Introduction

The mosaic appears everywhere and is considered to be an aggregation of basic heterogeneity, but, if we reduce or enlarge our vision, new patterns appear. Moving down, we expect to observe the appearance of heterogeneity. But what is the limit at which we establish that a system is simply heterogeneous? I consider this a poor question; heterogeneity appears and disappears according to the scale of observation. We can state that heterogeneity appears many times as we move across a changing scale, and the same happens for the mosaic.

In Fig. 4.1a hypothetical model is presented, in which mosaic and heterogeneity appear alternating with movement across different scales. This alternation can be perceived only under the condition that we change the scale of observation. We have to change either extension or resolution, and this is possible only if we imagine use of the sensors of different organisms. Often we maintain one of the two parameters or we consider only the human perception of our environment.

Mosaic and heterogeneity have fractal behavior, and this allows measurement of the complexity of "mosaics" and "heterogeneities" that are present across scales.

The investigation of the properties of a focal mosaic could be developed using fractal analysis and applying the indices of complexity to the entities that appear when we change the extension and resolution of the images. Considering j a value of extension and i a value of resolution we can measure the level of heterogeneity and patchiness at ji scale.

Heterogeneity reaches a maximum when all the categories have the maximum spatial invariance and a minimum when the spatial variance is at a maximum. Patchiness is at a maximum level when the contagion (see later in the chapter 7 on methods) is at a maximum (Fig. 4.2).

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