visualization in the scottish botanist robert brown observed that pollen particles suspended in water seemed to float around at random he had no plausible explanation for what came to be known as brownian motionand made no attempt to model it mathematically clear mathematical model of the phenomenon was first presented in in louis bachelier' doctoral thesisthe theory of speculation howeversince this thesis dealt with the then disreputable problem of understanding financial marketsit was largely ignored by respectable academics five years latera young albert einstein brought this kind of stochastic thinking to the world of physics with mathematical model almost the same as bachelier' and description of how it could be used to confirm the existence of atoms for some reasonpeople seemed to think that understanding physics was more important than making moneyand the world started paying attention times were certainly different brownian motion is an example of random walk random walks are widely used to model physical processes ( diffusion)biological processes ( the kinetics of displacement of rna from heteroduplexes by dna)and social processes ( movements of the stock marketin this we look at random walks for three reasons random walks are intrinsically interesting it provides us with good example of how to use abstract data types and inheritance to structure programs in general and simulations in particular it provides an opportunity to introduce few more features of python and to demonstrate some additional techniques for producing plots the drunkard' walk let' look at random walk that actually involves walking drunken farmer is standing in the middle of fieldand every second the farmer takes one step in random direction what is her (or hisexpected distance from the origin in nor was he the first to observe it as early as bcthe roman titus lucretiusin his poem "on the nature of things,described similar phenomenonand even implied that it was caused by the random movement of atoms "on the movement of small particles suspended in stationary liquid demanded by the molecular-kinetic theory of heat,annalen der physikmay einstein would come to describe as his "annus mirabilis that yearin addition to his paper on brownian motionhe published papers on the production and transformation of light (pivotal to the development of quantum theory)on the electrodynamics of moving bodies (special relativity)and on the equivalence of matter and energy ( mc not bad year for newly minted phd