Switched processes generalized mandelbrot sets for complex index number

2003 ◽  
Vol 24 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Wang Xing-yuan
Keyword(s):  
Index Number ◽  
Complex Index ◽  
Mandelbrot Sets ◽  
Generalized Mandelbrot Sets

scholarly journals Smooth Decomposition of Generalized Fatou Set Explains Smooth Structure in Generalized Mandelbrot Set

1988 ◽  
Vol 43 (1) ◽  
pp. 14-16 ◽  
Author(s):  
J. Peinke ◽  
J. Parisi ◽  
B. Röhricht ◽  
O. E. Rössler ◽  
W. Metzler
Keyword(s):  
Parameter Space ◽  
Initial Conditions ◽  
Logistic Map ◽  
Mandelbrot Set ◽  
Fatou Set ◽  
Smooth Structure ◽  
Mandelbrot Sets ◽  
Generalized Mandelbrot Sets

Abstract Generalized Mandelbrot sets arise in perturbed (non-analytic) versions of the complex logistic map. Numerically, it contains smooth portions as shown previously. To exclude that this result is specific to particular initial conditions only, the structure of the analogue to the Fatou set is looked at in the region in question. The set of non-divergent points is being "eaten up" by a smooth invading boundary. Therefore, the same type of decomposition applies independent of position in parameter space, in the region in question.

The Construction for Generalized Mandelbrot Sets of the Frieze Group

2013 ◽  
Vol 756-759 ◽  
pp. 2562-2566
Author(s):  
Feng Ying Wang ◽  
Li Ming Du ◽  
Zi Yang Han
Keyword(s):  
Dynamical System ◽  
Parameter Space ◽  
Mandelbrot Sets ◽  
Group A ◽  
Novel Method ◽  
Definition Of ◽  
Generalized Mandelbrot Sets

By an analysis of symmetric features of equivalent mappings of the frieze group, a definition of their generalized Mandelbrot sets is given and a novel method for constructing generalized Mandelbrot sets of equivalent mappings of frieze group is presented via utilizing the Ljapunov exponent as the judgment standard. Based on generating parameter space of dynamical system, lots of patterns of generalized Mandelbrot sets are produced.

scholarly journals Noise perturbed generalized Mandelbrot sets

2008 ◽  
Vol 347 (1) ◽  
pp. 179-187 ◽  
Author(s):  
Xingyuan Wang ◽  
Zhen Wang ◽  
Yahui Lang ◽  
Zhenfeng Zhang
Keyword(s):  
Mandelbrot Sets ◽  
Generalized Mandelbrot Sets

Two Partitioning Algorithms for Generating of M Sets of the Frieze Group

2013 ◽  
Vol 336-338 ◽  
pp. 2238-2241
Author(s):  
Feng Ying Wang ◽  
Li Ming Du ◽  
Zi Yang Han
Keyword(s):  
Dynamical System ◽  
Parameter Space ◽  
Mandelbrot Sets ◽  
Partitioning Algorithms ◽  
Generalized Mandelbrot Sets

Symmetric features of the frieze group equivalent mappings were analysed, and two partitioning algorithms are given for constructing generalized Mandelbrot sets of frieze group equivalent mappings in order to study the characteristics of generalized Msets. Based on generating parameter space of dynamical system, lots of patterns of generalized Mandelbrot sets are produced.

FRACTAL IMAGES OF GENERALIZED MANDELBROT SETS

Fractals ◽  
1994 ◽  
Vol 02 (01) ◽  
pp. 111-121
Author(s):  
AICHYUN SHIAH ◽  
KIM-KHOON ONG ◽  
ZDZISLAW E. MUSIELAK
Keyword(s):  
Complex Plane ◽  
Transformation Function ◽  
Real Numbers ◽  
Mandelbrot Sets ◽  
Fractal Images ◽  
Principal Value ◽  
Generalized Mandelbrot Sets

The transformation function z ← zα+βi+c, with both α and β being either positive or negative integers or real numbers, is used to generate families of mostly new fractal images in the complex plane [Formula: see text]. The calculations are restricted to the principal value of zα+βi and the obtained fractal images are called the generalized Mandelbrot sets, ℳ (α, β). Three general classes of ℳ (α, β) are considered: (1) α ≠ 0 and β = 0; (2) α ≠ 0 and β ≠ 0; and (3) α = 0 and β ≠ 0. Our results demonstrate that the shapes of fractal images representing ℳ (α, 0) are usually significantly deformed when β ≠ 0, and that the size of either stable (α > 0) or unstable (α < 0) regions in the complex plane may increase as a result of non-zero β. It is also shown that fractal images of the generalized Mandelbrot sets ℳ (0, β) are significantly different than those obtained with a non-zero α.

