Invariant measures of Markov operators associated to iterated function systems consisting of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>φ</mml:mi></mml:math>-max-contractions with probabilities

Georgescu, Flavian; Miculescu, Radu; Mihail, Alexandru

doi:10.1016/j.indag.2018.10.001

Cited by 8 publications

(3 citation statements)

References 15 publications

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“…For additional facts on idempotent IFS see [14,16,17]. We will not state the analogous facts for GIFS to avoid repetitions; these can be found in [20][21][22][23].…”

Section: The Hutchinson-barnsley Theorymentioning

confidence: 99%

Making the computation of approximations of invariant measures and its attractors for IFS and GIFS, through the deterministic algorithm, tractable

Cunha¹,

Oliveira²

2021

Preprint

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“…For additional facts on idempotent IFS see [14,16,17]. We will not state the analogous facts for GIFS to avoid repetitions; these can be found in [20][21][22][23].…”

Section: The Hutchinson-barnsley Theorymentioning

confidence: 99%

Making the computation of approximations of invariant measures and its attractors for IFS and GIFS, through the deterministic algorithm, tractable

Cunha¹,

Oliveira²

2021

Preprint

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“…They used the hidden Markov random process to control the modeling and coloring of fractal images, and then drew them with an irregular shape and color. (20,21) Zhuang et al proposed a texture-based IFS (TIFS) that introduced a method of texture synthesis into fractal image designs as a color rendering rule of fractal images to achieve a better rendering effect. (22)…”

Section: Relevant Workmentioning

confidence: 99%

Sensing and Controlling with Markov Process for Locally Independent Fractal Image

Li-liang¹,

Chang²,

Mao³

2020

Sensors and Materials

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We used the Markov process to impose parameter perturbation on affine transformations to overcome the self-similarity limitations of the fractal attractor of the classic iterated function system (IFS) and construct a fractal image with irregular shapes and features. Then, a control method for the IFS system for fractal image generation was proposed. This method decomposes the original IFS into several independent local subsystems. Then, we defined a transition probability matrix of the Markov process for each of the different local subsystems, and carried out image shape operation of a perturbation function to increase the control of the fractal image. This method can construct colorful fractal images effectively through computer image generation.

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“…The existence and uniqueness of µ {p i } i for the case that each fi is a weak contraction is originally shown by[Fan96] with use of an ergodic theorem. Alternative simpler proofs are given by [AJS17,GMM,O18]…”

mentioning

confidence: 99%

Some results for conjugate equations

Okamura

2018

Preprint

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In this paper we consider a class of conjugate equations, which generalizes de Rham's functional equations. We give sufficient conditions for existence and uniqueness of solutions under two different series of assumptions. We consider regularity of solutions. In our framework, two iterated function systems are associated with a series of conjugate equations. We state local regularity by using the invariant measures of the two iterated function systems with a common probability vector. We give several examples, especially an example such that infinitely many solutions exists, and a new class of fractal functions on the two-dimensional standard Sierpiński gasket which are not harmonic functions or fractal interpolation functions. We also consider a certain kind of stability. Contents 1. Introduction 1 2. Existence and uniqueness 3 3. Regularity 6 4. Examples for existence and uniqueness 14 5. Examples for regularity 19 6. Stability 23 7. Open problems 26 References 27

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Invariant measures of Markov operators associated to iterated function systems consisting of φ-max-contractions with probabilities

Cited by 8 publications

References 15 publications

Making the computation of approximations of invariant measures and its attractors for IFS and GIFS, through the deterministic algorithm, tractable

Making the computation of approximations of invariant measures and its attractors for IFS and GIFS, through the deterministic algorithm, tractable

Sensing and Controlling with Markov Process for Locally Independent Fractal Image

Some results for conjugate equations

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