Affine Transformations

Mandelbrot Browser

An interactive Mandelbrot viewer zoom in and out and pan around Mandelbrot and Julia fractals as well as some some of the 4D slices. Using the GPU means that the browsing can be done interactively, you won't have time to make a coffee while you are waiting for the results. Once of the downsides is that the floating point range is a bit limited, restricting how far you can zoom in.

Mandelbrot Complexity

A discussion of how the relatively simple equation generates these seemingly infinitely complex images. Allows you to interactively explore toe orbits of individual points.

Julia Set Complexity

Continues the Mandelbrot Complexity page with some observations specific to the Julia Sets.

Four Dimensional Representations

This page shows how the Julia and Mandelbrot sets are merely slices of an even more complicated 4-dimensional object.

Mandelbrot

More Mandlebrot pages

Newton-Raphson Fractal

An interactive viewer for this fractal. Works for up to 10th degree polynomials with real coefficients. Written in WebGL to take advantage of the GPU.

Countdown Numbers Game

An arithmetic challenge that appears on a TV show called "Countdown" where you have to use combinations of the given set of numbers to construct a target value.

This page allows you to challenge yourself by generating random objectives, or solve existing challenges by enter the given numbers.

Polynomial from Sequence

If you have a collection of values and you want to know what the polynomial that generates them is, this page will calculate it for you.

Shape-packing

This page implements a simulated anealing algorithm to find the best was to pack a number of shapes inside another shape. The outer shape can be a circle or a regular polygon with up to nine sides.

Pythagorean Triples

Searching for Cube Sums

3x + 1

One Dimensional, Five colours

A five colour one dimensional automata. Here time is represented as the second dimension to create the two dimensional images. The pattern evolves from top to bottom, the next state of a cell depending on its current state and the states of its two immediate neighbours.

One Dimensional, Six colours

A six colour one dimensional automata, this is essentially the same as the five colour automaton in the previous link, only with more colours.

Two Dimensional, Five colours

In the two dimensional version the pattern represents a single instance in time and the evolution is shown by incrementally updating the pattern, creating an animation. Cells evolve based on their contents and those of their 4 nearest neighbours.

Forest Fire

A forest Fire simulator. This is a two dimensional automaton, with the patterns changing over time. It is not fixed though, the cells vary through a cycle of grass to trees to fire and back to grass base on a set of probabilities that you can adjust. Once a cell is on fire it has a chance of spreading to neighbouring cells, and again you can adjust this probability.

This is really one for sitting and watching and snapshots don't do it justice, so I haven't included any.

Game of Life

Conway's famous "Game of Life". The image to the left arises if you run the default starting configuration on the "large" square grid.

Spirographs

Repeated Symmetry Operations

This page generates patters by starting out with a 2x2 collection of rectangles and triangles and then applies a variety of symmetry operations to generate more interesting patterns. The image on the left shows four copies of the starting pattern rotated 270°.

Colouring-in

Fibonacci Patterns

Constructed by colouring squares generated from successive terms in the Fibonacci sequence calculated using modular arithmetic.

Circle Patterns

Line Patterns

A remodelling of a very old page, originally written in Python. I've kep the link to the Python code, but this version is written in javascript. This page is now interactive and you can create a wider range of patterns. I need to add some colouring modes though.

Jigsaw

An interactive jigsaw. This contains a collection of images generated by the applications on this site that you can attempt to complete. There are three classes of piece shape and three difficultly levels. The pieces are generated randomly so you are unlikely to get the same jigsaw twice. This runs entirely in your browser, no data is collected, and there are no annoying adverts.

Sudoku

Page for solving Sodokus, the traditional 9x9, plus some other grids.

Maze Pages

More mazes. Draws mazes using various geometries, some of them can be explored interactively.

Interactive Maze

A 3D visualisation of the 2D interactive maze you can see on the mazes page.

Cathedral Game

Jigsaw Gallery

Some of the jigsaws I have completed in recent years.

2D Self Organisation

This page uses a Monte-Carlo simulation to calculate the thermodynamics of a set of interacting square molecules. The simulation is made more interesting by adding some stearic hindrance, which restricts the possible configurations the molecules can take up.

The image on the left shows a frame from one such simulation, it is set up so that the molecules are mutually repulsive, but forming links is energetically favourable. The resulting structure depends on the molecules' shapes. This image shows an example of structure taken from the main image.

Neil's WebGL playground

Neil's WebGL applications. This include a 3D gallery of some of Neil's drawings, which can be seen in the image that accompanies this link.

SVG Index

Butterflies

Doodles

Python Source Code

Before html 5 I didn't know of any way to create patterns interactively so I wrote these python routines to create patterns and render them as bitmaps. They are still available to download, though they are written in Python 2.6.