A note on the possibility of a motion without crossing a given subset
Reza Mirzaie
TL;DR
This paper investigates the conditions under which a motion can occur in Euclidean space without intersecting a specified fractal subset, focusing on the subset's fractal dimension.
Contribution
It introduces a theoretical framework linking the fractal dimension of a subset to the feasibility of non-crossing motions in Euclidean space.
Findings
Fractal dimension constrains possible motions.
Certain fractal subsets permit non-crossing paths.
Theoretical bounds for motion feasibility based on fractal properties.
Abstract
We study the fractal dimension of a given subset X of R^{n} such that a motion is possible without crossing X.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · Stochastic processes and statistical mechanics