: A trajectory or path composed of successive random steps
- Some examples: the path of a molecule moving through liquid or gas, the search path of a foraging animal, or the history of a share price in the market.
- Most often, all the steps in the walk are of similar length.
But a random walk is not the most efficient way to explore a space, if the items you're searching for are not evenly distributed. In the example of the foraging animal, imagine that a cow is searching for a particular type of sweet clover that doesn't grow all over, but in clumps scattered around the field. If the cow walks randomly, taking steps all relatively the same length, it will only be able to explore a small area of the field before being rounded up. The cow may never stumble across any of the clumps of clover. Similarly, if you're shopping for eggs in an unfamiliar market, the fastest way to find the eggs is not to walk up and down every aisle, but to look in one likely place, and if you don't find them there, move to another area to look in.
: A type of random walk with clusters of short steps connected by rarer long steps
- Used to describe chaotic systems
- Models data that clusters rather than randomly filling the space
- For example, most of a stock's movement often takes place on the best or worst few days
A recent study ("Hungry Sharks Take Strange Walks To Find Food
") suggests that marine predators use Levy flight to locate their prey with the least possible expenditure of energy. The study analyzed data from electronic tags attached to sharks, tuna, cod, sea turtles and
penguins, in various locations around the world. The data indicated that the predators use a series of small motions interspersed with large jumps to new foraging locations, which increases the chance of finding widely scattered food. One researcher said that this method appears to be "a general solution for success in complex and changeable environments."
As part of our ideation methods, we use Levy flights to explore an idea space filled not with an even distribution of ideas, but with semi-randomly distributed clusters of ideas. We lead participants to jump to different parts of the space; explore around that point; and then jump again to another part of the space. We make big jumps surrounded by small steps, to find rich clusters of ideas in the most efficient way.
In our ongoing research on the most efficient way to explore idea spaces to find the best possible new ideas, we've been thinking a lot about the Levy flight, named for Paul Pierre Lévy, a French mathematician/physicist. A Levy flight is a type of random walk, a mathematical concept used to analyze random processes in time.