Aranka Hrušková enrolled at the University of Cambridge to study mathematics in 2014 after completing her previous education in Prague. She would like to become a professional researcher, and did a minor project about continued fractions while in high school, for which she was awarded a silver medal at Intel ISEF. Apart from academic activities, Aranka enjoys playing the clarinet.
Project: Representation of Integers in Terms of 1s
Mathematica 11 features a new function called Groupings. Given a list and a positive integer k, Groupings returns all possible nested lists such that every nested sublist has k elements (when the resulting list of lists is evaluated in the tree form, every "List" node apart from the outermost one has k outgoing edges). Moreover, we can apply a function f in every "List" node in the tree, which correspond to different bracketings of the list.
If we feed Groupings a constant array of 1s and a function, we can study which functions succeed in producing all integers just from 1s and which don't.
Favorite 3-Color 2D Totalistic Cellular Automaton