Through random system analysis, I would like to determine both a trend for 2D motion between 2 locations and how altering specific real world variables can change this trend. I will be using Chapter 7 of the class text the most for the basic bulk of the code. However, I will be developing novel aspects for my code in order to simulate certain variables within the random journey.

This epic journey will be through the weary eyes of a Vassar student struggling and stumbling (strumbling, if you will) their way back from a long and alcohol filled night. We find this student past inebriation and past wasted: at this point, the poor soul is taking random steps in random 90 degree turns back to their room. They even fall down from time to time. However, there is hope yet! They have a friend with them that will guide them back to their dorm with a gentle push from time to time. How long will it take them to make it back?

The random variables listed above (and I will probably find some more) will be simulated by additional conditions in the MATLAB code and represent real and mathematic aspects of random motion. I will analyze their effects and relative weights of each via multiple graphs that will attempt to find a trend or average number of steps for a certain distance. I would then like to increase the distance gradually in order to find an expression for displacement traveled and the number of steps required.

I would like to present my data as scatterplots of steps required. By adding additional variables during the walk, I can compare their individual effects. In addition, I can watch the effects the relative weights each variable has on the outcome. For example, does a higher rate of falling down change the outcome more than less drift induced from the friend? Toying with relative weights can also make the journey more realistic.

This project allows me to use statistical analysis and probability to map the path of an independent data point with variables imposed on it. This introduces a lot of variance in the data and my largest stumbling block (get it?) will be extracting concrete data from this. Data might also be difficult to extract with pure random motion at long distances. This project also leaves different relationships between variables wide open so I can qualitatively compare variables if concrete data is weak.

Week 1

Writing the bulk of the code and determining whether there is a trend without drift.

Week 2

Implementing additional variables and watching their affect on steps required

Week 3

Data compilation and figure creation

Week 4

Hopefully I’m done around here but if not, I might add another variable to the mix and see how it affects the steps required to reach the destination. Data compilation might spill over into this week too.

Jenny Magnes– Relate your model to some realistic physics. For example, step length could be analogous to the distance traveled by a gas molecule before colliding with another gas molecule.