## Energy and Information Across a Mosaic

Mosaics can be created by the effects of local constraints that force crossing fluxes to divide into patches and to coalesce again and again.

According to this view a mosaic is created when a fluid crosses a medium in which there are some local constraints. This pattern can be observed in nature when we observe the gravel and sand deposits along a river after a flood. Water and debris are moved in a chaotic way along the river bed, finding local constraints like stones, abrupt curves, and human structures like bridges, basements, barriers, etc.

A clear example of such a mosaic is represented by the dynamics of a cloud. Air masses crossing the air matrix with well-differentiated constraints, such as wedges of cold air, act like attractors and create clouds that represent a type of mosaic in which every patch (cloud) after the constraint evolves toward a cloud formation.

Energy creates spontaneous mosaics of material differently spaced, and then such material can utilize additional energy internal to the system to auto-organize and to create different patterns.

In this way, a mosaic can be produced by the effect of energy in a highly dynamic material, like a fluid under locally spaced constraints.

In terms of information we can observe an increase in information moving from the center of each patch to the border where the information (uncertainty) reaches a maximum. This effect can be described in a very simple manner using a matrix in which two patches compose the entire mosaic. As you can see in Fig. 3.12, our mosaic is composed of two patches that have only one side in common, all the other sides are not considered. In other words, we have only the possibility to exchange information along the horizontal axis. In our model we consider the left and right side as the less informative for both the patches that meet the maximum of information at the center. We assume 0 as the value of the two columns placed respectively on the left and right end. We have not considered the upper and bottom sides. The reality is much more complicated, but this example may be useful to understand at least the behavior in one direction of the cells composing the mosaic.

The uncertainty based at the border of a patch can be incorporated in a system by adaptive mechanisms like the reinforcement of a cellular membrane and the increase of resistance to desiccation, to UV light, to animal browsing, etc. Genetic adaptation of organisms is very active at the border if compared with the interior.

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Fig. 3.12 If we consider every patch composed of n discrete entities (cells), it is possible to visualize that each cell has properties linked to position in Euclidean space. The closer a cell is to the border the greater the uncertainty. On the left side two patches are represented with an increase of darkness according to the increase of uncertainty. The right side shows the same image transformed into a numeric matrix