Phys 567 Problem 2

Due 4:00pm Friday, Feb 9.

The Mandelbrot set is a fractal structure in the complex plane defined by the iterative mapping

zi+1 = zi2 + c, where z0=c.

If |zi| < 2 as i tends to infinity, then the point c is within the Mandelbrot set. Other points will escape after some number of iterations; this number is called the count.

Your task is to calculate the surface area of the Mandelbrot set by MonteCarlo integration. Try using the output of your program to plot the Mandelbrot set. The picture above was created using 107 randomly generated points.

You may use canned routines for basic algorithms (Numerical Recipes, or the IDL and/or Matlab standard libraries, for example), as long as the grader has access to them.

Hand in all parts via email to the grader, including:

  1. A brief description of your results:
    1. What is the area of the Mandelbrot set?
    2. Estimate the accuracy of your calculation.
    3. Is your result an upper or lower limit?
  2. Your source code, commented so that it is readable.
  3. Any commands or scripts that you used to compile and/or run your code.
  4. A plot of the Mandelbrot set based on the randomly selected points used to estimate its area.
Please use portable formats such as plain text, Postscript, PDF, JPEG and PNG. Proprietary formats may put the grader in a bad mood.

Useful references:

http://en.wikipedia.org/wiki/Mandelbrot_set

http://mathworld.wolfram.com/MandelbrotSet.html