This talk will discuss work that Ian Sutherland and I have been doing on data layouts for disk arrays -- ways of arranging data and redundant information on a collection of disks to guarantee a high level of performance and fault tolerance. Previously, some of you have seen me or Ian discuss this work, but this week I plan to focus on extensions involving the efficient generation of these data layouts wihtout using lookup tables (our work and others'). Since several of you have not seen this material before, no previous knowledge will be assumed.