Papers › Search of fractal space-filling curves with minimal dilation
Search of fractal space-filling curves with minimal dilation
Yuri Malykhin, Evgeny Shchepin
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We introduce an algorithm for a search of extremal fractal curves in large curve classes. It heavily uses SAT-solvers~ -- heuristic algorithms that find models for CNF boolean formulas. Our algorithm was implemented and applied to the search of fractal surjective curves γ[0,1]→[0,1]ᵈ with minimal dilation sup_(t₁<t₂)(γ(t₂)-γ(t₁)ᵈ)/(t₂-t₁). We report new results of that search in the case of Euclidean norm. We have found a new curve that we call "YE", a self-similar (monofractal) plane curve of genus 5×5 with dilation 543/73=5.5890…. In dimension $3$ we have found facet-gated bifractals (that we call "Spring") of genus 2×2×2 with dilation <17. In dimension $4$ we obtained that there is a curve with dilation <62. Some lower bounds on the dilation for wider classes of cubically decomposable curves are proved.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections