[Solved]Julia Set Implement Iim Must First Find Point Z0 J F Fact Polynomial F F P P Either F P 1 Q37281012

Julia Set

To implement IIM, we must first find apoint z0 ∈ J(f). It is a fact that for any polynomial f, if f(p) =p and either |f′(p)| > 1 or f′(p) = 1, then p is in J(f). Heref′(p) is the derivative of f evaluated at p (a complex number). Fora polynomial fc(z) = z2 + c from the quadratic family, such a pointp always exists. Write a (small) program to find such a p forfc.

Using the z0 = p ∈ J(fc) you found inthe previous part, implement IIM for the quadratic family bycomputing the set JN(fc) defined above as a list of complexnumbers. As the name Inverse Iteration Method suggests, you willfind all preimages of z0 (i.e. all w with f(w) = z0), and then allpreimages of those points, etc. Then plot this list using Sage’slist_plot function or something similar.

    Modify yourIMM algorithm from (2) so that instead of producing a list, itproduces a grid represented as an array (as we did for draw_juliain class), where a grid square is assigned the value 1 if JN(f)contains some point in that grid square, and 0 otherwise. Then plotthis grid using matrix_plot or something similar. This will producean image with fewer “bunched together points”.

Can you help with the plottingthis as a matrix part (in bold)

Expert Answer

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Answer to Julia Set To implement IIM, we must first find a point z0 ∈ J(f). It is a fact that for any polynomial f, if f(p) = p … . . .