Monday, February 22, 2021

Make a Block II - The Recursive Koch Curve

   How to use Make a Block to program the famous Koch curve is the topic of this post. Below is a graphic that shows the stages (levels) of the curve's development. Instead of writing a script for each level, Make a Block and the programming technique known as recursion allows the program to be created using a single[ define recursive call side length level]script.

    Here's the working script. With side length = 297 and level as the only other input, this script will draw figures 1 through 5 as shown above.
   Teachers and/or students might like a free PDF file that steps through the development of the script shown above. The technique used in this Scratch program is applicable to many other similarity fractals like the Koch curve. It might interest you to know that mathematics still does not have an agreed upon definition for curve
   If any of the levels shown in the diagram above are drawn on the sides of an equilateral triangle the result is know as a Koch Snowflake. It can be shown that as the perimeter of the curve approaches infinity the area approaches 8/5 the area of the original equilateral triangle.

   This project can be viewed and downloaded from the Scratch MIT web site by clicking on this link:

   Teachers and/or students might also be interested in the free PDF document that describes the formula for the perimeter of the curve as a function of level.
   Either or both of the documents mentioned above can be obtained by sending an email request to I send my free PDF documents to teachers and students all over the world and I have never had a single complaint.

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