Fifteenth Annual
C
of
I
S
T
U
D
E
N
T
R
E
S
E
A
R
C
H
C
O
N
F
E
R
E
N
C
E
Saturday May 16, 2020
AUTHOR:
Oleksandr Tarasenko
FACULTY: Dr. Jonny Comes
DEPARTMENT: Math
STILL WAITING ON UPDATED ABSTRACT- In everyday life, our world mostly uses the decimal number system. In the system that the world uses there are 10 digits from 0 to 9. A digit is a single symbol used to make a numeral. Besides, the same system uses base 10, where the base is the number of different digits that a system of counting uses to represent numbers. In this project we study a connection between number systems and fractals. Fractals are defined as a series of approximations. In 1970, Davis and Knuth found that the set of all fractions in the binary number system, with 2 digits (such as 1 and 0), and the complex base (-1 + i), form a beautiful fractal in the complex plane called the twindragon. Here, by a fraction in the binary system we mean a number of the form 0.d_1d_2d_3… where d_n can be represented as 0 or 1. For our project, we decided to assign d_n to 0,1, or k, where k is a so-called quaternion. We used Python to generate numbers in a given number system and graph them. Analyzing these graphs together with several computations and proofs gave us a good understanding of this structure.
The College of Idaho 2112 Cleveland Blvd Caldwell, ID 8360 USA 208-459-5011 800-2C-IDAHO