ON ATTRACTORS OF TYPE 1 ITERATED FUNCTION SYSTEMS †

被引：0

作者：

Mathew, Jose ^{[1
]}

Mathew, Sunil ^{[2
]}

Secelean, Nicolae Adrian ^{[3
]}

机构：

[1] Deva Matha Coll Kuravilangad, Dept Math, Kottayam 686633, India

[2] Natl Inst Technol Calicut, Dept Math, Kozhikode 673601, India

[3] Lucian Blaga Univ Sibiu, Dept Math & Comp Sci, Sibiu 550024, Romania

来源：

JOURNAL OF APPLIED MATHEMATICS & INFORMATICS | 2024年 / 42卷 / 03期

关键词：

Iterated function system; type; 1; IFS; open set condition; connectedness; address system; SELF-SIMILAR SETS; SEPARATION PROPERTIES;

D O I：

10.14317/jami.2024.583

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. This paper discusses the properties of attractors of Type 1 IFS which construct self similar fractals on product spaces. General results like continuity theorem and Collage theorem for Type 1 IFS are established. An algebraic equivalent condition for the open set condition is studied to characterize the points outside a feasible open set. Connectedness properties of Type 1 IFS are mainly discussed. Equivalence condition for connectedness, arc wise connectedness and locally connectedness of a Type 1 IFS is established. A relation connecting separation properties and topological properties of Type 1 IFS attractors is studied using a generalized address system in product spaces. A construction of 3D fractal images is proposed as an application of the Type 1 IFS theory.

引用

页码：583 / 605

页数：23

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