Fractais, Congruências e Primos: Uma Estratificação Visual dos Números Inteiros via Fractais de Sierpinski

ABSTRACT

In this work we have built a visual enumerated display using fractals of the type Sierpinski n-gons ⁸ with the purpose of analyzing some sequences of integers, mainly the sequence of prime numbers and some of their classic sequences. This visual structure generates a stratification of ℤ that has a stable connection with modular arithmetic, thus becoming a helpful visualisation display for objects and results of the number theory. Inspired by the construction of the Sierpinski Triangle through the Pascal Triangle and Ulam’s work on the spiral of primes ⁹, this enumeration emerged naturally from the computational generation of fractals n-gons where we chose as a strategy the deterministic algorithm cited by Steven Schlicker and Kevin Dennis ⁸.

Keywords:
congruences; prime numbers; N-gons; Sierpinski fractal