Recurrence plots, bifurcation diagrams, and fractals

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 (5). The value are logarithmically scaled.

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.

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 .