code in python! Tough Question below:

The Mandelbrot set is an example of a fractal: an object that contains a structure within a structure, iteratively as far as we care to look. Consider the following iterative equation (all variables represent complex numbers): The Mandelbrot set considers a complex number c and sets z0-0 . The above equation is applied iteratively until 12 is above 2 or until z has been updated many times (to z100 , say). If is not found to ever exceed 2, then the point c is in the Mandelbrot set; if it does exceed 2, it is not in the Mandelbrot set. I. Consider a complex number in the form c=x+y. Consider a 100x100 grid of points on the complex plane constrained by -2Sx32 and-2Sys2 For each value of c on this grid, determine the number of iterations required for to exceed 2. If zl does not exceed 2, record the maximum number of iterations considered instead. Record these values on a100x100NumPy array. 2. 3. Save the array formed in step 2 to file. Then comment out the analysis code and instead load vour results from file. (This speeds things up as vou plav around in the following step!) Plot the array constructed in step 2 using: plt.imshow(, cmap ). Try different color maps until you find one that you like. The default colormaps available in matplotlib are listed here: http://matplotlib.org/examples/color/colormaps reference,html, (example: plt.imshow(a, cmap-'spectral')). 4. The Mandelbrot set is an example of a fractal: an object that contains a structure within a structure, iteratively as far as we care to look. Consider the following iterative equation (all variables represent complex numbers): The Mandelbrot set considers a complex number c and sets z0-0 . The above equation is applied iteratively until 12 is above 2 or until z has been updated many times (to z100 , say). If is not found to ever exceed 2, then the point c is in the Mandelbrot set; if it does exceed 2, it is not in the Mandelbrot set. I. Consider a complex number in the form c=x+y. Consider a 100x100 grid of points on the complex plane constrained by -2Sx32 and-2Sys2 For each value of c on this grid, determine the number of iterations required for to exceed 2. If zl does not exceed 2, record the maximum number of iterations considered instead. Record these values on a100x100NumPy array. 2. 3. Save the array formed in step 2 to file. Then comment out the analysis code and instead load vour results from file. (This speeds things up as vou plav around in the following step!) Plot the array constructed in step 2 using: plt.imshow(, cmap ). Try different color maps until you find one that you like. The default colormaps available in matplotlib are listed here: http://matplotlib.org/examples/color/colormaps reference,html, (example: plt.imshow(a, cmap-'spectral')). 4