scholarly journals Morphogenesis Analysis for Digital Image Production with L-System

2021 ◽  
Vol 9 (2) ◽  
pp. 153
Author(s):  
Arie Vatresia ◽  
Ferzha Putra Utama
Keyword(s):  
Iterated Function System ◽  
Image Transformation ◽  
Good Image ◽  
A Value ◽  
L System ◽  
Correct Color ◽  
Iterated Function ◽  
Fire Effect ◽  
Image Production ◽  
Color Composition

The process of forming an image requires a correct color composition, location and distance between the lines to produce a good image. Human abilities in both creativity and high imagination are very limited, especially in forming new images by utilizing existing image patterns or images that resemble old images. Here we showed the implementation of L-System to generate new image generations with additional flame as a fire effect/glow on images for image transformation. This research used the L-System algorithm, Iterated Function System, and Voronoi Diagram to improve the result of image transformation. The results of this study indicated that mathematical calculations can be applied in the formation of images and the resulting images can be abstract and symmetrical. The next generation of images produced in this research can be in unlimited numbers as the generation of morphogenesis processes. The process of generating images is carried out randomly by merging the two existing images with morphogenesis analogy. The resulting images can be exported into jpg, png, and svg formats. Furthermore, this research showed that the implementation of the calculation for the variation reach the value of 99.48% while the image variation composition has a value of 99.29%.

scholarly journals PEMANFAATAN METODE ITERATED FUNCTION SYSTEM (IFS) PADA PEMBANGKITAN KURVA NAGA

2020 ◽  
Vol 20 (2) ◽  
pp. 89
Author(s):  
Vian Hafid Suny ◽  
Kosala Dwidja Purnomo ◽  
Firdaus Ubaidillah
Keyword(s):  
Affine Transformation ◽  
System Approach ◽  
Rotation Angle ◽  
Iterated Function System ◽  
Function System ◽  
Production Rules ◽  
Fixed Angle ◽  
L System ◽  
System L ◽  
Iterated Function

Fractals have two types, namely fractals sets (artificial fractals) and natural fractals. Each type of fractal has a variety of fractal objects. One of the fractal objects is the Dragon Curve. Fractal objects can be generated through two methods, namely the Lindenmayer System (L-System) and the Iterated Function System (IFS). In previous studies, the Dragon curve can be generated through the L-System approach. The method is to start from determining the rotation angle, then determining the initial string, and the last one, which is determining the production rules. In this study, the Dragon curve is generated using IFS with Affine Transformation. The Affine transformation used in this study is dilation and rotation. Some variation is given on the scale of dilation and rotation angle. The variation is using a fixed angle with a variety of scale and using a fixed scale with a variation of angle. Each variation gives a different effect. This influence results in a varied visualization of the Naga curve. If the scale and angle that is varied approach a scale of one and an angle of 90° then the fractal formed approaches the Dragon curve of a scale of one with an angle of 90°. Conversely, if the scale and angle are varied away from one scale and angle of 90°, the fractal formed away from the Dragon curve of scale one with an angle of 90°. Keywords: Affine transformation, dragon curve, IFS method.

scholarly journals Graph directed Markov systems on Hilbert spaces

2009 ◽  
Vol 147 (2) ◽  
pp. 455-488 ◽  
Author(s):  
R. D. MAULDIN ◽  
T. SZAREK ◽  
M. URBAŃSKI
Keyword(s):  
Hausdorff Measure ◽  
Iterated Function System ◽  
Sufficient Conditions ◽  
Topological Pressure ◽  
Limit Set ◽  
Covering Theorem ◽  
Limit Sets ◽  
Markov Systems ◽  
Polish Spaces ◽  
Iterated Function

AbstractWe deal with contracting finite and countably infinite iterated function systems acting on Polish spaces, and we introduce conformal Graph Directed Markov Systems on Polish spaces. Sufficient conditions are provided for the closure of limit sets to be compact, connected, or locally connected. Conformal measures, topological pressure, and Bowen's formula (determining the Hausdorff dimension of limit sets in dynamical terms) are introduced and established. We show that, unlike the Euclidean case, the Hausdorff measure of the limit set of a finite iterated function system may vanish. Investigating this issue in greater detail, we introduce the concept of geometrically perfect measures and provide sufficient conditions for geometric perfectness. Geometrical perfectness guarantees the Hausdorff measure of the limit set to be positive. As a by–product of the mainstream of our investigations we prove a 4r–covering theorem for all metric spaces. It enables us to establish appropriate co–Frostman type theorems.

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 Novel Iterated Function System-Based Model for Coloured Image Encryption

2021 ◽  
Vol 12 (2) ◽  
pp. 1-10
Author(s):  
Amine Rahmani
Keyword(s):  
Image Encryption ◽  
Iterated Function System ◽  
Mathematical Concept ◽  
Logistic Equation ◽  
Encryption Scheme ◽  
Symmetric Encryption ◽  
New Model ◽  
Proposed Model ◽  
Iterated Function ◽  
Chaotic Cryptography

Chaotic cryptography has been a well-studied domain over the last few years. Many works have been done, and the researchers are still getting benefit from this incredible mathematical concept. This paper proposes a new model for coloured image encryption using simple but efficient chaotic equations. The proposed model consists of a symmetric encryption scheme in which it uses the logistic equation to generate secrete keys then an affine recursive transformation to encrypt pixels' values. The experimentations show good results, and theoretic discussion proves the efficiency of the proposed model.

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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