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.
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Lutz, J.H., Mayordomo, E. (2021). Algorithmic Fractal Dimensions in Geometric Measure Theory. In: Brattka, V., Hertling, P. (eds) Handbook of Computability and Complexity in Analysis. Theory and Applications of Computability. Springer, Cham. https://doi.org/10.1007/978-3-030-59234-9_8
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DOI: https://doi.org/10.1007/978-3-030-59234-9_8
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Online ISBN: 978-3-030-59234-9
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