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

Polynomiography

with Dr. BahmanKalantari


What is polynomiography

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

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

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 z 3 1

The Case of z3-1


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