Box Counting Dimension - Dynamical Systems | Lecture 36 скачать в хорошем качестве

Box Counting Dimension - Dynamical Systems | Lecture 36

One of the defining characteristics of a fractal is that its dimension is not an integer. But what does this even mean? For example, how can a mathematical set/object be 1.5 dimensional? In this lecture we introduce one method for determining the dimension of a set in mathematics. Precisely, we introduce the box counting dimension of a set. This measure of dimension generalizes our usual measure of dimension and allows us to classify objects with non-integer dimensions as "strange" or "fractal". To illustrate, we determine the box counting dimension of the Cantor middle-thirds set from the previous video, as well as a simple countable set collection of points that turns out to have nonzero dimension. The box counting dimension is sometimes referred to as the Minkowski-Bouligand dimension: https://en.wikipedia.org/wiki/Minkows... Another measure of dimension is the Hausdorff dimension: https://en.wikipedia.org/wiki/Hausdor... This course is taught by Jason Bramburger for Concordia University. More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates.