Polynomiography
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Polynomiography. w ith Dr. Bahman Kalantari. What is polynomiography ?. Dr. Kalantari informally defines polynomiography as a certain graph of polynomials

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Polynomiography

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Polynomiography

with Dr. BahmanKalantari


What is polynomiography?

  • Dr. Kalantari informally defines polynomiography as a certain graph of polynomials

  • He formally defines it as  the art and science of visualization in approximation of the zeros of complex polynomials, via fractal and non-fractal images created using the mathematical convergence properties of iteration functions


SLOW DOWN!

  • First of all, what’s an iteration function?

  • Newton’s Method is an example:N(z) = z − p(z)/p’(z)

  • Iteration functions are used to determine which points will eventually map to the roots of the function being analyzed, essentially the objective of polynomiography


The Result, the Objective

  • By producing a graph of these regions of convergence, or polynomiograph, we can represent functions is a new way:

    VS


The Case of z3-1


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