English

Algorithmic Fractal Dimensions in Geometric Measure Theory

Computational Complexity 2020-07-29 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2007.14346,
  title  = {Algorithmic Fractal Dimensions in Geometric Measure Theory},
  author = {Jack H. Lutz and Elvira Mayordomo},
  journal= {arXiv preprint arXiv:2007.14346},
  year   = {2020}
}
R2 v1 2026-06-23T17:28:16.267Z