Search of Fractal Space-Filling Curves with Minimal Dilation

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 CNF boolean formulas. Our was implemented and applied to the surjective $$\gamma :[0,1]\rightarrow [0,1]^d$$ with minimal dilation $$\begin{aligned} \sup _{t_1<t_2}\frac{\Vert \gamma (t_2)-\gamma (t_1)\Vert ^d}{t_2-t_1}. \end{aligned}$$ report new results case Euclidean norm. have found we call “YE”, self-similar (monofractal) plane genus $$5\times 5$$ $$5+{43}/{73}=5.5890\ldots $$ In dimension 3 facet-gated bifractals (which “Spring”) $$2\times 2\times 2$$ $$<17$$ . 4 obtained there is $$<62$$ Some lower bounds on wider classes cubically decomposable are proven.