The Mandelbrot Set

Plot the FORMAL (black-and-white) Mandelbrot Set, using this iterative equation: z = z^2+ cwhere z starts at zero, and c is a complex number that ranges from - 2 to 1 in the real component and- 1 to 1 in the imaginary component. If that iterative process does not escape to infinity, then that complex number belongs to the Mandelbrot set. Note that rather than testing whether any given iteration really escapes to infinity (and therefore is not formally a part of the Mandelbrot set), you can actually just check whether the number goes above 2. (That is, if the value gets past 2, then the iterative process WILL escape to infinity.)

The following English instructions should be translated into matlab code:

clear all your variables

clear the figure window

make a matrix of zeros that has 300 rows and 200 columns,

and call it Mandelbrot.

Start a for loop for the Real component going from -2 to 1 in steps of .01

Start a for loop for the Imaginary component going from -1 to 1 in steps of .01 (thus Real and Imag can also later be used for indexing cells in Mandelbrot)

Set the starting value of z to zero

Set zs to zero (this will collect your z values)

Start a for loop where n (the iteration counter) goes from 1 to 100

Enter the Mandelbrot equation here,

z = z^2+ c, making sure you treat c complex.

Save that recent z value as the nth element in zs.

End the n for loop

If all of zss values are not going to escape to infinity,

Then change the zero to a one in that cell of the Mandelbrot matrix (you will need to modify the Real and Imag numbers to use them as indices)

end that if statement

end the Imag for loop

end the Real for loop

set your colormap to three ones and three zeros

use the image command to plot a transposed version of the Mandelbrot matrix (you may need to multiply Mandelbrot by 2 for this colormap) (and you might want to set the x and y axes, in the image command, to be presented as- 2 to 1 in steps of .01 and 1 to-1 in steps of-.01, respectively.)

set your axis to be equal, so that the plot has commensurate x and y dimensions.