# Posts

Occasionally I will post here about things I find interesting.

### The Waiting Time Paradox

Why is my train always late? Do lightbulbs last longer than they should? These questions can be answered with the waiting time paradox and the inspection paradox.

### Julia Sets and the Mandelbrot Set

Julia sets and the Mandelbrot set arise naturally in complex dynamics. We explore some of their properties and methods for plotting them.

### motifcluster

A software package for motif-based spectral clustering of weighted directed networks.

### Goodstein Sequence Calculator

To complement my earlier post on Goodstein sequences, I wrote a Python script to calculate them.

### The Dirichlet Problem and Continuous Local Martingales

The Dirichlet problem is an important boundary value problem, with applications in physics. Although hard to solve analytically, we can construct probabilistic approximations using continuous local martingales.

### Goodstein Sequences

Goodstein sequences grow fast and appear to diverge to infinity. But a neat application of ordinal arithmetic gives a surprising result.

### Modes of Convergence

The notion of

*modes of convergence*is central to probability theory. This short article focuses on the relative strengths of these convergences, and includes a helpful diagram.### My New Website

Here is my new website, built using Jekyll and hosted with GitHub Pages.