# Rendering along the Hilbert Curve

arXiv: https://arxiv.org/abs/2207.05415 · HTML: https://mlsanity.com/paper/2207.05415/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2022.

## Built on by (most cited first, 2 of 2)

- [A Comparison of Selected Image Transformation Techniques for Malware Classification](https://mlsanity.com/paper/2509.10838/) (2025)
- [Frequency-Enhanced Hilbert Scanning Mamba for Short-Term Arctic Sea Ice Concentration Prediction](https://mlsanity.com/paper/2602.13522/) (2026)

## Abstract (arXiv)

Based on the seminal work on Array-RQMC methods and rank-1 lattice sequences by Pierre L'Ecuyer and collaborators, we introduce efficient deterministic algorithms for image synthesis. Enumerating a low discrepancy sequence along the Hilbert curve superimposed on the raster of pixels of an image, we achieve noise characteristics that are desirable with respect to the human visual system, especially at very low sampling rates. As compared to the state of the art, our simple algorithms neither require randomization, nor costly optimization, nor lookup tables. We analyze correlations of space-filling curves and low discrepancy sequences, and demonstrate the benefits of the new algorithms in a professional, massively parallel light transport simulation and rendering system.