We've detected that you're using an ad content blocking browser plug-in or feature. Ads provide a critical source of revenue to the continued operation of Silicon Investor. We ask that you disable ad blocking while on Silicon
Investor in the best interests of our community. If you are not using an ad blocker but are still receiving this message, make sure your browser's tracking protection is set to the 'standard' level.
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:
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".