In the second volume he turns to the topology of the plane, with all of the standard theorems of one-dimensional and two-dimensional topology, the fundamental theorems of algebra, the Brouwer fixed-point theorem, space-filling curves
, and so on.
In this context, a continuous curve is a connected and locally connected compact curve (Sagan 1994: Space-Filling Curves, Chapter 1, Introduction).
Tool path generation for five-axis NC machining using adaptive space-filling curves.
On the Locality Properties of Space-Filling Curves.
In [12, 14, 15] the author considered a family of fractals that can be described in term of space-filling curves, which can be modelled using geodesic laminations on the disc.
Moreover [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] In , it was shown that there is an space-filling curves associated to this expanding map.
Sirvent, Space-filling curves and geodesic laminations, Geom.
Hilbert and Sierpinski curves are space-filling curves.
Such space-filling curves were originally developed as conceptual mathematical
This coding technique could be successfully applied to the generation of other regular space-filling curves, such as the Peano curve.
Space-filling curves are commonly used to reduce a multidimensional problem to a one-dimensional problem; the curve is essentially a linear transversal of the discrete multidimensional space.
An approximation to a space-filling curve
is obtained by joining the centers of these sub-cubes by line segments such that each cell is joined to two adjacent cells.