What is this?

This is a quick hack implementation of a simulator for xkcd 2529's weirdly concrete problem. This is barely tested and I suck at computational geometry, so this implementation is likely not correct.

How does it work?

I generate self-avoiding walks using the dimer method described in this notebook. There is apparently some more fancy stuff, but I haven't gotten to that.

To find the largest distance line I find the convex hull using a Grahan scan and from that find antipodal points using the rotating caliper technique and take the maximal pair.

To find all the colinear points I just got lazy and brute forced it.

How do I run it?

The program depends on matplotlib and numpy.

There are two entry points:

• plot_main which will generate and plot a random walk, its marbles, its largest distance line, and the marbles colinear to that line.
• stat_main will generate many random walks, and find the mean and standard deviations of the number of marbles on the line.

What does the plot look like?