Incidentally how did you manage to fit the pattern into a single function ?

Sorry to take so long to respond. I used a least squares fit to get the equation which fitted the data best. This can be done in a spreadsheet or similar. I used a graphical package called EasyPlot which is left over from my days as a PhD student when I regularly did this sort of thing with quite large data-sets. This package is a lot easier and quicker than using a spreadsheet. The fit isn't perfect but the error is small, going to a third order polynimial makes hardly any difference to the accuracy and would take more run-time to calculate.

Paul