Implement a Matlab function that creates a Newton basin image with the

following inputs and outputs:

Inputs cThe c oordinates of a polynomial p(x)

ax = [r1 r2m1m2] the limits of the plane [r1 r2][im1 im2] of inital values in the

complex plane.

ng = [nr ni] the number of grid points in the real and imaginary direction, respec-

tively.

N - A maximum number of newton iterations.

Outputs

An image of ord(p)+1 colors, where each color corresponds to a dierent converged

root, and black corresponds to no root being found. While you may use any color

mapping you like (for example, the hsv, built-in color array) to correspond to

the dierent roots, please use black to denote that no root was found. Put the

polynomial in the title of the image. (Use a tolerance of 10??6 to check convergence)

The rst line of your code should read

function newton basin(c,ax,ng,N)

2. (35 points) Implement a Matlab function that creates a Newton basin image with the following inputs and outputs: Inputs CE Cn The coordinates of a polynomial p(z) stio fo n th i M . ax r r2 mi mal the limits of the plane [r1 r2] x [imi ?m2] of inital values in the complex plane. ng nr ni] the number of grid points in the real and imaginary direction, respec- tively. . N - A maximum number of newton iterations. Outputs . An image of ord(p)+1 colors, where each color corresponds to a different converged root, and black corresponds to no root being found. While you may use any color mapping you like (for example, the hsv, built-in color array) to correspond to the different roots, please use black to denote that no root was found. Put the polynomial in the title of the image. (Use a tolerance of 10-6 to check convergen The first line of your code should read function newton basin(c,ax, ng,N) 2. (35 points) Implement a Matlab function that creates a Newton basin image with the following inputs and outputs: Inputs CE Cn The coordinates of a polynomial p(z) stio fo n th i M . ax r r2 mi mal the limits of the plane [r1 r2] x [imi ?m2] of inital values in the complex plane. ng nr ni] the number of grid points in the real and imaginary direction, respec- tively. . N - A maximum number of newton iterations. Outputs . An image of ord(p)+1 colors, where each color corresponds to a different converged root, and black corresponds to no root being found. While you may use any color mapping you like (for example, the hsv, built-in color array) to correspond to the different roots, please use black to denote that no root was found. Put the polynomial in the title of the image. (Use a tolerance of 10-6 to check convergen The first line of your code should read function newton basin(c,ax, ng,N)