THE CRAB: A CONNECTED FRACTILE OF INFINITE CONNECTIVITY

Fractals ◽  
2011 ◽  
Vol 19 (03) ◽  
pp. 367-377 ◽  
Author(s):  
GILBERT HELMBERG
Keyword(s):  
Hausdorff Dimension ◽  
Hausdorff Metric ◽  
Unit Interval ◽  
Limit Set ◽  
Space Filling ◽  
Polygonal Path ◽  
Space Filling Curve ◽  
Dimension Formula ◽  
Filling Curve ◽  
Similar Copy

In the plane IR2, let A0 be the unit interval on the x-axis, and let A(1) be the polygonal path with nodes (0, 0), [Formula: see text], (½, 0), [Formula: see text], (1, 0). Let S be the operator which, applied to a segment B(0) in IR2, replaces it by a polygonal path B(1) = SB(0), a similar copy of A(1), but with the same endpoints as B(0). Denote by S(n) the n-th iterate of S. The limit set (with respect to the Hausdorff metric) A(∞) = lim n → ∞ S(n)A(0) is a space-filling curve which is the closure of its interior and the union of four half-size copies of itself, intersecting only in their boundaries. Although A(∞) is of infinite connectivity, it is a tile tessellating the plane. It is related to the set of Eisenstein fractions and has a boundary of Hausdorff dimension [Formula: see text]

Region of Interest Based MRI Brain Image Compression Using Peano Space Filling Curve

2016 ◽  
Vol 11 (2) ◽  
pp. 114-120 ◽  
Author(s):  
C. Peter Devadoss ◽  
Balasubramanian Sankaragomathi ◽  
Thirugnanasambantham Monica
Keyword(s):  
Image Compression ◽  
Region Of Interest ◽  
Space Filling ◽  
Brain Image ◽  
Space Filling Curve ◽  
Mri Brain ◽  
Filling Curve ◽  
Mri Brain Image

A Space Filling Curve

1983 ◽  
Vol 90 (4) ◽  
pp. 283
Author(s):  
Liu Wen
Keyword(s):  
Space Filling ◽  
Space Filling Curve ◽  
Filling Curve

scholarly journals Enhancing Quad Tree for Spatial Index Using Space Filling Curves

2020 ◽  
Vol 38 (1B) ◽  
pp. 15-25
Author(s):  
Ali A. Hussain ◽  
Rehab F. Hassan
Keyword(s):  
Spatial Databases ◽  
Space Filling ◽  
Space Filling Curve ◽  
Effective Implementation ◽  
Quad Tree ◽  
Implementation Time ◽  
Spatial Indexes ◽  
Space Requirements ◽  
Filling Curve ◽  
And Storage

Spatial indexes, such as those based on the Quad Tree, are important in spatial databases for the effective implementation of queries with spatial constraints, especially when queries involve spatial links. The quaternary trees are a very interesting subject, given the fact that they give the ability to solve problems in a way that focuses only on the important areas with the highest density of information. Nevertheless, it is not without the disadvantages because the search process in the quad tree suffers from the problem of repetition when reaching the terminal node and return to the behavior of another way in the search and lead to the absorption of large amounts of time and storage. In this paper, the quad tree was improved by combining it with one of the space filling curve types, resulting in reduced storage space requirements and improved implementation time

The LBF R-Tree

2010 ◽  
pp. 1-27
Author(s):  
Todd Eavis
Keyword(s):  
Hilbert Space ◽  
Data Warehousing ◽  
Experimental Results ◽  
Data Sets ◽  
Space Filling ◽  
Fully Integrated ◽  
Space Filling Curve ◽  
Filling Curve ◽  
Common User ◽  
Tree Performance

In multi-dimensional database environments, such as those typically associated with contemporary data warehousing, we generally require effective indexing mechanisms for all but the smallest data sets. While numerous such methods have been proposed, the R-tree has emerged as one of the most common and reliable indexing models. Nevertheless, as user queries grow in terms of both size and dimensionality, R-tree performance can deteriorate significantly. Moreover, in the multi-terabyte spaces of today’s enterprise warehouses, the combination of data and indexes ? R-tree or otherwise ? can produce unacceptably large storage requirements. In this chapter, the authors present a framework that addresses both of these concerns. First, they propose a variation of the classic R-tree that specifically targets data warehousing architectures. Their new LBF R-tree not only improves performance on common user-defined range queries, but gracefully degrades to a linear scan of the data on pathologically large queries. Experimental results demonstrate a reduction in disk seeks of more than 50% relative to more conventional R-tree designs. Second, the authors present a fully integrated, block-oriented compression model that reduces the storage footprint of both data and indexes. It does so by exploiting the same Hilbert space filling curve that is used to construct the LBF R-tree itself. Extensive testing demonstrates compression rates of more than 90% for multi-dimensional data, and up to 98% for the associated indexes.

Space Filling Curve for Data Filling: An Embedded Security Approach

2014 ◽  
Vol 6 (3) ◽  
pp. 188-197 ◽  
Author(s):  
Siva Janakirama ◽  
K. Thenmozhi ◽  
Sundararaman Rajagopala ◽  
Har Narayan Upadhyay ◽  
John Bosco Balaguru Rayappan ◽  
...  
Keyword(s):  
Space Filling ◽  
Space Filling Curve ◽  
Embedded Security ◽  
Filling Curve
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