Document Type

Honors Thesis


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.

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