Chapter 21
Fractal Analysis and Programming
of Elastic Systems Using
Container-Component Model
Alexander S. Semenov
Abstract The analysis and design of distributed algorithms is one of the main
reasons to use fractal programming. Its aims are to represent the distributed algorithm
as an “elastic object” that transforms dynamically at runtime. The use of containercomponent model provides the following advantages: the ability to select automatically a distributed configuration, building a visual model of the elastic computing
organization, and evaluating its effectiveness. Container-component model is integrated with the box-counting fractal analysis method and fractal control based on
dynamic sampling of the workload. The example of fractal analysis and programming
of the distributed gradient ascent algorithm is given.
21.1 Introduction
The analysis and design of distributed algorithms is one of the main reasons to
use fractal programming [1, 2]. Its aims are to represent the distributed algorithm
as an “elastic object” that transforms dynamically at runtime using strategy planning model and production rules. The distributed configuration of the algorithm
unfolds at the beginning of execution and folds at the end of execution. The use
of container-component model (CCM) for the analysis and programming of elastic
algorithms provides the following advantages: the ability to automatically select a
distributed configuration of the algorithm execution, building a visual model of the
elastic computing organization, and evaluation of its effectiveness.
Fractal analysis, design, and programming of complex elastic systems are integrated with the mathematical methods of the fractal analysis on the base of
CCM. Physically, a distributed system consists of a number of nodes (autonomous
computers) interconnected by a network. The nodes may be computers, physical
servers, agents, virtual machines, containers, or other entities that can connect to the
A. S. Semenov (B)
Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow
125993, Russian Federation
e-mail: semenov_alex@yahoo.com
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
L. C. Jain et al. (eds.), Applied Mathematics and Computational Mechanics for Smart
Applications, Smart Innovation, Systems and Technologies 217,
https://doi.org/10.1007/978-981-33-4826-4_21
307
Fractal Analysis and Programming
of Elastic Systems Using
Container-Component Model
Alexander S. Semenov
Abstract The analysis and design of distributed algorithms is one of the main
reasons to use fractal programming. Its aims are to represent the distributed algorithm
as an “elastic object” that transforms dynamically at runtime. The use of containercomponent model provides the following advantages: the ability to select automatically a distributed configuration, building a visual model of the elastic computing
organization, and evaluating its effectiveness. Container-component model is integrated with the box-counting fractal analysis method and fractal control based on
dynamic sampling of the workload. The example of fractal analysis and programming
of the distributed gradient ascent algorithm is given.
21.1 Introduction
The analysis and design of distributed algorithms is one of the main reasons to
use fractal programming [1, 2]. Its aims are to represent the distributed algorithm
as an “elastic object” that transforms dynamically at runtime using strategy planning model and production rules. The distributed configuration of the algorithm
unfolds at the beginning of execution and folds at the end of execution. The use
of container-component model (CCM) for the analysis and programming of elastic
algorithms provides the following advantages: the ability to automatically select a
distributed configuration of the algorithm execution, building a visual model of the
elastic computing organization, and evaluation of its effectiveness.
Fractal analysis, design, and programming of complex elastic systems are integrated with the mathematical methods of the fractal analysis on the base of
CCM. Physically, a distributed system consists of a number of nodes (autonomous
computers) interconnected by a network. The nodes may be computers, physical
servers, agents, virtual machines, containers, or other entities that can connect to the
A. S. Semenov (B)
Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow
125993, Russian Federation
e-mail: semenov_alex@yahoo.com
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
L. C. Jain et al. (eds.), Applied Mathematics and Computational Mechanics for Smart
Applications, Smart Innovation, Systems and Technologies 217,
https://doi.org/10.1007/978-981-33-4826-4_21
307