How do you draw a Koch snowflake in Python?
How do you draw a Koch snowflake in Python?
Construction
- Step1: Draw an equilateral triangle.
- Step2: Divide each side in three equal parts.
- Step3: Draw an equilateral triangle on each middle part.
- Step4: Divide each outer side into thirds.
- Step5: Draw an equilateral triangle on each middle part.
When was the Koch snowflake discovered?
1904
The Koch snowflake is sometimes called the Koch star or the Koch island. 2. It was discovered by the Swedish mathematician Helge Von Koch in 1904.
What is the equation for the Koch snowflake?
The length of the boundary of S(n) at the nth iteration of the construction is 3(43)ns 3 ( 4 3 ) n s , where s denotes the length of each side of the original equilateral triangle. Therefore the Koch snowflake has a perimeter of infinite length. The area of S(n) is √3s24(1+n∑k=13⋅4k−19k).
How does Koch snowflake work?
Instead of one line, the snowflake begins with an equilateral triangle. The steps in creating the Koch Curve are then repeatedly applied to each side of the equilateral triangle, creating a “snowflake” shape. The Koch Snowflake is an example of a figure that is self-similar, meaning it looks the same on any scale.
How do you make a Koch snowflake in Java?
Use Recursion to Draw Koch Snowflake in Java
- Divide each side of an equilateral triangle into three equal sections.
- Delete the middle section after taking the trisection of one side of the middle section for the side to construct an equilateral triangle.
- Draw a smaller triangle by repeating the first two steps.
Who discovered the Koch snowflake?
mathematician Niels Fabian Helge von Koch
The Koch Snowflake was created by the Swedish mathematician Niels Fabian Helge von Koch.
How do you find the area of a Koch snowflake?
Area of the Koch Snowflake For our construction, the length of the side of the initial triangle is given by the value of s. By the result above, using a = s, the area of the initial triangle S(0) is therefore √34s2 3 4 s 2 .
What is the dimension of Koch snowflake?
The relation between log(L(s)) and log(s) for the Koch curve we find its fractal dimension to be 1.26. The same result obtained from D = log(N)/log(r) D = log(4)/log(3) = 1.26.
What is a fractal in Python?
Fractal python turtle is used to make geometrical shapes with different scales and sizes. In this, it makes repeating shapes in geometry form which works on a different scale and size it is not same in shape.