Recall in our presentation of graphical iteration,
the pair of thick green lines connects
_{n}, x_{n})_{n+1}, x_{n+1}) |

To generate the return map, we want to plot a point
with y-coordinate x_{n+1} and x-coordinate x_{n}. |

The horizontal
line from _{n+1}, x_{n+1})_{n+1}. |

The horizontal
line from _{n}, x_{n})_{n}. |

This orange line intersects the diagonal in the return map square at the point
_{n}, x_{n}) |

The vertical line from this point
consists of points with x-coordinate x_{n}. |

Consequently, the vertical orange line
and horizontal light blue line intersect at the point _{n}, x_{n+1}) |

Return to the Return Map.