Koch's snowflake paradox: infinite perimeter and finite area - Coursework Example

Fractals are created by repetition of a simple process infinitely. There are various manifestation of fractals in nature. This include in things like coastlines, clouds, trees, hurricanes, sea shells among others (Pickover 2009). According to previous studies, it has been found that Koch Snowflake fractals have finite area with infinite perimeter (Bremigan, Bremigan and Lorch 2011). This makes the Koch fractals to be very puzzling and fascinating. This statement raises a lot of questions. How can a figure have a finite area and an infinite perimeter?

How can the two contradicting statements be true? This properties of the Koch Snowflake creates a paradox resulting into fascinating discussions about the Koch Snowflake fractals. Following this contradicting properties of the Koch Snowflakes, I’ve developed an urge to find out the trueness in its properties. In this journey of trying to find the truth of about the Koch fractals, I’ll try to find the proof of the fact that Koch Snowflakes have both a finite area and an infinite perimeter and also, create an example to see how the length, perimeter, and area vary with the number of iterations in a Koch Snowflake.

Finding out this relationship requires an in – depth understanding of how the Koch Snowflake are constructed. The construction of the Koch Snowflake is based on the Koch Curve. The creation of the Koch framework starts with starts with the construction of an equilateral triangle. Each of the line signet of the equilateral triangle then divided into thirds. The middle third is removed and then replaced with two line segments that have equal length resulting into formation of another equilateral triangle on the other original triangle’s sides (University of British Columbia 2011).

This process is repeated infinitely resulting into the formation of the Koch Snowflake fractal. The figure below illustrates the first steps followed in the