2. The Nagual environment to develop and visualize complex self-organized structures
The goal of the environment-experiment (Nagual [14]) described in this section is to show how a simple alife system can generate very complex structures characterized by a high degree of connectivity and an evolvability, much higher if compared to the classic neural network. The experiment tries to enhance some mechanisms of development of the information structures and of the internal complexity.
The life context is a two-dimensional space initially empty. At the beginning, few individuals are placed in the space and they begin to reproduce and develop a population. An individual is a filament which at the beginning is composed by a single cell. At each evolution cycle, the filament grows according to several models of movement and to a rate of growing. All the parameters for the dynamics, reproduction and death are recorded in a genetic map which is defined at the birth of an individual and remain constant throughout the individual life.
(Movie) Example of the dynamics of an evolution
The movement (modality of the filament growing) is the composition of a deterministic component and a random component. The reciprocal importance of the two components is regulated by a parameter. High values for this parameter cause a totally random movement; low values cause a totally deterministic movement. Different models defined characters have been developed for the deterministic component. For example, a movement with an uniform probability of changing direction; or a higher probability associated to pre-fixed curvature; or finally, a movement with a curvature evolving with the time.
The death of the individual can occur for accidental or natural reasons or when the length is reduced to zero. Furthermore, if the trail of an individual clashes against another individual, generally he dies. A very little probability of survival is allowed depending by the clash angle.
The reproduction is asexual and the sons have a genetic map similar to that one of the fathers, but some mutations in the genetic parameters can occur depending by the mutation rate. Through this mechanism, the population evolves and different phenotypes can be developed in the same evolution.
Emergent behavior
The first observation is that the collective development constitutes a new entity with its own autonomous and coherent pattern and with characteristics descending from the interaction and features of the population of individuals. Changing the parameters of the process, the set up generates very different patterns remembering the growth of populations (plants, animals, neural networks), landscapes (rivers, fractures, mountains, cultivated fields), human artifacts (chips, glass fragments, architectures) or biological shapes (anthropomorphous shapes, animals). All these shapes are characterized by a completely different distribution in the space and by different fractal dimensions.

The evolution process generates strong changes in the modality of the colonization of the life space. This mechanism is due to the dynamic action of dominant individuals which act like pioneers who push the life in the void space. During this colonization they create strong divisions in the space and the subsequent colonization develops local communities of individuals (micro-societies). The action of the pioneers creates a mechanism of islanding which appears in the images as the coexistence of close different graphical phenotypes with a limited contamination. The global result is the development of biodiversity in terms of different phenotypes.

Another interesting aspect is the changes in the individual phenotypes during the evolution due to an emergent selection. At the beginning, the smooth curvatures are favorite due to the higher average life they are able to reach. During the evolution the micro-societies characterized by straight lines are filtered because of they are not able to bypass obstacles (high coherence, low flexibility). Excess of chaotic micro-societies (high level of irrationality in the curvature changes) are filtered because of individuals clash each other (internal fight and chaos). In the final part of the evolution, the available space is very little and the most favorite phenotypes are micro-societies characterized by short paths, high reproduction rate and medium irrationality. These societies are able to penetrate in every available space. This mechanism produce interesting evolving patterns in colors and in the sound organization during the evolution.

Concluding this section we want to remark that this environment is able to develop a high level of structured complexity in the connectivity tissue. In this sense it generates a potential of information connectivity much more similar to the real neural network than the classical artificial networks because it is founded on the space and on more biological mechanism of development. For this reason, these images evoke the natural shapes. Furthermore the dynamics of the development is based on adaptation and self-organization dynamics and therefore this approach is very promising in term of evolvability.
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