LévyFlight

Lévy flight is a random walk model in which each step is chosen from a probability distribution that follows the Lévy distribution. This distribution is characterized by a power-law decay of probability with distance, and is often used to simulate movements that have a greater tendency to take longer, more unpredictable steps in certain directions. This type of movement is often observed in natural phenomena, such as the flight patterns of birds and insects.

The Lévy flight model was named after Paul Lévy, a French mathematician who first described this probability distribution in the 1920s. The model has been used to describe the movement patterns of many species, including birds, fish, and insects. It has also been used to simulate the movement of humans in crowds and cities.

One of the key features of the Lévy flight model is its ability to capture the long-tailed distributions of movement that are often observed in nature. This is in contrast to the Brownian motion model, which assumes a much more uniform distribution of movement. The Lévy flight model is also able to capture the fact that many movements are not perfectly random, but instead have a preference for certain directions or distances.

The Lévy flight model has been used in a variety of applications, including the study of animal migration patterns, the simulation of search and foraging behavior, and the modeling of human movement in crowds and cities. It is often used in conjunction with other models, such as Brownian motion, to simulate more complex movement patterns.