We present a novel algorithm for implementing Owen-scrambling, combining the generation and distribution of the scrambling bits in a single self-contained compact process. We employ a context-free grammar to build a binary tree of symbols, and equip each symbol with a scrambling code that affects all descendant nodes. We nominate the grammar of adaptive regular tiles (ART) derived from the repetition-avoiding Thue-Morse word, and we discuss its potential advantages and shortcomings. Our algorithm has many advantages, including random access to samples, fixed time complexity, GPU friendliness, and scalability to any memory budget. Further, it provides two unique features over known methods: it admits optimization, and it is invertible, enabling screen-space scrambling of the high-dimensional Sobol sampler.

翻译：本文提出了一种实现Owen加扰的新算法，将加扰位的生成与分布过程融合为单一紧凑的自包含流程。我们采用上下文无关文法构建符号二叉树，并为每个符号赋予可影响所有子节点的加扰码。我们指定了基于避免重复的Thue-Morse词推导的自适应规则瓦片（ART）文法，并讨论了其潜在优势与不足。该算法具有多项优势，包括样本的随机访问、固定的时间复杂度、GPU友好性以及可扩展至任意内存预算。此外，与现有方法相比，它提供两个独特特性：支持优化且具有可逆性，从而能够对高维Sobol采样器进行屏幕空间加扰。