The following demonstration shows the output from a perfect simulation of an 11 dimensional autogamma distribution, known in the technical literature as the pump model. This was first introduced by Gelfand and Smith (1990, Journal of the American Statistical Association 85:398-409) and has been used ever since as a simple benchmark problem. Simulating approximately from this distribution is possible using a Gibbs sampler.

To produce independent perfect samples from this distribution using a Gibbs sampler, we can use Wilson's Read Once CFTP algorithm, which literally recognizes specific random times when the Markov chain is exactly in equilibrium. All we need to do is couple the random flow which gives rise to the chain, using catalysts. This is explained in detail in the accompanying paper, and you won't understand the output below unless you read it.

Alternatively, you may wish to download the Java source.