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Recurrence plots Recurrence plot of  over the   ‐plane. Bifurcation-related plots Nestings of the map  starting with  as a function of  . The number of iterations increases from red (0) to blue (80). Nestings of the map  starting with  as a function of  . The initial iterations are ignored. Iterations and powers in the complex plane The real part and the imaginary part of the scaled value of  in the  . The left graphic shows the real part and the right graphic shows the imaginary part. The real part and the imaginary part of the scaled value of  in the  . The left graphic shows the real part and the right graphic shows the imaginary part. Lattice sums The real part and the imaginary part of the lattice sum  in the  . The left graphic shows the real part and the right graphic shows the imaginary part. Because  , one basically recovers the function  (modulo a  ‐independent factor). Fractals and Julia sets Mandelbrot set of the map  over the  . The coloring indicates the number of iterations before  . Julia sets of the map  over the  .
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