RESEARCH FRACTAL STRUCTURES OF GENERALIZED M-J SETS USING THREE ALGORITHMS

Fractals ◽  
2008 ◽  
Vol 16 (01) ◽  
pp. 79-88 ◽  
Author(s):  
XING-YUAN WANG ◽  
LI-NA GU
Keyword(s):  
Phase Angle ◽  
Time Algorithm ◽  
Decomposition Algorithm ◽  
Fractal Structures ◽  
Structural Character ◽  
Mandelbrot Sets ◽  
Generalized Mandelbrot Sets

Extreme modulus escaping time algorithm, decomposition algorithm and fisheye algorithm are analyzed in this thesis, and we construct a series of generalized Mandelbrot-Julia (M-J) sets using these three algorithms. By studying the structural character of generalized M-J sets, we find: (1) extreme modulus escaping time algorithm and decomposition algorithm are simple modifications of classic escaping time algorithm, they can both construct the structure of non-boundary areas of generalized M-J sets; (2) non-boundary areas of generalized M-J sets have fractal characters; (3) generalized M-J sets have symmetry, and the process of evolvement depends on range of phase angle; (4) we can observe not only the whole structure of generalized Mandelbrot sets but also the details of some parts by using fisheye algorithm.

High Antibody Levels to Prothrombin Imply a Risk of Deep Venous Thrombosis and Pulmonary Embolism in Middle-aged Men

1997 ◽  
Vol 78 (04) ◽  
pp. 1178-1182 ◽  
Author(s):  
Timo Palosuo ◽  
Jarmo Virtamo ◽  
Jari Haukka ◽  
Philip R Taylor ◽  
Kimmo Aho ◽  
...  
Keyword(s):  
Pulmonary Embolism ◽  
Venous Thrombosis ◽  
Deep Venous Thrombosis ◽  
Plasma Proteins ◽  
Alpha Tocopherol ◽  
Index Number ◽  
Thromboembolic Events ◽  
Middle Aged ◽  
Phospholipid Binding ◽  
Antiprothrombin Antibodies

SummaryAntibodies against phospholipid-binding plasma proteins, such as β2-glycoprotein I (β2-GPI) and prothrombin, are associated with thromboembolic events in patients with systemic lupus erythematosus and also in subjects with no evident underlying diseases. We wanted to examine whether increased levels of antibodies to negatively-charged phospholipids (cardiolipin), to phospholipid-binding plasma proteins β2-GPI and prothrombin and to oxidised low-density lipoprotein (LDL) were associated with risk of deep venous thrombosis or pulmonary embolism in subjects with no previous thrombosis. The antibodies were measured in stored serum samples from 265 cases of deep venous thrombosis of the lower extremity or pulmonary embolism occurring during a median follow-up of about 7 years and from 265 individually matched controls. The study subjects were middle-aged men participating in a cancer prevention trial of alpha-tocopherol and beta-carotene and the cases of thromboembolic events were identified from nationwide Hospital Discharge Register.The risk for thrombotic events was significantly increased only in relation to antiprothrombin antibodies. As adjusted for body mass index, number of daily cigarettes and history of chronic bronchitis, myocardial infarction and heart failure at baseline, the odds ratio per one unit of antibody was 6.56 (95% confidence interval 1.73-25.0). The seven highest individual optical density-unit values of antiprothrombin antibodies were all confined to subjects with thromboembolic episodes.In conclusion, the present nested case-control study showed that high autoantibody levels against prothrombin implied a risk of deep venous thrombosis and pulmonary embolism and could be involved in the development of the thrombotic processes.

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