# Complex Systems, Emergence, and Multiscale Analysis: A Tutorial and Brief Survey
## 2 Basics of Complex Systems and Emergence  
### Complex Systems and Emergence: Working Definitions  
To better understand which systems can be considered complex, we first explain how complexity is quantified. There are two major types of measures. One is called Deterministic complexity, which increases with the degree of randomness. See Figure 1 (left). Widely used measures in this category include Shannon entropy [15], Kolmogorov-Sinai (KS) entropy [16,17], Kolmogorov-Chaitin complexity [18, 19, 20], and the Lempel-Ziv (LZ) complexity [21]. The other is called _Structural complexity_. Here, the measure attains a maximal value for an intermediate level of randomness. See Figure 1 (right). Let us now examine the main features of a complex system. It is often thought that a complex system must consist of many interconnecting components or parts. The individual components together with their dynamics could be quite simple. The system as a whole, however, must exhibit complex dynamics. Note that with this view, a pendulum with chaotic behavior is no longer considered a complex system. In addition, note that some researchers (e.g., [PERSON] et al. [22]) advocate to assign a complex system with many more quantifiable features, such as feedback loops, multiple inputs and multiple outputs, non-Gaussian distributions of the outputs, nonlinear interactions, multiple stable states, fractal and chaotic behaviors, self-organized criticality, hierarchy, and so on. Our view is that it is extremely rare for a single system to simultaneously possess so many distinguished properties at the same time. Therefore, simpler definitions that give more room and freedom to think and work could be more beneficial. Complex systems often defy pure statistical analysis. To illustrate the idea, let us discuss an author ([PERSON])'s personal experience. [PERSON] worked at Guangxi University in Nanning for a few years. The campus was full of natural wonders, with flowers blossoming and  
Figure 1: Deterministic vs. structural complexity. many kinds of tropical and subtropical fruits dangling on trees all year long. Thus, [PERSON] and many of his friends truly enjoyed the campus. Approximately 100,000 people, including University employees and students, lived on campus. [PERSON] used to buy vegetables and meat at a farmer's market in the east campus of the University. Although the farmer's market was a bit shabby, it was in a convenient location and was visited by a lot of customers everyday. In the market, there was a pork meat seller who normally would sell out all the meat within 2.5 h before 11 am in the morning. Around October 2017, the market was relocated to a new place about 7 min walk from the original site. Surprisingly, the number of customers to the market dropped considerably. As a result, the pork meat seller would still be selling meat around 1-2 pm. After that, the seller had to take the meat to some fast food restaurants, as otherwise the pork, not refrigerated, would become spoiled and smelly. Surely, quite a few fruit and vegetable sellers eventually gave up. Such dramatic drop in customer number is very difficult to predict with statistical models, however sophisticated they are. One can readily see that to truly understand the phenomenon, one has to systematically analyze the dynamics of the customer behavior by considering diverse factors such as the variety, cost, and freshness of food; convenience of the market; competitors of the market; and customer psychology. Next, let us consider emergence in complex systems. Emergence is a bulk property of the system involving many of the interacting components of the system [23; 24]. As a result, its scale usually is much larger than that of the individual component.