koch curve

source: Tino Duong, 2003

Description:

(Note: Description and question was taken from Dr. J. Boyd)

 

 

Your job is to write a function that computes Kn+1 from Kn. Generate all the data points needed to make K10. For K0 use (0,0) to (0,1).

Requirements:

• Write a function that will generate the Koch curve in an iterative manner
• Write a function that will generate the Koch curve in a recursive manner
• Have the program prompt the user to see which whether they wish to create it iteratively or recursively
• The program must output the data points to a file called output.txt
• Once you have written the co-ordinance for all the K10 curve, plot it using gnuplot (example of how to use gnuplot given below) and hand it in along with the source code.
• Note: for the K10 curve, gnuplot might take a couple of minutes to graph it
   

    The format of the file MUST look like this

    0 0
    0.111111 0
    0.166667 0.096225
    0.222222 0
    0.333333 0
    0.388889 0.096225
    0.333333 0.19245
    0.444444 0.19245
    0.5 0.288675
    0.555556 0.19245
    0.666667 0.19245
    0.611111 0.096225
    0.666667 0
    0.777778 0
    0.833333 0.096225
    0.888889 0
    1 0

As you can see, this is just two columns of numbers. Each row is a data point (x,y) indicating the position of the point in the graph. The above points represents the data points for a K2 curve. The points from top to bottom are represent each point in the curve from left to right. Make sure your functions output the curve points in this order, to ensure proper display of the curve.

To view the graph of the K2 curve.

1. Copy the above data points exactly in a file called "output.txt"
2. Start "gnuplot" by typing gnuplot at the command terminal
3. When gnuplot is running type:    plot "output.txt" with lines

    This fill create a graph of the curve.

Concepts:

• Pointers
• Dynamic memory
• Recursion
• Algorithm
• File Input/Output

Updated: August 10, 2005 11:10 PM