Cayley hash values are defined by paths of some oriented graphs (quivers) called Cayley graphs, whose vertices and arrows are given by elements of a group $\mathfrak{H}$. On the other hand, Brauer messages are obtained by concatenating words associated with multisets constituting some configurations called Brauer configurations. These configurations define some oriented graphs named Brauer quivers which induce a particular class of bound quiver algebras named Brauer configuration algebras. Elements of multisets in Brauer configurations can be seen as letters of the Brauer messages. This paper proves that each point $(x,y)\in \mathcal{V}=\mathbb{R}\backslash \left\{0\right\}\times \mathbb{R}\backslash \left\{0\right\}$ has an associated Brauer configuration algebra ${\Lambda }_{{\mathfrak{B}}^{(x,y)}}$ induced by a Brauer configuration ${\mathfrak{B}}^{(x,y)}$. Additionally, the Brauer configuration algebras associated with points in a subset of the form $(\lfloor (x)\rfloor ,\lceil (x)\rceil ]\times (\lfloor (y)\rfloor ,\lceil (y)\rceil ]\subset \mathcal{V}$ have the same dimension. We give an analysis of Cayley hash values associated with Brauer messages $\mathfrak{M}\left({\mathfrak{B}}^{(x,y)}\right)$ defined by a semigroup generated by some appropriated matrices $A_0,A_1,A_2\in \mathrm{GL}(2,\mathcal{R})$ over a commutative ring $\mathcal{R}$. As an application, we use Brauer messages $\mathfrak{M}\left({\mathfrak{B}}^{(x,y)}\right)$ to construct explicit solutions for systems of linear and nonlinear differential equations of the form $X^{″}\left(t\right)+MX\left(t\right)=0$ and $X^{\prime }\left(t\right)-X^2\left(t\right)N\left(t\right)=N\left(t\right)$ for some suitable square matrices, M and $N\left(t\right)$. Python routines to compute Cayley hash values of Brauer messages are also included.

We introduce an algorithm based on posets and tiled orders to generate emerging images. Experimental results allow concluding that images obtained with these kinds of tools are easy to detect by human beings. It is worth pointing out that the emergence phenomenon is a Gestalt grouping law associated with AI open problems. For this reason, emerging images have arisen in the last few years as a tool in the context of the development of human interactive proofs.