Document Type
Honors Thesis
Abstract
Pascal’s Triangle forms the well-known Sierpinski Triangle fractal when divided by a prime number. The fibonomial triangle has been shown to exhibit similar behavior for certain primes. In this paper, we show that for primes p with one zero in the period of the Fibonacci sequence mod p,(n+ip∗pmk+j p∗pm) F ≡p (ij) (nk)F, and for primes with two zeroes in the period, (n+ip∗pm k+j p∗pm) F ≡p (−1) ij−nk (ij) (nk) F. This substantially increases the size of the collection of primes for which a fractal structure is proven to exist, and the remaining case can be handled using the same methods we employ. We also describe the resulting fractals and compute their Hausdorff dimension.
Publication Date
5-1-2017
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
DeBellevue, Michael, "FRACTAL NATURE OF THE FIBONOMIAL TRIANGLE MOD P FOR A GENERAL RANK OF APPARITION" (2017). 2017 Spring Honors Capstone Projects. 21.
https://mavmatrix.uta.edu/honors_spring2017/21