Year Branch S E Computer Engineering Subject Name

Year & Branch: S. E. Computer Engineering Subject Name: Computer Graphics (210251) Unit-6: Curves and Fractals Mr. Bhushan S. Gholap 1

Koch Snowflake. . • The Koch Snowflake also known as Koch curve , Koch star, or Koch island. • The Koch snowflake can be built up iteratively, in a sequence of stages. • The Koch snowflake is usually constructed starting with an equilateral triangle by replacing the middle third of each side with an equilateral triangular, doing this again to the resulting polygon, and so on. Mr. Bhushan S. Gholap 2

Koch Snowflake Mr. Bhushan S. Gholap 3

Construction of Koch Snowflake. . • Draw an equilateral triangle. (It’s best if the length of the sides are divisible by 3, because of the nature of this fractal. ) Mr. Bhushan S. Gholap 4

Construction of Koch Snowflake. . • Divide each side in three equal parts. (This is why it is handy to have the sides divisible by three. ) Mr. Bhushan S. Gholap 5

Construction of Koch Snowflake. . • Draw an equilateral triangle on each middle part. Measure the length of the middle third to know the length of the sides of these new triangles. Mr. Bhushan S. Gholap 6

Construction of Koch Snowflake. . • Divide each outer side into thirds. You can see the 2 nd generation of triangles covers a bit of the first. These three line segments shouldn’t be parted in three. Mr. Bhushan S. Gholap 7

Construction of Koch Snowflake. . • Draw an equilateral triangle on each middle part. • The Koch snowflake is the limit approached as the above steps are followed indefinitely. Mr. Bhushan S. Gholap 8

Construction of Koch Snowflake Mr. Bhushan S. Gholap 9

University Questions 1. Explain Koch Snowflake with example. 2. What is fractal ? Explain Koch snowflake in detail. 3. Write short note on – Koch Snowflake Mr. Bhushan S. Gholap 10

Assignment No. 8: Write C++/Java program to generate snowflake using concept of fractals. • By taking Koch Curve sample code reference, design your own logic for this practical assignment. Mr. Bhushan S. Gholap 11

• To be continue… Mr. Bhushan S. Gholap 12