, accompanied by pictures (many in color), cover all aspects of Maple graphics. The examples can be easily customized to suit the individual needs of the reader. The approach is context-independent, and as such will appeal to students, educators, and researchers in a broad spectrum of scientific disciplines. For the general user at any level of experience, this book can serve as a comprehensive reference manual. For the beginner, it offers a user-friendly elementary introduction to the subject, with mathematical requirements kept to a minimum. For those interested in advanced mathematical visualization, it explains how to maximize Maples graphical capabilities. In particular, this book shows how to turn Maple into an excellent modeling tool capable of generating elaborate surfaces that conventional modelers cannot produce. These surfaces can be exported to an external ray tracer (e.g., POV-ray) for sophisticated photo-realistic rendering. All of the Maple code segments which are presented in the book, as well as high-resolution pictures showing alternative rendering of some of the books color plates, are included on the accompanying DOS diskette.

Invariant pluricomplex Green functions

The purpose of this paper is to present a concise survey of the main properties of biholomorphically invariant pluricomplex Green functions and to describe a number of new examples of such functions. A concept of pluricomplex geodesics is also discussed.

Saving and Exporting Maple Graphics

This chapter is divided into two sections. The first one explains straight-forward methods of saving, editing, and printing images created within Maple. The second section shows how to export numerical data, related to surfaces generated in Maple, to an external renderer. This approach rewards the user with smooth-looking surfaces with a photo-realistic finish. A wide variety of interesting textures can be applied, thus making those surfaces translucent, metallic, highly reflective, patterned, and so on. Furthermore, multiple light sources of different types are available (like spotlights or area lights), and all objects in the plotted scene have proper shadows.

Two-Dimensional Plots

The purpose of this chapter is to explain in detail the basic types of two-dimensional plots that can be executed in Maple. In contrast to the three-dimensional case, most choices are straightforward and can be mastered very quickly. We will discuss planar plots of a more specialized nature in Section 8.3.

Three-Dimensional Plots

Plotting in three-dimensional space bears a number of similarities to the corresponding process in two dimensions, but these similarities are rather superficial. At times it can be difficult to achieve a convincing representation of a three-dimensional object on a two-dimensional screen. The human perception of space and color is more complicated than most of us realize, and it imposes strict demands on what is acceptable. In the case of three-dimensional graphics, the optional arguments used within main plotting commands have a more significant impact on the final result than they have in the two-dimensional case. For instance, an incorrect use of perspective can produce distortions to the shape we want to graph. Wrong use of color and lighting can hide or exaggerate certain features of plotted objects. Consequently, these topics require as much attention as the syntax of Maple commands. We already know from the previous chapter, albeit only theoretically, how to control the perspective projection and how to specify the position of directional lighting. Here we will put this knowledge to use. Furthermore, two sections of this chapter will be devoted specifically to color and lighting. We will also examine data structures generated by plotting commands and various ways of modifying such structures.

The plottools Package

One of the most significant changes implemented in the area of graphics in Maple V Release 4 is the introduction of a new package called plottools. Because this chapter is devoted entirely to this subject, readers who use Maple V Release 3 might want to skip it altogether. On the other hand, Release 3 users may find many of the techniques explored here easy to replicate in their version of Maple.

Functions and Procedures

All the types of graphics discussed in this book are related in one way or another to functions. Various types of functions are used to parametrize curves and surfaces and to control the red, green, and blue components of colors in many pictures. This is why it is important and convenient to have a separate chapter describing the most common methods of defining functions. Much of this book is designed in such a way that it can be understood with a limited knowledge of functions. In several instances, however, some familiarity with functions defined via procedures is indispensable. For example, in this chapter we describe spline interpolation, which provides an important tool for graphics, and we show how to use iteration of functions to plot some fractal sets.