Abstract: I investigate the trade-off between regularity and randomness in Bridget Riley's early Op art, focusing on White Discs 2 (1964) and Fragment 6/9 (1965). I build on this to investigate the trade-off more generally. I analyse these two works and undertake three experimental investigations based on my observations. I first consider different types of randomness and the effect they have on the generated artwork. I then look at whether the introduction of randomness can be left to the computer or needs the artist's direction. For best æthetic effect, there is some evidence that the choices made are not truly random. Finally, I consider how much randomness needs to be added to a regular pattern in order to produce a work that balances regularity and randomness in an aesthetically pleasing way. There is evidence that around two-thirds of the pattern needs to be retained.