The altepetl is a category that describes the organizational structure of the territory and the social hierarchy of pre-Hispanic societies in Mesoamerica. This category is used to understand the basic generator of territorial and political complexity in pre-Hispanic times. It is proposed that the repetition of itself, its iteration, increases social complexity until reaching structures comparable to big cities and great empires. These complex cultural developments are self-similar to the basic structure that generates them, the altepetl. The modeling of the pre-Hispanic altepetl is based on contributions made by ethnohistory to a spatial and social organization of territory and on the characteristics of alliances and segregations. These constitute the mechanisms that can explain linearization, increasing complexity or collapse of societies. The interactions between the altepetl and its agency capability are studied from the perspective of complexity theories to understand the relationships between neighboring entities. The study seeks to demonstrate the fractal properties of the structure and dynamics of Mesoamerican groups, based on the iteration principle of the generator component: the altepetl.
- complex systems
The historical reconstruction of pre-Hispanic civilizations of Mexico has been undertaken from a traditional point of view, building on the western concept of “City.” Associated with this approach is a linear perspective of history that emphasizes the origin of civilization, its climax, and its collapse, forming a path that resembles a Gaussian function. Civilization and complex societies, the city that characterized them and their collapse have been considered as a unique historical event.
Pre-Hispanic history of Mesoamerica was characterized by the civilizing and cultural climax of the Classic Horizon, and its catastrophic collapse was an enigma that archaeology tried to solve. The terms “Maya collapse” or “end of the Classic Horizon” allude to the idea that for the whole of the cultural area, climax occurred between 400 and 800 AD and that the cultures that the Spanish conquerors observed 700 years later were the decadent remains of great civilizations (Figure 1).
The representation of this linear process does not allow to observe the fractal properties of the evolution of pre-Hispanic cultures; it is seen as having an integer dimension, and not a fractional one. However, for example, from an epigraphic and ethnohistorical exploration, Joyce Marcus has observed that this view was incorrect and that the pre-Hispanic history of the Mayas was characterized by permanent fluctuations; small and big collapses could be observed, some local and other of a regional scale. Her perspective was based on two processes: linearization and segregation, that is, the alliances and ruptures that characterized the social dynamics of the Maya .
López Aguilar and Bali analyzed the fluctuations and instabilities inherent to the evolution of pre-Hispanic societies. They included in their study three variables obtained from available archaeological information: maximum extent of the territory of a system, the size of the capital, and the hierarchical levels of the subordinated settlements. The hierarchical levels considered what some scholars have called
Criss-cross oscillations of the three trajectories—between the lower limit defined by the structure of the
The collapse of these two systems resulted in a small fluctuation that started around 650 AD and it gave place to a plateau-type stability phenomenon that collapsed with the expansion and linearization of the Central trajectory in the sixteenth century. The hypothesis that guided this research was that fluctuations of social systems of pre-Hispanic Mesoamerica had self-similar fractal properties based on the reiteration of a basic generating unit: the
The discussion of the fruitfulness of this ethno-category for the comprehension of the Mesoamerican indigenous world is beyond the scope of this work. The intention here is to start a modeling process of Mesoamerican dynamics that builds on a symbiosis of the ethno-category with models, concepts, and metaphors taken from complexity sciences and fractals as families of models , inspired by auto-organized criticality research  and complex agents .
To date, the exact configuration of the structure of the
With time, the pre-Hispanic interaction system started a long and irreversible fragmentation process, indicating that the Mesoamerican attractor no longer existed. In the sixteenth century AD, with Spanish conquest and the insertion of America in the capitalist world-system, the long history of fluctuations of the indigenous social organization was shattered, which gave place to an a synchronic pulverization of the
Gradually, the mechanisms of linearization and segregation were lost, the scope of action and control of indigenous rulers was reduced as a consequence of territorial conflicts generated by the Spanish and mestizo invasion of the space of the
However, the segregation and fragmentation of the territory of the
Bounded in the time and space of the Mesoamerican attractor, the dynamics of growth and collapse of pre-Hispanic cultures was based on a system of alliances and conquests, of segregations and independences. Alliances permitted the aggregation of similar structures to the body of the
The reiteration of the
The basic structure of government entailed at least three discernible hierarchical posts: the
In the conical clan, social organization and economy were beyond the level of an equalitarian community. Even if production was based on domestic units, the population had to collaborate in the construction of extensive works, like temples or palaces, and products and services were exacted for the purposes of the clan, the deities or for the hierarchy of the rulers [11, pp. 45–46]. This system was repeated in the neighborhoods, the hamlets, the capital, in the
This basic structure repeated itself by means of alliances of different types, especially through marriage bonds (a higher level
In the opposite direction, one or several
In the environment of each
Minor autonomous or subordinate entities (lineages,
As corporative systems, in the lineage, in the conical clan, and in the
The agent’s action has a cultural horizon that establishes the limits and conditions of knowledge, of know-how, and of awareness of problems, dilemmas, solutions, and strategies to follow. What is not in the framework of their traditions, their knowledge, and of their historically determined cultural horizon cannot be done, thought, practiced, or even imagined [16, pp. 21–32].
Dynamics and fluctuations of Mesoamerican systems can be modeled by a space where N elementary agents (lineages) have K interactions with their peers. The dynamics of this NK space result in the emergence of an agent of a higher degree of complexity: the
Collapses were a historical possibility in any moment of the evolution of the system in the
One of the dilemmas faced by the fractal modeling of Mesoamerican pre-Hispanic societies is that the history and the evolutionary path of these cultures have been undertaken from a perspective that does not contemplate oscillations and fluctuations that characterize a dynamical complex system.
In this long-term research, we analyze the self-similar fractal properties that occur in systems that emerge from the NK space of interactions of the
The NK interactions of the
Interconnections between agents are the basis of Kauffman’s model, in which a network of N agents is constructed such that each is randomly connected to K others. The interactions between each agent and its K neighbors can be cooperative, competitive, or a mixture of both. Now, instead of all agents reacting to a few environmental variables, each agent reacts to the actions of the K other agents in its communication network. Each agent, therefore, has a unique set of conditions governing its behavior. Optimal strategies in the present moment may not be what they were before, because they depend on the previous actions of other agents. This result is a “Red Queen” effect, in that agents are forced to keep evolving (i.e., searching the fitness landscape) toward higher fitness peaks just to stay competitive [18, p. 13].
Kauffman’s model  establishes that interactions among agents depend on the value of the interconnections among them and that they react differently when they have a moderate connection than when they are completely interconnected. In the first case, they can adapt easily and make small adjustments in their strategies to avoid greater risks, while in the other case, each agent has so many unfavorable interconnections that the favorable ones do not seem to exist, and the quest toward a decision is not better than chance [18, p. 13].
Kauffman’s model was used by Kohler to analyze the Plaza people that occupied the Pajarito plateau in New Mexico toward the thirteenth century AD. Kohler focused principally on the interaction between households (N) and observed that their number increased while their interconnections (K) practically remained constant [20, p. 381].
When the NK interactions of the
This characteristic was repeated until a configuration of higher hierarchy and control entities were established. In the case of Teotihuacan, up to seven hierarchical levels above the
The Mesoamerican attractor, characterized by three intertwined trajectories of stability, instability, and semi-stability, included the fractal self-similarity of the interaction among agents that formed its cultures, with independence of the scale of hierarchical complexity of the system.
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- Altepeme is the plural of altepetl.