分形的推广、应用和某些基本问题

Extension,Applications and Some Basic Questions on Fractals

首先简要介绍分形和自相似性.其次讨论分形的推广,包括笔者提出的复数维.第三探讨分形的某些应用,包括应用于社会科学和文学.第四研究分形中的若干基本问题,特别是分维、分形中量纲的奇异性,D维分形物体的量纲是不同的(cm)D.最后探索宇观-微观分形、泛量子理论和对分形的展望.

First, fractal and self - similarity are introduced briefly. Next, the extensions of fractal are discussed, which includes the complex dimension proposed me. Third, some applications of fractal are searched, which includes to apply to social science and literature. Fourth, some basic questions in fractal are investigated. In particular, the dimension of fractal is fantastic, which is different （cm）o for D -dimensional fractal objects. Finally, the cosmic -microscopic fractal, the extensive quantum theory and a forecast of fractal are researched.