Pine Needle Tracks

Guest Post by Dan Drake of the University of Puget Sound:

The attached picture is of the entrance to the library at the University
of Puget Sound. It's autumn here in Tacoma and there are lots of fallen
pine needles outside which the students track in. The door opens on the
right (on the left, to entering students) and you can see the
distribution is shifted that way near the door. The pine needles are
concentrated in the middle but show a few outliers, and the light color
in the middle shows dust and dirt brought in -- so there's a discrete
and continuous distribution.

The two dimensions of the carpet show a sort of time series: near the
door, people (and hence the dirt and pine needles) are shifted towards
the side of the door that opens, and as they walk into the library, they
tend to move to the center of the entryway.

Thanks for maintaining the blog -- I (and hopefully my students...)
enjoy it!

Thank you Dan for your interest and submission.
I'll have more on pine needles next week.

Queue Server Distribution

These are the feet of tourists at the Charleston, South Carolina visitor's center. The tourists queue up to get information about tours around the city and its attractions. There are only three servers helping them book their tours. These are the feet of the tourists being served. Others, waiting to be served, are standing to the left of the brass pole. 

If no servers were busy, an approaching tourist would be served at the first position nearest the pole. This is on the right of this picture, where four people in one party are discussing their vacation options. Further down the line, two people are talking to server number two, and further still (at the top left of this picture) a lone visitor is with server number three.

The first server position gets the most business and other servers are called in to fill positions two and three as the queue requires.

We can see the server frequency of use in the next picture. There is more floor scuffing and wear at position one, less at position two, and the smallest amount of wear at position three - a discrete frequency distribution of server use.

Subtle Condiment Curve

Here is a subtle wear pattern.
This is a table at our favorite restaurant. The right-hand edge is against the windows. Look carefully at the tabletop along this edge. The luster of the glossy tabletop has been worn down to a mat finish along this window edge. There is less wear, leaving a mat finish, at the corners of the table, closest and farthest from the camera. There is much more wear, along the window edge, in the middle. The rest of the table has a shiny glossy luster. The next picture shows us why:

The missing condiments appear! 

Salt, pepper, cheese, and a container of sweeteners live most often near the middle of this window edge. After use, they are repeatedly returned to this central location along the window edge, leaving more wear (shown by the greater area of mat finish). Occasionally, they are slid to the corners of the table - perhaps to get them out of the way for plates of food or for cleaning the table for the next customers. This wears less off the glossy table top. Smaller regions of mat finish are left near the corners.

A subtle bell-shaped pattern of wear is left behind. More wear in the middle less along the corners.

Garage Dings

One-car garages can be very small. Here is the driver's side wall of one such garage (thanks Laura). It displays the dings from opening the driver's side door in the tight space. Of course, the car is not parked in the same spot every time. Sometimes it rests a little farther forward in the garage and the door hits the wall more to the right in this image. Sometimes the car is parked just inside of the garage and the door dings fall on the left of this image. Most often the car is parked more centrally in the garage, leaving a greater frequency of door dings in the middle of the wall. This is a common pattern  on this blog: little wear on the left, much more in the middle, and then little wear on the right. This is the typical pattern of a bell-shaped, symmetric normal distribution, although any unimodal even roughly symmetric distribution could be described similarly.

Perhaps the wall needs a little tweak along these lines:

These are plots that highlight, with color, the highest density regions of a measurement, like the location of the door dings. The densities are estimated by the smooth curves. The measurements are shown by their random arrangement of tickmarks on the horizontal axes below the density curves - just like the garage door dings. These are the plots from Hyndman, R.J. (1996) "Computing and graphing highest density regions" American Statistician, 50, 120-126. These plots are one of many featured graphics in the R graph gallery.

Laura needs some blue, red, and green tape!

Banging on the Exit

Dollar stores value their shopping carts. So much so they corral them with vertical poles that prevent their being rolled out the exit. Of course, many shoppers attempt to exit with the carts. The poles hit  the top of the exit marking, scraping, and gouging the wall above the exit door. More wear near the center of the exit, less as the shoppers realize they can't leave with the cart and shove their eventual empty cart down the wall further marking its travels. A bell-shaped pattern of wear is left.