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.

Typically voter models assume that recruitment occurs between two interacting individuals. Obviously recruitment can occur only if these individuals have different opinions. While nothing will happen if these individuals hold the same opinions. Though Latane social impact [1] predicts that support provided by like-minded individuals can also play a role.

In a previous post we have consider the case when support prevents both recruitment and independent transitions. This needs not to be the case if we assume that independent transitions are not influenced by the support provided by the peers. This yields another variation of the noisy voter model with supportive interactions, which exhibits a more complicated phase portrait. This model is also a part of my last paper of the postdoctoral project [2].