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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). The left graphic shows the real parts and the right graphic shows the imaginary parts. Nestings of the map  starting with  as a function of  . The initial iterations are ignored and the real parts are shown. 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. The steep vertical walls are caused by branch cuts of the individual summands. 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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