One of the key characteristics of complex systems is their sensitivity to initial conditions, often referred to as the butterfly effect. Small changes in the initial state of the system can lead to vastly different outcomes. This sensitivity is a result of the system's nonlinear dynamics and the interactions between its components.
Complex systems can be classified into several categories based on their structure and behavior. For example, cellular automata are discrete models studied in computability theory, mathematics, theoretical biology, and physics. They consist of a regular grid of cells, each in one of a finite number of states, such as on and off. The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell. An initial state (time t = 0) is selected by assigning a state for each cell. A new generation is created (advancing t by 1), according to some fixed rule that determines the new state of each cell in terms of the current state of the cell and the states of the cells in its neighborhood.
Another example of a complex system is a neural network, which is a computational model inspired by the way biological neural networks in the brain process information. Neural networks consist of interconnected nodes, or neurons, that process and transmit information. They are used in various applications, such as pattern recognition, classification, and optimization.
Complex systems are also found in social sciences, where they are used to model and understand phenomena such as the spread of information, the formation of social networks, and the dynamics of economic systems. In these systems, the interactions between individuals or groups can lead to complex patterns of behavior that are not easily predictable.
In summary, kompleksoituneita, or complex systems, are systems composed of many interacting parts that exhibit complex behavior and emergent properties. They are found in various fields and can be classified into different categories based on their structure and behavior. Understanding complex systems is a challenging but important task, as they play a crucial role in many aspects of our lives.