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6 purposes of this set of lectures, the next few lectures, at least, the only thing we're going to get out of this is a bunch of tools for drawing pretty graphs. And we won't get to those today, probably, so don't worry about it. But it's a nice package, which you'll be glad to learn. OK, now let's move on to the code, which has got things that should look familiar to you. And I know there used to be a laser -- ah, here's the laser pointer. So we'll see at the top location, it is a class. By now you've gotten as familiar as you want to be in many senses, with classes. It's got an underbar underbar init that gives me, essentially, a point with an x-coordinate and a y-coordinate. It's got get coords, the third function, or method, and what you can see what that does is it's returning a tuple of two values. I could have had it get x and get y, but it turned out, in fact, my first iteration of this it did have a get x and get y, and when I looked at the code that was using it, I realized whenever I got one, I wanted both, and it just seemed kind of silly, so I did something that made the using code a little bit better. It's got get distance, the last method. You saw this in Professor Grimson's lecture, where he used the Pythagorean theorem to basically compute the distance on a hypotenuse, to tell you how far a point was from the origin. That's why I wanted math. And then the one thing it has that it's unlike the example you saw from Professor Grimson, was up here, this move. And this basically takes a point, a location, and an x- and a y- coordinate, and returns another location, in which I've incremented the x and the y, perhaps incrementing by 0. And so now you can see how I'm going to be able to mimic 1 step or any number of steps by using this move. Any questions about this? Great, all right. The next one you'll see is compass point. Remember, this was the abstraction that was going to let me conveniently deal with directions. The first thing you'll see is, there's a global variable in the sense that it's external to any of the methods, and you'll note it's not self dot possibles, but just possibles. Because I don't want a new copy of this for every instance. And this tells me the possible directions, which I've abbreviated as n, s, e, and w. And I leave it to you to figure out what those abbreviations stand for. Then I've got init, which takes a point and it first checks to see if the point is in self dot possibles. Should I have bothered saying self? Do I need to write self there? This is a test of classes. It'll work. What do you think? Who thinks I need to write self, and who thinks I don't? Who thinks I need to write self, raise your hand? Who thinks I don't need to write self? The don't needs have it. So in an act of intense bravery, since I have not run it without this, we'll see what happens when it comes time to run the program. So if point is in possibles, it will take self dot p t will be assigned p t. Otherwise, I'll raise a value error. And this is a little piece of programming, and what I typically do at a minimum, when I raise these exceptions, is make sure that it says where it's coming from. So this says it's gonna raise this value error in the method compass point dot underbar underbar init, underbar underbar. This is so when I run the program, and I see a message, I don't have to scratch my head figuring out where did things go wrong? So just a convention I follow a lot. And then I've got

9 this case one. All right? We've now finished all of this sort of groundwork that we need to go and actually build the simulation that will model our problem. So let's look at how we use all of this. I've now got a function perform trial, which will take a time in a field. So I'll get a starting point of f dot getloc, wherever the drunk happens to be at this point in time in the field. And then for t in range 1 to time plus 1, I'm going to call field dot get drunk, that will give me the drunk that's in the field, and then I'll get the move function for that drunk. So what you see here is I can actually, in this dot notation, take advantage of the fact, where are we, we're down here, I've got to get far enough away that I can see it -- Where was I? STUDENT: You were in the right place right there, down slightly. PROFESSOR: -- down slightly, here, right. I've called the function, which has returned an object, f dot get drunk returns an object of class drunk. And then I can select the method associated with that object, the move method, and move the drunk. This gets back to a point that we've emphasized before, that these objects are first class citizens in Python. You can use functions and methods to generate them, and use them just as if you'd typed them. So that will get me that, and then I'll call the move of that drunk with the field. Then I'll get the location, the new location, and then I'll say, distance equals new loc dot get distance of start, how far is the new location from wherever the starting location was? I'll append it to a list, and then I'll return it. So now I have a list, and in the list I have how far away the drunk is after each time step. I'm just collecting the list of distances. So I don't have a list of locations, I don't know where, I can't plot the trajectory, but I can plot the distances. OK, now, let's put it all together. So I'll say the drunk is equal to, is drunk of Homer Simpson. I had thought about using the name of someone on campus and decided that, since it was going to be taped for OpenCourseWare, I didn't want to go there. Sometimes I lack courage. Then for i in range 3, and all this says is I'm going to test, I'm going to run the simulation three different times, f is equal to field of drunk and location 0, 0, starting in the middle of the field. Distances equal perform trial 500, 500 steps on that field, and the rest of it is magic you don't need to understand because we'll come back to next lecture, which is, how do I put all this in a pretty picture? So ignore all of that for now, and that's just the Pylab stuff for plotting the pictures. All right, we're there, let's run it. Huh. Remember the change we made? Guess what? Well, we know how to fix that. And we'll come back to it and ask what's really going on here. What does self refer to here? It refers to the class compass point, rather than an instance of the class. Again, driving home the point that classes are objects just like everything else. STUDENT: [INAUDIBLE] PROFESSOR: Oh, sorry. Thank you. It did it have in here, right. All right, now let's run it, see what we get. We get a picture. Well, so we see that, at least for these three tests, the majority of the public was wrong. It seems that the longer we run it, the further from the origin Homer seems to be getting. Well, let's try it again. Maybe we just

10 got unlucky three times. You can see from the divergence here, that, of course, a lot of things go on. I hope you can also see the advantage of being able to plot it rather than having to look at those arrays. Well, we get different answers, but you know what? The trend still seems pretty clear. It does seem over time, that we wander further away. I know, further away. So, looks at least for the moment, that perhaps we were wrong. Well, this is rather silly for me to keep running it over and over again. So clearly what I ought to do is, do it in a more organized way. So now if we go back, and see the, kind of the right way to do it, I'm going to get rid of this stuff here, which was used just to stop the previous computation. I'm going to write a function called perform sim. And what that does, is it takes the time and the number of trials that we wanted to do. It takes distlist equals the empty list in this case, to start with, and then it is basically going to call perform trial, the function we already looked at over and over again. And get a whole bunch of lists back, a list each time it calls it. And then, compute an average. Well, not yet, so it says, it says d equals drunk, field start in zero, distances equals perform trial, append the new list, and what it does, is it returns a list of lists. Where each list is what we had for the previous trials. Make sense? And then I'm going to have 1 more function call, answer a question. Which takes the maximum time and the number of trials, and it's going to do some statistics on all of the lists. We'll come back to this a week from today. If you are, have absolutely nothing to do for the next week, I'll give you a hint. I have salted a bug here in this latest code, and you might have some fun looking at what that bug is.

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