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Complexity

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Home - Dassault Systèmes. Internet of Everything. Complexity. Complexity is generally used to characterize something with many parts where those parts interact with each other in multiple ways. The study of these complex linkages is the main goal of complex systems theory. In science,[1] there are at this time a number of approaches to characterizing complexity, many of which are reflected in this article.

Neil Johnson admits that "even among scientists, there is no unique definition of complexity - and the scientific notion has traditionally been conveyed using particular examples... " Ultimately he adopts the definition of 'complexity science' as "the study of the phenomena which emerge from a collection of interacting objects. "[2] Overview[edit] Definitions of complexity often depend on the concept of a "system"—a set of parts or elements that have relationships among them differentiated from relationships with other elements outside the relational regime.

Disorganized complexity vs. organized complexity[edit] Varied meanings of complexity[edit] Fractal. Figure 1a. The Mandelbrot set illustrates self-similarity. As the image is enlarged, the same pattern re-appears so that it is virtually impossible to determine the scale being examined. Figure 1b. The same fractal magnified six times. Figure 1c. Figure 1d. Fractals are distinguished from regular geometric figures by their fractal dimensional scaling. As mathematical equations, fractals are usually nowhere differentiable.[2][5][8] An infinite fractal curve can be conceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.[7]:48[2]:15 There is some disagreement amongst authorities about how the concept of a fractal should be formally defined.

Introduction[edit] The word "fractal" often has different connotations for laypeople than mathematicians, where the layperson is more likely to be familiar with fractal art than a mathematical conception. History[edit] Figure 2. The Art of Complex Problem Solving.