MINKOWSKI’S QUESTION MARK FUNCTION
Friday 21st April, 2017 16:00-17:00 Boyd Orr ?
Farey tree, F, is the branch of Stern-Brocot’s tree on the interval [0, 1]. Imagine a random non-backtracking walker moving from top to the bottom of F. We can define probability functions on the junctions of F using the probabilities for choosing which way to advance. These induced functions define Borel measures over F with the natural topology generated by the edges. The constant function 1/2 generates a Borel measure, called Minkowski’s measure. It’s cumulative distribution function (c.d.f) is known as Minkowski’s Question Mark Function (or Slippery Devil’s Staircase) and has several interesting fractal properties. In this talk, I will discuss about its construction and fractal properties.