[math-fun] How AB-normal can numbers get?

This talk of pi being 'normal' got me to thinking: "How bad can an ab-normal number get?" I'm not talking about numbers like 1.000000...; I'm talking about numbers which "look" random to the unaided eye, but which are quite abnormal -- e.g., they might be quite compressible by something as simple as zip or gzip. In particular, a gzip'd number might be 1/100'th the size of the un-gzip'd number. Are there easy constructions for such numbers -- hopefully constructions which don't involve individual bits or Turing Machines ? Perhaps using only "calculator" functions ?