Figure 9a shows the Peano curve. Figure 9b shows [X.sub.scale] of Peano curve using the CM partition.
We found that Peano curve is self-similar, Moore curve is not self-similar, Meander curve is self similar and Lebesgue curve is self-similar.
Both references use the existence of a continuous surjection from [0, 1] onto [[0, 1].sup.2] (a Peano curve
in [[0, 1].sup.2] or a spacefilling curve).
Considering that the dynamics of the complex system entities take place on continuous but nondifferentiable curves, that is, fractal curves (e.g., the Koch curve, the Peano curve
, or the Weierstrass curve [11-14,17,18]), they are given by the fractal operator [??]/dt (for details see Appendices A and B):
Having in view the geometrical characteristics, the Peano curve fractal may be used for heat pipe device.
For example a Peano curve is built by Hilbert (Fig.
In this example, we will look on the Peano curve and show how we can construct a Chinese lattice based on this curve.
Let us recall the shape and properties of the Peano curve. There are many ways of defining a Peano curve.
This would enable the construction of other forms of space-filling curve, such as the Peano curve
All well-known fractal curves, such as Koch curve , Peano curve
, Giuseppe Peano curve
, and Hilbert Curve [23, 24], are preferably designed into dipole or monopole antennas.
The results from the Section Peano Curves
and Semigroup ability were a part of a very first version of the paper .
Because Giuseppe Peano (1858-1932) was the first to discover one of the filling curve constructions, space-filling curves in 2-dimensional planes are sometimes called Peano curves
. Some of the most celebrated are the Hilbert curve and the Sierpimki curve .