Iterated Function Systems and Two-Dimensional Shape Representation

10.5244/c.3.9 ◽  
1989 ◽  
Author(s):  
P. A. Giles ◽  
A. Purvis ◽  
D. Waugh ◽  
R. Garigliano
Keyword(s):  
Shape Representation ◽  
Iterated Function Systems ◽  
Two Dimensional ◽  
Iterated Function ◽  
Dimensional Shape

On the Mathematical Reconstruction of Two Dimensional Plants

2006 ◽  
Vol 26 (2) ◽  
pp. 113-129 ◽  
Author(s):  
Zbigniew J. Grzywna ◽  
Przemysław Borys ◽  
Gabriela Dudek
Keyword(s):  
Pattern Recognition ◽  
Quantitative Analysis ◽  
Medicinal Plants ◽  
Surface Density ◽  
Iterated Function Systems ◽  
Linear Ordering ◽  
Mathematical Representation ◽  
Computer Memory ◽  
Two Dimensional ◽  
Iterated Function

A set of 10, chosen medicinal plants (some of them with a reputation as remedies for tuberculosis) has been investigated through Partitioned Iterated Function Systems-Semi Fractals with Angle (PIFS-SFA) coding, Lempel, Ziv, Welch with quantization and noise (LZW-QN) compression, and surface density statistics (f(α)-SDS) discrimination techniques. The final outcomes of this quantitative analysis were, firstly: the linear ordering of the plants in question accompanied by the hope that it reflects their medical significance, secondly: the mathematical representation of each of the plants, and thirdly: the impressive compression achieved, leading to remarkable computer memory saving, and still permitting successful pattern recognition i.e., proper identification of the plant from the compressed image.

scholarly journals C1 ROBUSTLY MINIMAL ITERATED FUNCTION SYSTEMS

2010 ◽  
Vol 10 (01) ◽  
pp. 155-160 ◽  
Author(s):  
F. H. GHANE ◽  
A. J. HOMBURG ◽  
A. SARIZADEH
Keyword(s):  
Iterated Function Systems ◽  
Compact Manifolds ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Iterated Function

We construct iterated function systems on compact manifolds that are C1 robustly minimal. On the m-dimensional torus and on two-dimensional compact manifolds, examples are provided of C1 robustly minimal iterated function systems that are generated by just two diffeomorphisms.

scholarly journals THE AESTHETICS AND FRACTAL DIMENSION OF ELECTRIC SHEEP

2008 ◽  
Vol 18 (04) ◽  
pp. 1243-1248 ◽  
Author(s):  
SCOTT DRAVES ◽  
RALPH ABRAHAM ◽  
PABLO VIOTTI ◽  
FREDERICK DAVID ABRAHAM ◽  
JULIAN CLINTON SPROTT
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Iterated Function Systems ◽  
Two Dimensional ◽  
Computer Scientist ◽  
Large Community ◽  
Iterated Function ◽  
Fractal Images ◽  
The Relationship ◽  
Aesthetic Judgments

Physicist Clint Sprott demonstrated a relationship between aesthetic judgments of fractal images and their fractal dimensions [1993]. Scott Draves, aka Spot, a computer scientist and artist, has created a space of images called fractal flames, based on attractors of two-dimensional iterated function systems. A large community of users run software that automatically downloads animated fractal flames, known as "sheep", and displays them as their screen-saver. The users may vote electronically for the sheep they like while the screen-saver is running. In this report we proceed from Sprott to Spot. The data show an inverted U-shaped curve in the relationship between aesthetic judgments of flames and their fractal dimension, confirming and clarifying earlier reports.

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