论文标题
几何度量理论中的算法分形维
Algorithmic Fractal Dimensions in Geometric Measure Theory
论文作者
论文摘要
在本世纪，算法分形维度的发展与几何测量理论，尤其是欧几里得空间中的分形几何形状有许多富有成果的相互作用。我们调查了这些事态发展，重点是与真实的可计算功能的联系，算法维度的最新用途在证明古典（非偏金属）分形几何形状中的新定理以及未来研究方向上。
The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially fractal geometry in Euclidean spaces. We survey these developments, with emphasis on connections with computable functions on the reals, recent uses of algorithmic dimensions in proving new theorems in classical (non-algorithmic) fractal geometry, and directions for future research.
