Robert - About Me

Do you want to know a bit about the author of Bounce Metronome? I'm a mathematician and programmer by training, with a keen interest in music of course, which is how I got into music software development. My instrument is the recorder, am an amateur musician, and also amateur composer.

Here I am playing one of my pieces on recorder

Youtube Video

Tune for recorder, composed 7th February 2006 - Robert Walker

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

This isn't the computer. This is just the machine you use to punch out the cards which you then take to the desk to hand in.  The computer was a huge machine in a room to itself which only the computer operators entered.

I left the punched cards with the operators, who ran the program. A little later I'd come back and collect the output, probably the next day. Most often the output would just say "syntax error on line ...":) which means it didn't actually run. That's because you couldn't even do syntax checking without putting your cards through the computer first, and programmers always  have to fix syntax errors  - things like missing commas and semicolons - because the language is so strict that anything like that means your program won't 'run at all.

So - in those days programming was a very long process over several days to get even the simplest of programs to run. 

You could use the one at Culham to make colour movies of the program's output, to play back on a projector - very advanced for the time. Not interactively of course, you write the program and then later on you can collect the colour movie it made and then can play that back to see what it did.

Also, you could interact with the program while it was running using a teletype in the corner of the computational physics laboratory where I worked - this was a case of typing onto a scrolling sheet of paper - then you press the return key and the computer would respond with its reply in a new line of text below the line you typed in yourself. 

I was at Culham only for a year, in 1971, before going to university, but that's what started me with programming. So, I first learnt about computing from Richard Peckover, in the computational physics laboratory at Culham.

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.

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 anaglyphsinteractive 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. Though I haven't done any maths research now for a decade or so.

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!

My first published software was Fractal Tune Smithy which makes fractal tunes. It also has micorotonal capabilities, and I used it for microtonal compositions myself. This lead to interest from microtonal composers and I developed that aspect of the program more and more. At one point it was about the only program that could be used for microtonal composition on Windows. Nowadays there are several other options, but Tune Smithy is still used by microtonal composers.

Another program I wrote early on makes a particular type of fractal trees, for VRML models. See the Virtual Flowers page.

Siuce then I also developed Lissajous 3D and of course Bounce Metronome.

Hobbies and interests

Music, playing the recorder. Compose for recorder.

I love hill walking.

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

Click here to send me some e-mail

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

I'm a bit older now, here is a more recent photo: