scholarly journals Generation of 3D Fractal Images for Mandelbrot and Julia Sets

2011 ◽  
pp. 14-18
Author(s):  
Bulusu Rama ◽  
Jibitesh Mishra
Keyword(s):  
Real World ◽  
Julia Set ◽  
Computational Modelling ◽  
Mandelbrot Set ◽  
Self Similarity ◽  
3D Images ◽  
Scale Down ◽  
Fractal Images ◽  
Similarity Scale ◽  
Fractal Landscapes

Fractals provide an innovative method for generating 3D images of real-world objects by using computational modelling algorithms based on the imperatives of self-similarity, scale invariance, and dimensionality. Images such as coastlines, terrains, cloud mountains, and most interestingly, random shapes composed of curves, sets of curves, etc. present a multivaried spectrum of fractals usage in domains ranging from multi-coloured, multi-patterned fractal landscapes of natural geographic entities, image compression to even modelling of molecular ecosystems. Fractal geometry provides a basis for modelling the infinite detail found in nature. Fractals contain their scale down, rotate and skew replicas embedded in them. Many different types of fractals have come into limelight since their origin. This paper explains the generation of two famous types of fractals, namely the Mandelbrot Set and Julia Set, the3D rendering of which gives a real-world look and feel in the world of fractal images.

LIMITING DYNAMICS FOR THE COMPLEX STANDARD FAMILY

1995 ◽  
Vol 05 (03) ◽  
pp. 673-699 ◽  
Author(s):  
NÚRIA FAGELLA
Keyword(s):  
Cross Sections ◽  
Julia Set ◽  
Three Dimensional ◽  
Mandelbrot Set ◽  
Dimensional Parameter ◽  
Quadratic Polynomials ◽  
New Family ◽  
Standard Family ◽  
The Family ◽  
Characteristic Features

The complexification of the standard family of circle maps Fαβ(θ)=θ+α+β+β sin(θ) mod (2π) is given by Fαβ(ω)=ωeiαe(β/2)(ω−1/ω) and its lift fαβ(z)=z+a+β sin(z). We investigate the three-dimensional parameter space for Fαβ that results from considering a complex and β real. In particular, we study the two-dimensional cross-sections β=constant as β tends to zero. As the functions tend to the rigid rotation Fα,0, their dynamics tend to the dynamics of the family Gλ(z)=λzez where λ=e−iα. This new family exhibits behavior typical of the exponential family together with characteristic features of quadratic polynomials. For example, we show that the λ-plane contains infinitely many curves for which the Julia set of the corresponding maps is the whole plane. We also prove the existence of infinitely many sets of λ values homeomorphic to the Mandelbrot set.

Mobile Fractal Generation

2011 ◽  
pp. 399-413 ◽  
Author(s):  
Daniel C. Doolan ◽  
Sabin Tabirca ◽  
Laurence T. Yang
Keyword(s):  
Mobile Phone ◽  
Ubiquitous Computing ◽  
Mobile Devices ◽  
Mobile Phones ◽  
New Age ◽  
Mandelbrot Set ◽  
Processing Task ◽  
The Past ◽  
Fractal Images ◽  
Mobile Phone Usage

Ever since the discovery of the Mandelbrot set, the use of computers to visualise fractal images have been an essential component. We are looking at the dawn of a new age, the age of ubiquitous computing. With many countries having near 100% mobile phone usage, there is clearly a potentially huge computation resource becoming available. In the past years there have been a few applications developed to generate fractal images on mobile phones. This chapter discusses three possible methodologies whereby such images can be visualised on mobile devices. These methods include: the generation of an image on a phone, the use of a server to generate the image and finally the use of a network of phones to distribute the processing task.

scholarly journals RePro3D: Full-parallax 3D Display for Superimposing 3D Images onto the Real World using Retro-reflective Projection Technology

2012 ◽  
Vol 66 (4) ◽  
pp. J101-J107
Author(s):  
Takumi Yoshida ◽  
Sho Kamuro ◽  
Kouta Minamizawa ◽  
Hideaki Nii ◽  
Susumu Tachi
Keyword(s):  
Real World ◽  
3D Display ◽  
3D Images ◽  
The Real

scholarly journals Autoencoder-based patch learning for real-world image denoising

2019 ◽  
Vol 13 ◽  
pp. 174830261988139
Author(s):  
Fei Chen ◽  
Haiqing Chen ◽  
Xunxun Zeng ◽  
Meiqing Wang
Keyword(s):  
Image Denoising ◽  
Real World ◽  
State Of The Art ◽  
Compact Representation ◽  
Natural Image ◽  
Great Success ◽  
Image Patch ◽  
Self Similarity ◽  
Coding Scheme ◽  
World Image

