Upper Bounds for the Hausdorff Dimension of Weierstrass Curves

  • Ted Alexander California State University, Fullerton
  • Tommy Murphy California State University, Fullerton
DOI: https://doi.org/10.46787/pump.v5i0.3324
Keywords: iterated function systems; Weierstrass--type functions; Hausdorff dimension

Abstract

We produce an upper bound for the Hausdorff dimension of the graph of a Weierstrass-type function. Whilst strictly weaker than existing results, it has the advantage of being directly computable from the theory of hyperbolic iterated function systems (IFS).

Author Biography

Tommy Murphy, California State University, Fullerton

http://www.fullerton.edu/math/faculty/tmurphy/

Published
2022-12-12
How to Cite
Alexander, T., & Murphy, T. (2022). Upper Bounds for the Hausdorff Dimension of Weierstrass Curves. The PUMP Journal of Undergraduate Research, 5, 199-205. https://doi.org/10.46787/pump.v5i0.3324
Issue
Vol. 5 (2022): PUMP Journal of Undergraduate Research
Section
Articles

Copyright (c) 2022 Ted Alexander, Tommy Murphy

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.