sobol

This project explores the Sobol' family of generators, which produce low-discrepancy sequences in high dimensions. We use the direction numbers and primitive polynomials shared in the below paper by Joe and Kuo.

Plots

These plots compare the first two dimensions of the Sobol' generator against Python's random.random() generator at 16, 64, 256, and 1024 samples.

Sobol	Uniform

References

• Physically Based Rendering, Ch. 7: Sampling and Reconstruction
• Sobol Sequence Generator
• P. Bratley and B. L. Fox, Algorithm 659: Implementing Sobol’s quasirandom sequence generator
• S. Joe and F. Y. Kuo, Constructing Sobol sequences with better two-dimensional projections

See Also

• sobol-rs