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A simple random walk example is presented to il-lustrate the key ingredients of antithetic coupling for perfect sampling as well as its potential benefit.

Various summary statistics are presented, and estimation and examples of the use of such are given.

(There are numerous examples inwhich conditions 1 or 2 do not hold.) Diaconis and Freedman give a survey of the literature on stochastically recursive sequences; a few representative articles are listed below.

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Graphical illustration of some examples related to the article ``Iterated random functions'' by Diaconis and Freedman.

Abstract:Figures are presented to illustrate some examples of iterated random functions of the kind described in the article in this issue by Diaconis and Freedman.

The theoreticalconcepts underlying perfect simulation have a long history, but they werefirst drawn together to form a practical simulation technique in the ground-breakingpaper of Propp and Wilson [75], which showed (for example) howto obtain exact draws from (for example) the critical Ising model.

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Gallery of Pictures and Java Applets Relevant to the ArticlesPostscript illustration of monotone coupling from the past (CFTP)Postscript illustration of the Murdoch-Green rejection couplerPostscript illustration of the Murdoch-Green partitioned multigamma couplerPostscript illustration of the Green-Murdoch random walk Metropolis bisection couplingPostscript illustration of Green-Murdoch random walk Metropolis bounded CFTPJason Woolever's random tiling applets (using monotone-CFTP)Wilfrid Kendall's animated comparsion of forwards and backwards couplingGeorgii's perfect continuum Ising model picturesJeffrey Rosenthal's monotone-CFTP applet for the chainMacKay's perfect simulation picturesrandom 3 colorings of the square and cubic lattices 2-state Potts 3-state Potts 4-state Potts 5-state PottsThe 2-state, 3-state, 4-state, and 5-state Potts models at their respective critical temperatures on the 2D grid, generated by monotone-CFTP on the Fortuin-Kasteleyn random-cluster model.

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