Internal patch prior (e.g. self-similarity) has achieved a great success in image denoising. However, it is a challenging task to utilize clean external natural patches for denoising. Natural image patch comes from very complex distributions which are hard to learn without supervision. In this paper, we use an autoencoder to discover and utilize these underlying distributions to learn a compact representation that is more robust to realistic noises. By exploiting learned external prior and internal self-similarity jointly, we develop an efficient patch sparse coding scheme for real-world image denoising. Numerical experiments demonstrate that the proposed method outperforms many state-of-the-art denoising methods, especially on removing realistic noise.

CHAOS AND FRACTAL OF THE GENERAL TWO-DIMENSIONAL QUADRATIC MAP

2008 ◽  
Vol 22 (20) ◽  
pp. 3461-3471
Author(s):  
XINGYUAN WANG
Keyword(s):  
Fractal Dimension ◽  
General Feature ◽  
Strange Attractors ◽  
Two Dimensional ◽  
Control Parameters ◽  
Self Similarity ◽  
Boundary Equation ◽  
Quadratic Map ◽  
Fractal Images ◽  
Stable Points

The nature of the stable points of the general two-dimensional quadratic map is considered analytically, and the boundary equation of the first bifurcation of the map in the parameter space is given out. The general feature of the nonlinear dynamic activities of the map is analyzed by the method of numerical computation. By utilizing the Lyapunov exponent as a criterion, this paper constructs the strange attractors of the general two-dimensional quadratic map, and calculates the fractal dimension of the strange attractors according to the Lyapunov exponents. At the same time, the researches on the fractal images of the general two-dimensional quadratic map make it clear that when the control parameters are different, the fractal images are different from each other, and these fractal images exhibit the fractal property of self-similarity.

Local self-similarity descriptor for point-of-interest reconstruction of real-world scenes

2015 ◽  
Vol 26 (8) ◽  
pp. 085010 ◽  
Author(s):  
Xianglu Gao ◽  
Weibing Wan ◽  
Qunfei Zhao ◽  
Xianmin Zhang
Keyword(s):  
Real World ◽  
Self Similarity ◽  
Point Of Interest

scholarly journals Revisiting foraging approaches in neuroscience

2018 ◽  
Author(s):  
Sam Hall-McMaster ◽  
Fabrice Luyckx
Keyword(s):  
Real World ◽  
Optimal Foraging ◽  
Ecological Validity ◽  
Computational Modelling ◽  
Optimal Foraging Theory ◽  
Foraging Theory ◽  
Behavioural Ecology ◽  
Formal Models ◽  
The Way

Many complex real-world decisions, such as deciding which house to buy or whether to switch jobs, involve trying to maximise reward across a sequence of choices. Optimal Foraging Theory is well suited to study these kinds of choices because it provides formal models for reward-maximisation in sequential situations. In this article, we review recent insights from foraging neuroscience, behavioural ecology and computational modelling. We find that a commonly used approach in foraging neuroscience, in which choice items are encountered at random, does not reflect the way animals direct their foraging efforts in real-world settings, nor does it reflect efficient reward-maximising behaviour. Based on this, we propose that task designs allowing subjects to encounter choice items strategically will further improve the ecological validity of foraging approaches used in neuroscience, as well as give rise to new behavioural and neural predictions that deepen our understanding of sequential, value-based choice.

scholarly journals Multicorns are not path connected

2014 ◽  
Author(s):  
John Hamal Hubbard ◽  
Dierk Schleicher
Keyword(s):  
Julia Set ◽  
Mandelbrot Set ◽  
Quadratic Polynomials ◽  
Unicritical Polynomials ◽  
Path Connected ◽  
Special Case ◽  
Connectedness Locus

This chapter proves that the tricorn is not locally connected and not even pathwise connected, confirming an observation of John Milnor from 1992. The tricorn is the connectedness locus in the space of antiholomorphic quadratic polynomials z ↦ ̄z² + c. The chapter extends this discussion more generally for antiholomorphic unicritical polynomials of degrees d ≥ 2 and their connectedness loci, known as multicorns. The multicorn M*subscript d is the connectedness locus in the space of antiholomorphic unicritical polynomials psubscript c(z) = ̄zsubscript d + c of degree d, i.e., the set of parameters for which the Julia set is connected. The special case d = 2 is the tricorn, which is the formal antiholomorphic analog to the Mandelbrot set.

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