Newton’s method for your personal monic cubic

(5 pts by Friday, January 25)

Continuing with your personal monic cubic, use out Newton’s method for complex polynomials tool to generate an image of the basins of attraction for Newton’s method as applied to your personal monic cubic.

My personal monic cubic was f(x) = x^3 + 2x + 3.

Using the tool provided above, I generated the following image of the basins of attraction for Newton’s method of f(x):

download.png700×700 26.6 KB

My personal cubic is x^3+2x^2+x+1, corresponding to the coefficients 1,1,2,1.

Thus, the basins of attraction for Newton’s Method appear as follows.

image.png628×628 116 KB

Using Mark’s tool, I found that the basins of attraction for my polynomial f(x)=x^3=x^2-x+1 look like this:

Basins.png700×700 30 KB

Pretty neat!

My personal monic cubic was f(x)=x^3+x^2+2x.
Using the tool provided, I get this image.

download.png700×700 19.7 KB

My personal monic cubic is f(x) = x^3 + x, which generates the following Newton’s method plot:

personalCubic.png700×700 21.7 KB