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Fractal Action

Fractal Music Composer

Martin Russ looks at a program that generates music from chaos.

Mandlebrot Set image and dialogue box.

Chaos theory deals with the study of changing systems, so it is strange that the best known symbol for the subject is the Mandlebrot Set: a very static image for a dynamic branch of mathematics. The Mandlebrot Set is just one example of an image generated by fractals — you can zoom into any part of the image and more detail will be exposed, forever. Fractals have the fascinating property that they have infinite complexity but can be generated by very simple formulae. For musical purposes the analogy between music and fractals is quite striking: both are not random, but they can have a pattern and structure which is complex and not completely regular.

Hugh McDowell's Fractal Music Composer is a suite of programs written to allow you to explore using the Mandelbrot and Julia Sets as starting points for generating music, and for making fractal images. The two music programs can produce standard MIDI Files for easy loading into a compatible sequencer for subsequent editing, and a simple MIDI File player program is included so that you can replay the files without loading the main programs.


There are two major control screens. The setup screen lets you set the number of MIDI channels on which the program will generate music, the MIDI channels, highest and lowest note (with buttons to check that these notes are within the playing range of your MIDI equipment). You can also set the length of notes and the number of repeats of one note length. Clicking on the MIDI Clock Out button provides MIDI Clock messages for synchronising drum machines etc. You can save or recall up to eight of these setups.

The Tonalities page provides control over key changes and the scale used (major, dominant 7, minor, diminished, whole tone and chromatic). You can create up to 36 tone maps by defining the transposition and the number of quarter notes to play whilst using that map — the program then cycles through the maps as it plays.

The Mandlebrot Set image (or another image produced with the Zoom program) is then used to generate sets of notes. You drag out rectangles on parts of the image for each track using the left mouse button for notes and the right button for note lengths. As you might expect, the more interesting parts of the image produce the most interesting music. After specifying a tempo, playback will commence and you can change the tempo with the '+' and '-' buttons on your numeric keypad.

Pressing the spacebar stops the music and lets you save the music as a MIDI File (you need to have a formatted disk ready to save onto!).


This program has a similar setup and tonality page, but adds a rhythm map page which allows rhythm cycles to be used. You then choose one point on the Mandelbrot Set image (it acts as a catalogue for the Julia Sets) for each track. As the music plays a Julia Set is drawn on the screen for each track — the co-ordinates of each point correspond to the pitch and loudness of the notes.

Both programs have simple control systems based on dialogue and alert boxes, which presumably maximises the amount of memory free for storing notes (more than 50,000 on my 1040 ST). The programs are key-disk protected, so the master must be in drive A, although a copyable working disk is provided. The documentation is clear and detailed, although it only hints at the mathematics and gives no information about how the chosen parts of the fractal images are linked to the music production process.


The music produced by the programs initially sounds much like many of the random composition programs for the ST, with glimpses of 'nice tunes' surrounded by a jungle of meandering notes. The high level structure provided by the tone maps gives quite a lot of control over the results, and it is perhaps this which makes this 'fractal' music more interesting — you can explore cadences and modulations very easily by using the tone maps.

But the ability to load a MIDI File of the results of fractal composition into a sequencer means that you can then edit the most interesting bits and re-use them in your music. You can produce melodies, pads and fills, even drum parts like hi-hat patterns, where a little chaos can help to emulate a drummer's uneven playing. Viewed in this way, these programs could be either triggers to creativity, or even a way of avoiding your own personal cliches in melodies. This explains why the program is called Fractal Music Composer — it is a compositional aid for use in creating music. Used in such a way, the computer can become a useful tool for extending and enhancing your music skills: it's not what you've got, but how you use it that matters!

Further information

£65 (+2 P&P) inc VAT.

Fractal Music Ltd, (Contact Details).


MANZOOM (hi and med rez) and LOWZOOM (low rez) are the two programs which allow you to visually explore the Mandelbrot Set image. The computational limits of the ST mean that you cannot actually zoom in on any part of the image indefinitely, but it should take you quite a while to come up against the end-stops. The images look at their best on a colour monitor using the ST's 16-colour low resolution mode, although the contouring used in high resolution is very effective.

A comprehensive Public Domain GEM program called Fractal Zoom (available from Goodmans Enterprises on (Contact Details)) allows more graphically impressive explorations of many fractal images. You can change the colour palettes and add shadowing to make the image look 3-D.

All this computational activity takes time: it can take 10 or 20 minutes (or more) for a single screen to be generated (but compare this with my old BBC B computer, where you would leave it working overnight to get just one Mandlebrot Set image).


For the ST, Dr.T's M and RealTime also have some interactive randomising elements. Steinberg's Cubase has the Interactive Phrase Synthesizer, which is more algorithmic than random in nature.

There are some simple random music generator programs in the Public Domain, although none of these produce MIDI Files in their current versions. Mike Yocum's Algorithmic Musical Instrument produces 4-track music and is quite interesting, whilst the author's own monophonic Random MIDI Music Maker tends to concentrate on some almost-musical cliches. IROS, a simple 16-note sequencer with a novel randomisation feature, can liven up bass lines, and is great to jam with if you are into German synth heroes.

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Sound On Sound - Copyright: SOS Publications Ltd.
The contents of this magazine are re-published here with the kind permission of SOS Publications Ltd.


Sound On Sound - Feb 1992

Review by Martin Russ

Previous article in this issue:

> Crystal Clear

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