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## Something about me and what I do

Hi, I'm Robert.

I invent board games, research into mathematics when I can find the time, and write programs connected with my games, mathematics, or other inventions.

My first ever programming experience was with a machine like this.

I left the punched cards with the operators, who ran the program. A little later I'd come back and collect the output.

You could use the one at Culham to make colour movies of the program's output, to play back on a projector. You could interact with the program while it was running using a teletype in the corner of the computational physics laboratory where I worked.

I was at Culham only for a year, in 1971, before going to university, but that's what started me with programming.

My mathematical research interests are in the areas of geometry; a special way of thinking about infinity in mathematics; and mathematics inspired by games and puzzles (recreational mathematics, as it is usually called).

Here is a picture of a Penrose tiling done by one of my programs.

Penrose cartwheel - click to see larger region

The pattern is made up of only two tiles. You have to place them together so that the red and blue lines run continuously from each tile to the next.

If you do that, it is possible, though not easy, to continue the pattern as far as you please.

Patches of the pattern repeat, like the blue decagon with a red pentagon inside, but the whole pattern never does. What is special is that though you can tile as far as you like, there is no way to place the tiles together to make a repeating pattern like wallpaper.

Cartwheel tiling with the two Penrose tiles, and two extra tiles by Pavlobitch and Kléman- click to see larger region

What's different are the wandering red lines - they are there because of two extra tiles.

And here is one I thought I'd invented myself, only to find that Socolar had got there first:

Tiling by De Bruijn, colouring rules by Socolar, and my own colouring and design for the lines.

The shapes such as a triacontrahedron made up of golden rhombs on the anaglyphs, interactive models, and rhombic dodecahedron, triacontrahedron, and golden rhombohedra pages are also related to my research. I look at some of the ways people have added colours to three dimensional generalisations of the Penrose tilings. Again, I've thought I had invented new colouring rules, only to find someone else had invented them first. However there is plenty left to investigate.

I love mathematics, and look forward to any times I have free to continue research on it.

I have invented many board games and puzzles. These are games you play with actual pieces, the type you'd buy in a box with pieces and a rules book. I have done programs to play some of them too, for demonstration purposes, to send to Games Companies. I don't have anything of that sort suitable for general release at present, though I do have some ideas for making something available, maybe as a web page applet. One idea is for a program for playing games with a wide range of rules, by choosing the rules before the start of the game, that could also be of interest to other game inventors.

None has been published yet. One came very close, to the extent of getting a number of test versions printed and cut out. Sadly, it has not yet been published for technical reasons because it required especially fine registration of cutter and artwork, and no suitable manufacturing methods have been found so far for the pieces at an acceptable cost to the company that accepted it for publication. Suggestions welcome!

However I do have a couple of programs (shareware, with freebie cut down or limited versions). One makes fractal melodies and is available now. See the new section Fractal Tune Smithy.

The other makes a particular type of fractal trees, for VRML models, and will be available some time in the next couple of months or so. See the Virtual Flowers page.

As a taster, here is a little scene I made using fractal trees. It is called the Andromodean philosopher - Andromeda as in the Andromeda galaxy (where ET came from in the film).

Scene with Andromodean Philosopher

I made that one before starting on the program.

The program also makes various geometrical shapes. Here is one of its output files: Star whirl.

You will need a VRML browser such as Cosmo Player to see it.

Hobbies and interests

Music, playing the recorder.

I love hill walking whenever I am in a suitable area - Oxford, where I live is alas a place of gentle slopes for the most part, but my relatives live in Skye, Mull, and the Scottish borders.

Also an armchair astronomer - enjoy reading and keeping up to date on the latest discoveries about planets, stars, galaxies etc.

Something of a bookworm like most of my relatives. Particularly fond of impressionist art. Rather keen on science fiction.

You can e-mail me at hi@rcwalker.freeserve.co.uk

Here is a picture of me on holiday in the Isle of Skye, Scotland: