scholarly journals Introdução à Geometria Fractal no Ensino Médio Técnico: Uma Abordagem com Programação Python

2021 ◽  
Author(s):  
Gustavo Vieira Ferreira ◽  
Weliton Dal Pizzol Maria ◽  
Adriano Rodrigues de Melo
Keyword(s):  
High School ◽  
Fractal Geometry ◽  
Cantor Set ◽  
Koch Curve ◽  
Analytical Geometry ◽  
Technical High School ◽  
Sierpinski Triangle ◽  
Python Language ◽  
Fractal Patterns ◽  
Bibliographic Search

This work is inserted in the context of technical high school andit aimed to analyze the integration between the branches of FractalGeometry, Analytical Geometry and Computer Programming.For this purpose, we carried out a bibliographic search about whatcharacterizes and distinguishes Fractal Geometry from EuclideanGeometry, we also seek in our readings to list the most famousfractals. Then, we developed (in python language) several fractalgeneration programs. It was possible to work with amazing andeasily programmable fractal shapes, such as the Cantor Set, theHilbert Curve and Sierpinski Triangle. We also built two new familiesof fractal shapes from a generalization of the Koch Curve. Weconclude that programming fractals in the context of technical highschool is productive and challenging, as it requires many changesin the representations of fractal patterns.

GENERATING FRACTAL PATTERNS BY USING p-CIRCLE INVERSION

Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550047 ◽  
Author(s):  
JOSÉ L. RAMÍREZ ◽  
GUSTAVO N. RUBIANO ◽  
BORUT JURČIČ ZLOBEC
Keyword(s):  
Inversion Formula ◽  
Koch Curve ◽  
Basic Properties ◽  
Sierpinski Triangle ◽  
Fractal Patterns

In this paper, we introduce the [Formula: see text]-circle inversion which generalizes the classical inversion with respect to a circle ([Formula: see text]) and the taxicab inversion [Formula: see text]. We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the [Formula: see text]-circle inversion.

Fractal Patterns and Chaos Games

2004 ◽  
Vol 98 (4) ◽  
pp. 228-233
Author(s):  
Robert L. Devaney
Keyword(s):  
Middle School ◽  
Secondary School ◽  
Koch Curve ◽  
Sierpinski Triangle ◽  
Fractal Patterns ◽  
Chaos Game ◽  
The Many

One of the most wonderful ways to introduce students in middle school or secondary school to the beauty and excitement of contemporary mathematics is to involve them in the many variations of the “chaos game” which produces such intriguing fractal patterns as the Sierpinski triangle and the Koch curve.

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