What is Moggie?

Moggie is an applet written in Java for playing with the MOG.

O.K. then, what's the MOG?

The MOG (or Miracle Octad Generator) is a tool for performing calculations with the remarkable S(5,8,24) Steiner system and various interesting finite groups (in particular, the Mathieu group M24). It was invented by R. T. Curtis, and full details can be found in Curtis' original paper [1]. Another account is given by Conway [2].

Briefly, the points of the system are represented in a 6 × 4 grid, and it is fairly easy to complete a set of 5 points to a block of the Steiner system by hand. I wrote this program to help me while I was still learning how to use the MOG from Conway's book.


Moggie is experimental code, and its functionality and interface might change without notice (or they might not; the applet has been unchanged for about a year now). It was written by a mathematics student with not that much experience of Java, so it is not very slick as applets go. Moreover, while I believe that bug-free software exists, I have never seen a constructive proof of the fact. In other words, it is fairly likely that there are bugs. If you find any, please send a bug report to me at


There are 24 cells in the MOG array, arranged in a 6 x 4 grid. A cell is red if it contains a 1 and white if it contains a 0. Other colours have various meanings depending on which button you've pressed. Here is a (brief) explanation of what the buttons do.

The applet

You appear not to have Java enabled, so unfortunately you will not be able to play with Moggie.


[1] 'A new combinatorial approach to M24', R. T. Curtis, Math. Proc. Camb. Phil. Soc. 1976, 79, 24

[2] 'The Golay codes and the Mathieu groups', J. H. Conway, chapter 11 in 'Sphere Packings, Lattices and Groups', J. H. Conway & N. J. A. Sloane, Springer-Verlag 1999