This can be more easily visualized if x is viewed as a two-dimensional array. One dimension is k and the other dimension is the particle number. For example, x ( k , i ) would be the i particle at k and can also be written x k ( i ) (as done above in the algorithm). Step 3 generates a potential x k based on a randomly chosen particle ( x k − − 1 ( i ) ) at time k − − 1 and rejects or accepts it in step 6. In other words, the x k values are generated using the previously generated x k − − 1 .