中文摘要：

大自然千奇百怪，大自然用其“无形之手”造就了奇妙无比的分形世界，在自然形胜之处，形成了无数的自然-人工分形复合体．它们逐渐吸引人们的关注．渐进由旅游景物-景点-景群-景区-风景区以及风景区域等而形成不同规模、不同层次的旅游网络系统。旅游网络系统的最基本要素之一是景区（点），不同等级、不同层次、不同规模的景区（点）由各种旅游线路和廊道（交通线路）相串通、连接，从而形成旅游系统的网络空间结构。文中首先明确指出了将分形理论应用于旅游地理学研究的科学意义．系统提出了旅游系统网络空间结构在旅游景点、旅游线路与旅游交通三方面的分形科学问题：并进而以北京市旅游景点为例，定量给出了旅游网络系统空间结构的分形证据：最后．还指出了积极支持开展分形旅游研究对促进我国旅游地理学理论研究水平的提升和在国际旅游学领域尽快占据分形旅游研究前沿之地的积极意义。

英文摘要：

Fractal world is constructed by the invisible hands of nature. Coastline, mountain ridges, faults, river basins, and etc. are fractal objects. Human beings select to stay in the beautiful places, so the natural and man-made integrated objects are tormed gradually, l hen the network space of tourism system is formed accordingly. Mandelbrot stated the uncertainty of the coastline length in his paper ＂How long is the coast of Britain？ Statistical self-similarity and fractional dimension＂ published in ＂Science＂ in 1967. The concepts of fractal and fractal dimension were presented for the first time in that paper and have been applied to quantitatively describe the difference of crooked coastlines of British and South Africa. Based on extensive and thorough observation of a large amount of geographical, geological and economic phenomena, Mandelbrot discovered an inherent character in nature that he called fractal, and he also considered the fractal dimension as a quantitative parameter to describe numerous irregular phenomena in nature. As a new tool to picture the complexity of nature, the fractal theory has been widely used in many fields. Compared with the Euclidean geometry of more than two thousand years of history, fractal and fractal dimension are fitter for describing various complicated objects in nature. The fractal theory has been applied to many fields, which has actually constituted a scientific field with a broad frontier called Fractal. At present, it becomes a field with vast potential for use and application in many disciplines. And no doubt it also provides new analytical capability and scope to the innovation of tourism study. As to the study of tourism, researches on the fractal characteristics and fractal dimensions of the network space of tourism system have not been attempted till now. In this paper,the scientit~c signit~cance and research aspects are prospected. As a case study of Beijing, the fractal proof is provided in terms of the network space of tourism system. It is useful to a