# Mathematics

CHAOS WORKSHOP POSTERS. By Dave Miller, Richard Bridges and Joe Miller. Keele Mathematical Education Publications (KMEP). pound;45 for the set of 16

These posters recreated for me the excitement of the late 1970s and early 1980s, when Chaos was what might be described as the "underground" mathematics in schools.

Sixth-formers, some not especially renowned for their interest in mathematics, would come up to me after lessons or in the corridor. "I went for a university interview last week. They gave me a computer programme. Look what it did." The print-out would be of the Mandelbrot set. Soon the sixth-form was awash with print-outs, and more students would be producing them and buying computers with greater processing power and better quality colour printers. Ian Stewart's popular mathematics publications rapidly became dog-eared. One colleague produced a series of postcards of fractals. So enticingly beautiful were they that a display of them disappeared without a trace during an open day.

It is clear from the production and design quality of these posters that the development team is similarly excited by Chaos and wants to share with others the wonder, awe and creativity that this subject inspires. I think they will succeed.

One of the set of 16 laminated, A3-size posters tells us something about the group behind the posters, known collectively as the Chaos Workshop, and the rest go into the subject itself. They are in no specific order and each one is designed to stand on its own, but several cros-references are built in. The posters cover the Mandelbrot set, the Lorenz attractor, Julia sets, the chaos game, and the logistic equation with its associated bifurcation and cobweb diagrams. Little is omitted.

The design has been thought through very carefully. The posters are colourful and seek to intrigue the observer, posing questions rather than answering them. Equations are kept to a minimum, but are sufficient to prompt secondary pupils to want to follow up and explore them further.

One poster describes the creation of the Koch curve and snowflake, and features several iterations. The challenge is then to repeat the process with other polygons, looking carefully at the area and perimeter of the iterations. But there are no equations; the approach is almost entirely visual.

On the other hand, the logistic equation poster prompts many investigations, and uses graphics extremely well to support and illustrate the algebra.

I like these posters very much. They got me doing some mathematics and wanting to talk to people about it. However, while I used a graphics calculator for my own investigations, I wondered if I might need some program support for the computer were I to use the posters in the secondary classroom.

KMEP also produce Fractals and Chaos in the Classroom by Dave Miller et al, and its associated software, Fractint. This software would certainly help with some of the posters.

Tom Roper is a senior lecturer in mathematics education at the University of Leeds

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