I hope... few of them, so you have and idea of the richness. First is the Pearson random walk, in which each step is a fix length, but in a random direction. What I am showing here, is a There are many types of random walks, and are fixed length and the direction are Another example is a Lattice random walk, in which the random walks are constraint to move between nearest neighbour sites of typical trajectory of such a Pearson random walk. some regular lattice. So, here the steps either in north, east, south or west. Another type of random walk is so called Levy flight. In the Levy flight, there is a broad distribution of single step lengths but each step is in random direction. Here, we will see that the displacement after many steps can be dominated by the longest single step of the walk. Another example that dear to my heart is the example of Shrinking steps that is a random walker getting lazier and lazier as time is going on and the length of nth-step is landed to end where lambda is less than 1. An amazing aspect of this type of random walk is diversity of type of probability distributions as a function of the Shrinking factor lambda (λ) Know the λ = 0.61, in fact most precisely is the golden ratio, (1 + sqrt(5))/2, the probability distribution is beautiful, self similar pattern that repeats on all scales so the middle blob is same as the entire distribution in inside the middle blob is something which reproduces the entire distribution again Another interesting special case is λ= 0.707 which is actual 1/sqrt(2) Here the probability distribution is made up of 3 linear segments, two tilted lines and one flat line. And there are many other beautiful special cases of this type of random walk Shrinking steps Another important example that appears in nature, turbulent diffusion or random walks that are moving in random convection field In this case, the typical step of length of random walk is a growing with time. And one can get plume like behaviour as you see here from smoke rising from oil fires in the ocean Here are the types of random walks we have just discussed. As we will see, the first 4-types lie in the domain of celebrated central limit theorem in which the probability distribution is asymptotically a Gaussian, independent of details of the microscopic motion. This universality is extremely useful principle in many collective phenomena