Unification of two fractal families

Ying Liu

doi:10.1117/12.211985

16 June 1995 Unification of two fractal families

Ying Liu

Proceedings Volume 2488, Visual Information Processing IV; (1995) https://doi.org/10.1117/12.211985
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

Barnsley and Hurd classify the fractal images into two families: iterated function system fractals (IFS fractals) and fractal transform fractals, or local iterated function system fractals (LIFS fractals). We will call IFS fractals, class 2 fractals and LIFS fractals, class 3 fractals. In this paper, we will unify these two approaches plus another family of fractals, the class 5 fractals. The basic idea is given as follows: a dynamical system can be represented by a digraph, the nodes in a digraph can be divided into two parts: transient states and persistent states. For bilevel images, a persistent node is a black pixel. A transient node is a white pixel. For images with more than two gray levels, a stochastic digraph is used. A transient node is a pixel with the intensity of 0. The intensity of a persistent node is determined by a relative frequency. In this way, the two families of fractals can be generated in a similar way. In this paper, we will first present a classification of dynamical systems and introduce the transformation based on digraphs, then we will unify the two approaches for fractal binary images. We will compare the decoding algorithms of the two families. Finally, we will generalize the discussion to continuous-tone images.

Citation Download Citation

Ying Liu "Unification of two fractal families", Proc. SPIE 2488, Visual Information Processing IV, (16 June 1995); https://doi.org/10.1117/12.211985

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
13 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Fractal analysis

Iterated function systems

Dynamical systems

Laser induced fluorescence

Stochastic processes

Binary data

Classification systems

Show All Keywords

Keywords/Phrases

Search In:

Publication Years