Space-filling curves of self-similar sets (II): edge-to-trail substitution rule
نویسندگان
چکیده
منابع مشابه
Unconventional Space-filling Curves
A 2-dimensional space-filling curve, here, is a surjective continuous map from an interval to a 2-dimensional space. To construct a new space-filling curve distinct and much different from Hilbert’s, Peano’s, and the Z-order, we first observe that all three of these curves are based on self-similar fractals–in particular, the recursive definition of the sequences of functions that converge to t...
متن کاملSelf-similar space-filling packings in three dimensions
We develop an algorithm to construct new self-similar space-filling packings of spheres. Each topologically different configuration is characterized by its own fractal dimension. We also find the first bicromatic packing known up to now.
متن کاملSelf-Similar Structure in Hilbert's Space Filling Curve
Hilbert's spacelling curve is a continuous function that maps the unit interval onto the unit square. The construction of such curves in the 1890s surprised mathematicians of the time and led, in part, to the development of dimension theory. In this paper, we discuss how modern notions of selfsimilarity illuminate the structure of this curve. In particular, we show that Hilbert's curve has a ba...
متن کاملSpace filling curves in steganalysis
We introduce a new method to increase the reliability of current steganalytic techniques by optimising the sample order. Space filling curves (e. g., Hilbert curve) take advantage of the correlation of adjacent pixels and thus make the detection of steganographic messages with low change densities more reliable. The findings are applicable, but not limited to LSB steganalysis. An experimental c...
متن کاملContext-based Space Filling Curves
A context-based scanning technique for images is presented. An image is scanned along a context-based space filling curve that is computed so as to exploit inherent coherence in the image. The resulting one-dimensional representation of the image has improved autocorrelation compared with universal scans such as the PeanoHilbert space filling curve. An efficient algorithm for computing context-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nonlinearity
سال: 2019
ISSN: 0951-7715,1361-6544
DOI: 10.1088/1361-6544/ab1275