Properties of Bourbaki's Function
Joey McCollum
TL;DR
This paper investigates Bourbaki's function, a continuous but nowhere-differentiable function, analyzing its properties, identities, antiderivative, and fractal dimensions of its graph.
Contribution
It provides a comprehensive analysis of Bourbaki's function's properties, including new insights into its functional identities and fractal dimensions.
Findings
Bourbaki's function is continuous and nowhere differentiable.
The function's antiderivative is characterized.
The box and Hausdorff dimensions of the graph are determined.
Abstract
We examine Bourbaki's function, an easily-constructed continuous but nowhere-differentiable function, and explore properties including functional identities, the antiderivative, and the box and Hausdorff dimensions of the graph.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals