scholarly journals An Iterated Function System based Method to Generate Hilbert-type Space-filling Curves

2015 ◽  
Vol 7 (12) ◽  
pp. 12-22 ◽  
Author(s):  
Ruisong Ye ◽  
◽  
Li Liu
Keyword(s):  
Iterated Function System ◽  
Function System ◽  
Space Filling ◽  
Type Space ◽  
Space Filling Curves ◽  
Iterated Function ◽  
Hilbert Type

scholarly journals A Matrix Iterative Approach to Systematically Generate Hilbert-type Space-filling Curves

2015 ◽  
Vol 14 (12) ◽  
pp. 6281-6294
Author(s):  
Ruisong Ye ◽  
Li Liu
Keyword(s):  
Point Of View ◽  
Iterative Approach ◽  
Matrix Approach ◽  
Space Filling ◽  
Type Space ◽  
Space Filling Curve ◽  
Space Filling Curves ◽  
The Matrix ◽  
Filling Curve ◽  
Hilbert Type

Hilbert-type space-filling curve has attracted much interest thanks to its mathematical importance and extensive applications in signal processing. In this paper, we construct the complete six Hilbert-type space-filling curves form amatrix point of view. The address matrix for each considered Hilbert-type space-filling curve can be easily generated by a recursive manner. Besides the six Hilbert-type space-filling curves, we also construct their corresponding variation versions. The merit of the matrix approach is that the iterative algorithm is easy to implement and can be generalized to produce any other Hilbert-type space-filling curves and their variation versions.

ARCLENGTH AS THE INVARIANT MEASURE FOR AN IFS WITH PROBABILITIES

Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550046
Author(s):  
D. LA TORRE ◽  
F. MENDIVIL
Keyword(s):  
Invariant Measure ◽  
Iterated Function System ◽  
Function System ◽  
Iterated Function

Given a continuous rectifiable function [Formula: see text], we present a simple Iterated Function System (IFS) with probabilities whose invariant measure is the normalized arclength measure on the graph of [Formula: see text].

Stochastic Fractal Modeling and Process Planning for Machining Using Two-Dimensional Iterated Function System

2008 ◽  
Vol 392-394 ◽  
pp. 575-579
Author(s):  
Yu Hao Li ◽  
Jing Chun Feng ◽  
Y. Li ◽  
Yu Han Wang
Keyword(s):  
Path Planning ◽  
Tool Path ◽  
Iterated Function System ◽  
Numerical Control ◽  
Function System ◽  
Tool Path Planning ◽  
Ongoing Research ◽  
Iterated Function ◽  
Planning Algorithm ◽  
Path Planning Algorithm

Self-affine and stochastic affine transforms of R2 Iterated Function System (IFS) are investigated in this paper for manufacturing non-continuous objects in nature that exhibit fractal nature. A method for modeling and fabricating fractal bio-shapes using machining is presented. Tool path planning algorithm for numerical control machining is presented for the geometries generated by our fractal generation function. The tool path planning algorithm is implemented on a CNC machine, through executing limited number of iteration. This paper describes part of our ongoing research that attempts to break through the limitation of current CAD/CAM and CNC systems that are oriented to Euclidean geometry objects.

A graphical representation of protein based on a novel iterated function system

2014 ◽  
Vol 403 ◽  
pp. 21-28 ◽  
Author(s):  
Tingting Ma ◽  
Yuxin Liu ◽  
Qi Dai ◽  
Yuhua Yao ◽  
Ping-an He
Keyword(s):  
Graphical Representation ◽  
Iterated Function System ◽  
Function System ◽  
Iterated Function

Fractal dimension and iterated function system (IFS) for speech recognition

1992 ◽  
Vol 28 (15) ◽  
pp. 1382 ◽  
Author(s):  
E.L.J. Bohez ◽  
T.R. Senevirathne ◽  
J.A. van Winden
Keyword(s):  
Fractal Dimension ◽  
Speech Recognition ◽  
Iterated Function System ◽  
Function System ◽  
Iterated Function
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