Apollonian gasket generator
One of my hobbies is creating fractals and one of the most interesting is the Apollonian gasket. An area defined by some arcs and straight lines is recursively filled with circles and in all cases (except the trivial case of a single circle) this process recurses infinitely, making counting circles challenging.
Box plotter
One of the most popular ways to compare results in particle physics is to create plots that show different results with horizontal bands (sometimes known as boxes), making comparisons easier on the eye. Unsatisfied with the quality of available solutions at the time, I created my own scripts which would make these plots for use in my thesis.
Ciphers
This page contains some simple ciphers. This was going to be extended to include some more sophisticated ciphers, but I didn't have the time or incentive to develop this page further.
Circle from three points
This project was thrown together rather quickly to solve a geometrical problem: How can you analytically find the circle which passes through three given points? The construction simply demonstrates that the method works, and it not intended to give any further information to the user.
Complex polynomial
On the Numberphile YouTube channel I saw a video that gave a proof that all complex polynomials have at least one solution. The method involved moving one point about the complex plane while another is mapped around a path elsewhere in the plane. I decided to map this out using Javascript!
Conway's Game of Life
Conway's game of life is a very famous mathematical model with a rich variety of "creatures" that can interact with one another. This script is a simple interactive sandbox where the user can "paint" cells to create different shapes. There are a number of predefined boards that the user can choose to investigate some small and interesting patterns as they evolve.
Project Euler
To hone my problem solving skills I occasionally take part in Project Euler, which is a series of mathematical and computational problems. These pages summarise my solutions and strategies.
Mathematical inverter
This project performs the mathetical inversion transformation. A curve on the plane is inverted such that points within the unit circle are mapped outsid the unit circle and vice versa.
Iterated path
This project is a mathematical toy to see what happens when a simple rule is repeated many times. It starts with a straight line and then moves the points relative to this line. The process is then repeated many times, leading to some beautiful patterns.
Mandelbrot explorer
This project estimates the Mandelbrot set using the HTML5 canvas. It's one of my longest running projects that has been implemented in PHP, SVG, HTML5 canvas, HTML tables, and even in ROOT.
Neuron simulator
One of my friends wanted to develop a genetic algorithm that was capable of learning and adjusting a neuronal network to suit its environment. I got as far as making a genetic algorithm before abandoning the project as my friend's interest seemed to move at the same time as my knowledge of the problem was exhausted.
Pebbling a Chessboard
One of the channels I follow on YouTube is called Numberphile, and they give plenty of good ideas for mathematical games. In this game the user has to move pieces around a chessboard in order to liberate "clones" from a prison. On Numberphile, they suggested playing this game using an actual chessboard, but I decided that a better way to do it would be to write my own game. So here it is.
pi estimation
This project was put together quickly while waiting for a physics job to finish. It was an exercise to see how quickly I could make a useful page with my current setup on my website. Including time to research, write, upload, and test the page it took around 20 minutes.
Reflections
A "reflection" is a term in particle physics for when a decay of one particle looks like the decay of another. It's a topic which has been studied for about fifty years, and seemed like an excellent chance to combine physics and coding.
Skyline generator
One of the features I want on my webpage is the silhouette of a skyline to use as background image. This project is aimed at allowing the user to draw a complex skyline, with the possibilty for animation.
Sliding tile game solver
I was playing a PuzzelScript game involving sliding blocks that i just couldn't solve. So I wrote an algorithm to solve it.
Spectrum
This project was made around the same time as the Reflections project, but I cannot remember which was written first.
Image transformer
When I discovered I could manipulate images with PHP one of the first things I wanted to do was perform coordinate transformations. They have fascinated me since I first came across them and so I developed this project to satifsy my curiosity about what a skyline might look like when transformed into polar coordinates.
Wolfram rules
I enjoy playing with recreational mathematics and the Wolfram rules are a rich source of complex behaviour from simple rules. So I created this project to explore how the rules can lead to different patterns.
