### Monday April 26, 2004

**Speaker**: Greg Huber (U Mass Boston)

**Title**: Q theory: From the integers to informatic
turbulence

**Abstract**:
In 1979, Hofstadter introduced and briefly discussed a chaotic, recursively-defined
function which he called *Q*:

* Q(n) = Q(n-Q(n-1)) + Q(n-Q(n-2))*
Over the past 25 years, a number of mathematicians have studied this function
and a handful of variants of it, and though some statistical details about *Q*'s
type of chaos have been observed, no one has managed to prove a single fact about
*Q* - not even that it -is- a function! In my talk, I'll describe a new avenue
of (mostly empirical) which looks at a family of variants of *Q*, and which
borrows some ideas from other disciplines. It turns out that this family of
functions, on the collective level, exhibits an amazing degree of regularity, and yet
within the framework of that family-level regularity, there are very weird irregular
patterns unlike any seen before. I'll discuss what is currently known and unknown
about this new family of functions, presenting the ideas mainly through a series of
computer-generated graphs which display the tantalizing eccentricities that have been
recently uncovered.