When teaching Numerical Methods and Matlab I like to challenge myself and take upon doing some new practical project to show my students how to apply their newly acquired skills to do something fun. Last time I have built a simple statistical football model and "played" a few fictional seasons to see how likely was the outcome of the studied season. This year I have decided to look into "solving" Monopoly using Linear Algebra.

While doing literature review for my postdoctoral project I have taken a look at [1]. I have even implemented related interactive apps, but I have forgotten about them and not written a post about the model on Physics of Risk.

In this post I am sharing an app which implements partisan voter model on a two dimensional grid. There is nothing special about this particular version of the model. Just the average consensus time for this topology ought to be a bit shorter.

While doing literature review for my postdoctoral project I have taken a look at [1]. I have even implemented related interactive apps, but I have forgotten about them and not written a post about the model on Physics of Risk.

In this post I'll introduce you to the, idea of which is quite simple - voters are partisans in a sense that they will more readily accept opinions, if they are already predisposed. And I'll share an interactive app, which implements the model on a fully connected network.

It is obvious that you can perfectly tile floor of a room using square or rhomboid tiles. Similarly it would be easy if we would triangular or hexagonal tiles. Furthermore in all these case we could rotate these patterns by less than 360 degrees and still get valid layouts. Namely you could rotate rhomboid tiles two times, triangles - 3 times, squares - 4 times and hexagons - 6 times. But what about 5 rotations? Or 5-fold symmetry?

More details in a more attractive video form are given in the video by Veritasium, which touches upon fractal created by British mathematician Sir Roger Penrose - Penrose fractal.

In the last few posts we have discussed voter model with supportive interactions. In most cases the support is strong and drives even non-extensive model, which is described by a broad stationary distribution in the absence of support, to a stationary point. Yet there are cases when such driving is not overly strong and some stochastic behavior is retained. In this post we present an app, which also allows you to examine stationary PDF of the model, where support suppresses recruitment.