Escape-Time Modified Algorithm for Generating Fractal Images Based on Petri Net Reachability
Summary :
This paper presents a new approach to computer image generation via three proposed methods for translating the evolution of a Petri net into fractal image synthesis. The idea is derived from the concept of fractal iteration principles in the escape-time algorithm and chaos game. The approach uses a Petri net as a powerful abstract modeling tool for fractal image synthesis via its duality, deadlock, inhibitor arc, firing sequence and marking reachability. The objective of this approach is to enhance the analysis technique of a Petri net and use it as a novel technique for fractal image synthesis. Generating fractal images via the dynamics of a Petri net allows an easy and direct proof for the similarity and correspondence between the dynamics of complex quadratic fractals by the recursive procedure of the escape-time algorithm and the state of a Petri net via a reachability problem. The reachability problem will be manipulated in terms of the dynamics of the fractal in order to generate images via three proposed methods. Validation of our approach is given by discussion and an illustration of some experimental results.
- Publication
- IEICE TRANSACTIONS on Information Vol.E82-D No.7 pp.1101-1108
- Publication Date
- 1999/07/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Image Processing,Computer Graphics and Pattern Recognition
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Hussein Karam HUSSEIN, Aboul-Ella HASSANIEN, Masayuki NAKAJIMA, "Escape-Time Modified Algorithm for Generating Fractal Images Based on Petri Net Reachability" in IEICE TRANSACTIONS on Information,
vol. E82-D, no. 7, pp. 1101-1108, July 1999, doi: .
Abstract: This paper presents a new approach to computer image generation via three proposed methods for translating the evolution of a Petri net into fractal image synthesis. The idea is derived from the concept of fractal iteration principles in the escape-time algorithm and chaos game. The approach uses a Petri net as a powerful abstract modeling tool for fractal image synthesis via its duality, deadlock, inhibitor arc, firing sequence and marking reachability. The objective of this approach is to enhance the analysis technique of a Petri net and use it as a novel technique for fractal image synthesis. Generating fractal images via the dynamics of a Petri net allows an easy and direct proof for the similarity and correspondence between the dynamics of complex quadratic fractals by the recursive procedure of the escape-time algorithm and the state of a Petri net via a reachability problem. The reachability problem will be manipulated in terms of the dynamics of the fractal in order to generate images via three proposed methods. Validation of our approach is given by discussion and an illustration of some experimental results.
URL: https://global.ieice.org/en_transactions/information/10.1587/e82-d_7_1101/_p
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@ARTICLE{e82-d_7_1101,
author={Hussein Karam HUSSEIN, Aboul-Ella HASSANIEN, Masayuki NAKAJIMA, },
journal={IEICE TRANSACTIONS on Information},
title={Escape-Time Modified Algorithm for Generating Fractal Images Based on Petri Net Reachability},
year={1999},
volume={E82-D},
number={7},
pages={1101-1108},
abstract={This paper presents a new approach to computer image generation via three proposed methods for translating the evolution of a Petri net into fractal image synthesis. The idea is derived from the concept of fractal iteration principles in the escape-time algorithm and chaos game. The approach uses a Petri net as a powerful abstract modeling tool for fractal image synthesis via its duality, deadlock, inhibitor arc, firing sequence and marking reachability. The objective of this approach is to enhance the analysis technique of a Petri net and use it as a novel technique for fractal image synthesis. Generating fractal images via the dynamics of a Petri net allows an easy and direct proof for the similarity and correspondence between the dynamics of complex quadratic fractals by the recursive procedure of the escape-time algorithm and the state of a Petri net via a reachability problem. The reachability problem will be manipulated in terms of the dynamics of the fractal in order to generate images via three proposed methods. Validation of our approach is given by discussion and an illustration of some experimental results.},
keywords={},
doi={},
ISSN={},
month={July},}
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TY - JOUR
TI - Escape-Time Modified Algorithm for Generating Fractal Images Based on Petri Net Reachability
T2 - IEICE TRANSACTIONS on Information
SP - 1101
EP - 1108
AU - Hussein Karam HUSSEIN
AU - Aboul-Ella HASSANIEN
AU - Masayuki NAKAJIMA
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E82-D
IS - 7
JA - IEICE TRANSACTIONS on Information
Y1 - July 1999
AB - This paper presents a new approach to computer image generation via three proposed methods for translating the evolution of a Petri net into fractal image synthesis. The idea is derived from the concept of fractal iteration principles in the escape-time algorithm and chaos game. The approach uses a Petri net as a powerful abstract modeling tool for fractal image synthesis via its duality, deadlock, inhibitor arc, firing sequence and marking reachability. The objective of this approach is to enhance the analysis technique of a Petri net and use it as a novel technique for fractal image synthesis. Generating fractal images via the dynamics of a Petri net allows an easy and direct proof for the similarity and correspondence between the dynamics of complex quadratic fractals by the recursive procedure of the escape-time algorithm and the state of a Petri net via a reachability problem. The reachability problem will be manipulated in terms of the dynamics of the fractal in order to generate images via three proposed methods. Validation of our approach is given by discussion and an illustration of some experimental results.
ER -
English
