Levy- flight Scale-free survival strategy? Yes.

Kovács István

What does the it mean?

Levy (1937) flight : the length-distribution of the linear sections of the way. If you make random trips with scale-free length-

distribution you find more food - the probability to return to the same site is

smaller than Gaussian - the number of new sites is larger than Brownian

An extract from Peter’s book

• When a bumble bee, an albatross, a deer, a member of a hunter-gatherer society, a homeless person or a scientist makes a search, the length of individual trips follows a scale-free distribution. Most of the cases we explore the immediate neighborhood (small trips), because it is cost-efficient. However, seldom we make a bigger jump and rarely we go really far to find our target be it pollen, fish, grass, fruit, chunks of bread in the garbage can or the quotation starting the next sentence. Viswanathan et al. (1999) showed that this has a reason. The reason is simple. This is the best.

Two examples: Rain & Earth-quakes

constant in-flow of energy tension relaxation relaxation comes in power-law bursts

Foraging by bumble-bees

The motion of the eye

Surfing on the web

Let’s see again Peter’s book! Length-distribution of the spaces between the citations

1

10

100

1000

1 10 100Length of distance

Occu

renc

e

CsApo

Cshsp

CSbba

2001rev

barabasi

stressz

weak

Our Questions

• The slope of the fitted line seems to be characteristic of the papers author.

• Depends it really on the writer?• Is the exponent of the Levy-flight the same,

if anyone writes an article or watches the girls on the beach?

• Can we find more properties of the distributions to analyse deeper the flights?