Steiner Tree vs The Matrix Mentor

This app computes Steiner trees using an evolutionary algorithm. You can place, drag, and delete points of your tree. The optimal number and position of Steiner points is computed. A minimal spanning tree (MST) connects a given set of points in a plane so that the sum of all edges is minimal. Often this sum of all edges can be reduced, if additional points are added. These points are called Steiner points, and the corresponding minimal spanning tree Steiner tree. If more than 3 points are given, it is a hard optimization problem to compute the optimal number and position of Steiner points. This app uses a simple evolutionary algorithm for demonstration purposes. It uses a population of individuals. Each individual represents a MST containing some Steiner points. The population develops towards the optimal Steiner tree in an evolutionary loop: Initially, each individual sets random Steiner points, and constructs the corresponding Steiner tree. The minimal length of the Steiner tree in the population is stored. Each individual has now a fitness value, which is the higher, the closer its Steiner tree length is to the minimal length in the population. Fitter individuals have more descendants by reproduction, and less fit individuals die out. In order to explore better solutions, reproduction does not create descendants that are identical to the parent individual, i.e. do not have their Steiner points at the same position. Rather these positions are shifted randomly by mutation, using a Gaussian distribution. How far they are shifted on average is determined also by their fitness: Good individuals shift their Steiner points less than worse individuals. How fast a good solution is found, depends thus on the population size, and the mutation strength.

Are matrices getting you down? Don’t worry… THE MATRIX MENTOR IS HERE TO HELP The Matrix Mentor provides a visual understanding of linear transformations. Where others may teach you the mathematical rules that can be hard to remember, our playground provides a visual and interactive demonstration of the inner workings. SCARED OF MATRICES? DON'T BE! At its core, The Matrix Mentor is a visual learning tool, designed to bring matrices from an abstract mathematical concept to a concrete application. Whether you think about vectors as 3D points or a RGB color value, the fundamentals hold true. - Experiment with different types of transformations - Discover how matrices interact with a given vector, or a whole grid of points - Develop your intuitive sense for reading matrices and linear transformations Do yourself a favour, and start playing with The Matrix Mentor today!