The code that made the diagrams in this post can be found at https://github.com/Atrix256/ToroidalProgressiveStratification1D I stumbled on this when working on something else. I'm not sure of a use case for it, but I want to share it because there may be one I'm not thinking of, or it may be inspire something else. Let's…

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A novel sampling technique called "toroidally progressive stratified sampling" combines the benefits of stratified sampling with golden ratio ordering to create a sampling pattern that maintains quality at any number of samples and can seamlessly restart without quality degradation. The method uses a low discrepancy shuffle iterator based on rank 1 lattices to visit stratified bins in golden ratio order, making it particularly useful for applications like temporal anti-aliasing where different processes may restart integration at different times while sharing the same sampling sequence.

Toroidally Progressive Stratified Sampling in 1D