Generatter

Generatter is a term that combines "generator" and "attractor." It refers to a concept in dynamical systems and chaos theory, where a system exhibits both generating behavior and attracting behavior. This means that the system can produce complex patterns or behaviors (generation) and also has the ability to pull nearby trajectories towards it (attraction).

The term generatter was popularized by the mathematician and physicist Robert L. Devaney. In his book "An Introduction to Chaotic Dynamical Systems," Devaney discusses how certain systems can exhibit both generating and attracting properties. This dual behavior is often observed in chaotic systems, where small changes in initial conditions can lead to vastly different outcomes over time.

Generatters are of particular interest in the study of chaos because they provide a bridge between simple, predictable systems and complex, unpredictable ones. Understanding generatters can help in modeling and predicting the behavior of real-world systems, such as weather patterns, economic trends, and biological systems.

The concept of generatters is closely related to the idea of strange attractors, which are sets of points towards which nearby trajectories converge. However, generatters go a step further by also considering the ability of the system to produce new behaviors or patterns.

In summary, generatter is a term used in dynamical systems to describe systems that exhibit both generating and attracting behavior. This dual property makes generatters an important concept in the study of chaos and complex systems.