  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 $\gamma\colon[0,1]\to[0,1]^d$ with
minimal dilation $$
\sup_{t_1<t_2}\frac{\|\gamma(t_2)-\gamma(t_1)\|^d}{t_2-t_1}. $$
  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 $5\times 5$ with dilation $5\frac{43}{73}=5.5890\ldots$. In dimension
$3$ we have found facet-gated bifractals (that we call "Spring") of genus
$2\times2\times 2$ 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.
