Nathaniel Johnston

It seems that I write about superpermutations way too frequently, and today I’m going to continue the trend. Recall that a superpermutation is a string on n symbols that contains all n! permuta...

https://njohnston.ca/2024/05/minimal-injective-superstrings-a-simpler-generalization-of-superpermutations/

Back in September 1995, David Buckingham showed how to construct oscillators and glider guns of any period at least 61 in Conway’s Game of Life. His method was based on a tool called a “Hersc...

https://njohnston.ca/2024/04/herschel-tracks-in-conways-game-of-life-part-1-making-oscillators-and-glider-guns-of-any-period-61-or-larger/

Lights Out is a puzzle that sits in a very interesting place mathematically: while many puzzles can be solved with the help of math, Lights Out is solved exactly and completely by math (linear al...

https://njohnston.ca/2024/03/solving-the-lights-out-puzzle-via-linear-algebra/

I’ve been meaning to make a series of videos on Conway’s Game of Life for a few years now, and I finally decided that rather than rehashing topics that are already covered in the textbook, I�...

https://njohnston.ca/2024/03/first-true-period-15-and-16-glider-guns-found-in-conways-game-of-life/

After a 3-year hiatus, I’m back making math videos, not least of all thanks to my new fancy-schmancy basement studio: This time I’m trying this crazy technique called “editing”, rather th...

https://njohnston.ca/2024/03/what-is-the-maximum-possible-area-of-3-circles-in-a-triangle/

One of the standard applications of orthogonal projections to function spaces comes in the form of Fourier series, where we use (B = {1,cos(x),sin(x),cos(2x),sin(2x),ldots}) as a mutually orthogo...

https://njohnston.ca/2018/07/taylor-polynomials-from-orthogonal-projections/