On the Koch snowflake curves

• Main Authors: Lao, Geraldine T., Tan, Jocelyn
• Format: text
• Language: English
• Published: Animo Repository 1996
• Subjects: Curves; Fractals; Dimension theory (Topology); Quadrics
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16308
• Institution: De La Salle University

This thesis is about fractals, specifically the Koch Snowflake Curve. A fractal is a shape made of parts similar to the whole in some way. In other words, fractals are geometric figures in which a pattern repeats itself indefinitely. Fractals can be used to describe the fragmentary aspects of nature. It can stimulate landscapes and objects in nature such as trees and mountains. There are different types of fractals. Some examples are Cesaro Curves, Peano Curves, Julia Sets, Mandelbrot Sets and Koch Curve. This paper also discusses the construction of the Snowflake Curves in detail and shows the parameters of the Snowflake Curve on the first three construction stages for the regular polygons having 3, 4 and 5 sides, in tabular form. In addition, formulas for the perimeter and area of the Snowflake Curve and their limits are also discussed. The paper also includes the definition of fractal dimension, the generation of the Koch Snowflake Curve and the Quadric Koch Curve.