Fractais, Congruências e Primos: Uma Estratificação Visual dos Números Inteiros via Fractais de Sierpinski
DOI:
https://doi.org/10.5540/tema.2020.021.03.483Keywords:
Congruência, Números Primos, N-gons, Fractais de SierpinskiAbstract
Neste trabalho construímos um painel visual enumerado usando fractais do tipo Sierpinski n-gons com o objetivo de analisar algumas sequências de números inteiros, principalmente a sequência dos números primos e algumas de suas subsequências clássicas. Essa estrutura visual gera uma estratificação do conjunto dos inteiros que tem forte ligação com a aritmética modular, tornando-se assim um bom painel de visualização para objetos e resultados da teoria dos números. Inspirados na construção do Triângulo de Sierpinski por meio do Triângulo de Pascal e pelos trabalhos de Ulam sobre a espiral de primos, esta enumeração surgiu naturalmente a partir da geração computacional de fractais $n$-gons onde tomamos como estratégia o algoritmo determinístico citado por Steven Schlicker e Kevin Dennis.
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