Random walk 1 D Random walk Random toss

Random walk

1 D Random walk Random toss of a coin: H- head, T -tail

Brownian motion

Random walk

B. Hayes – How to avoid yourself, American Scientist, vol 86, p. 314 (1998)

Random coil model of polymer (freely joint chain) End-to-end distance

Random walk dispersion Swarm of many particles

A pseudorandom algorithm for selecting points in a square tries to ensure that all points have the same probability of being chosen and that all the choices are independent of one another. The aim of a quasirandom algorithm for selecting points in a square is not equiprobability or independence but rather equidistribution: spraying the points as uniformly as possible across the area of the square.

Random map PHP Rand()

A plot of the first 1600 decimal digits of π (mod 2) is shown above (left figure), with the corresponding plot for 22/7 shown at right.

Each bar plot below represents the number of occurrences of a digit in the decimal expansion of pi. The y-axis is an index, and the frequency x is counted over the range of digits y*20 to y*20+400.

Von Neumann 1946 Middle-square method What number with all its 4 non-zero digits repeats itself? What number with all its 4 non-zero digits has period four?

Uniform distribution of pseudo-random number generator

Independence of pseudo-random numbers Shortcomings of linear congruence generator

RANDU pseudo-random number generator

How much time will take to know that the Sun is dead? (no fusion in its center) If we assume the sun is dense with electrons, and each little “step” is a tenth of a millimeter, to go straight from the center of the sun to the edge will take 7 trillion steps for a photon.

Our photon is a drunk, its true path will take the square of 7 trillion steps, which works out to 49 trillion collisions before it reaches the surface. Even moving at the speed of light, that will take, more than half a million years. 500. 000 years!

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