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Graphical iteration

The graphical iteration method is a way to compute successive iterations of a map starting from an initial value . Given , its iterate is the ordinate of the point of the graph of having abscissa , therefore, to compute the sequence of iterations it is necessary to bring the various ordinates along the abscissa axis: this is achieved by means of the bisector of the first and third quadrants, whose points have equal abscissa and ordinate. The sequence is obtained by passing alternately from the graph of to the bisector along a line parallel to the abscissa axis and vice versa along a line parallel to the ordinate axis.