Using fractal self-similarity and functional-expectation relations, the classical theory of box integrals is extended to encompass a new class of fractal string-generated Cantor sets" (SCSs) embedded in unit hypercubes of arbitrary dimension. Motivated by laboratory studies on the distribution of brain synapses, these SCSs were designed for dimensional freedom-a suitable choice of generating string allows for  fine-tuning the fractal dimension of the corresponding set. We also establish closed forms for certain statistical moments on SCSs and report various numerical results.


Prof. Jonathan Borwein

Research Area

Applied Seminar


School of Mathematical and Physical Sciences, University of Newcastle


Thu, 02/08/2012 - 3:00pm to 4:00pm


Old Main Building 145