I go to a boarding school in Pennsylvania called Mercersburg Academy. I completed all of the math courses my school had to offer by my junior year, including all of the post-AP courses, which I took at Stanford University’s summer program, along with a course in programming abstractions. For my junior year, I took a directed study on Mathematica under my former precalculus teacher. About a month later, I took the certification exam. Originally, we were going to study NKS throughout the spring term, but instead, I converted to an independent study and took up updating the school’s database system. Nevertheless, I remained interested in NKS, so my teacher suggested that I apply to this summer school.
Project: Experimenting with Concatenation Sequences
One can form a sequence by concatenating the digits of successive integers. The NKS book looks at such a sequence of numbers in their binary forms. Conducting a FoldList function on this sequence that progressively increments or decrements the result by 1 depending on whether the next digit in the sequence is a 1 or a 0 (respectively) and then graphing the result yields a nested structure. For my project, I will explore concatenation sequences of different representations of numbers and observe whatever properties they may exhibit. For example, I may investigate sequences of numbers represented in different base forms, sequences of functions of numbers, or concatenation sequences of the numbers from another sequence.
Favorite Four-Color Totalistic Cellular Automaton