Toroidally Progressive Stratified Sampling in 1D
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Toroidally Progressive Stratified Sampling in 1D is an August 2025 blog post by demofox2 on The blog at the bottom of the sea about making stratified 1D Monte Carlo samples progressive by visiting strata in golden-ratio shuffle order.
It compares white noise, golden-ratio quasirandom, sequential stratification, and StratifiedGR on integrands such as triangle, step, sine, and Gaussian functions, with log-log error plots and final error tables. It explains coprime rank-1 lattice shuffles so each bucket is hit once, notes toroidal progressiveness when the finite sequence wraps, and connects the idea to TAA-style restarts that share one global sample sequence.
It is for intermediate rendering engineers working on sampling patterns, low discrepancy sequences, and temporal accumulation.
The post is free HTML with diagrams and points to a companion GitHub repo that generated the figures; related demofox posts on shuffle iterators are referenced in prose only.
It is useful when you need stratified quality that stays good for any prefix and any start index, including wrap-around reuse.