| From: Frank Sully | 12/20/2020 10:19:20 AM | | | | | | OT: What is a Julia Set? The behavior of a complex polynomial P(z) (a polynomial of a complex variable z = a + bi, where i is the square root of -1) viewed as a iterated dynamical system is determined by an embedded chaotic repellor called a Julia set, after the French mathematician Gastow Julia who first studied these mathematicaly at the turn of the 20th Century (amazingly before the advent of computers). These are very beautiful as well as having many interesting mathematical properties. My doctoral dissertation in the mid-1980's was based on relating three quantities with a simple equation" The fractional Hausdorff dimension of the Julia set J, HD(J), the exponential expansiveness of the polynomial P(z) or Lyapunov exponent, lambda(P), and the randomness or entropy of the polynomial P(z), h(P): the equation is:
h(P) = HD(J) x lambda(P).
Amazing! Here is a basic video on Julia sets.
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| To: Frank Sully who wrote (981) | 12/20/2020 10:34:26 AM | | From: Frank Sully | | | | OT: Julia Set Zoom: Besides the fascinating mathematical properties of Julia sets, the advent of powerful digital computers and their graphical abilities enabled the study of the fractal properties via "zooms".
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