An algebraic fractal approach to Collatz Conjecture
Tutor / director / evaluatorSerra Albó, Oriol
Document typeBachelor thesis
Rights accessOpen Access
The Collatz conjecture is one of the most easy-to-state unsolved problems in Mathematics today. It states that after a finite number of iterations of the Collatz function, defined by C(n) = n/2 if n is even, and by C(n) = 3n+1 if n is odd, one always gets to 1 with independence of the initial positive integer value. In this work, we give an equivalent formulation of the weak Collatz conjecture (which states that all cycles in any sequence obtained by iterating this function are trivial), based on another equivalent formulation made by Böhm and Sontacchi in 1978. To such purpose, we introduce the notion of algebraic fractals, integer fractals and boolean fractals, with a special emphasis in their self-similar particular case, which may allow us to rethink some fractals as a relation of generating functions.