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This simulation visualizes dynamic patterns, emergent linear models, of data in a multidimensional resource space. To simplify the presentation, a few dozen low-dimensional resource samples index a complex environment. The emergent models determine processes that can be used to represent and estimate resource intensities, cybernetic equilibria. The simulation is based on cybernetic systems where activities x are linear (and optionally sparse) balancing transformations of resource residuals ū and emergent models phi are adapted towards local matching of mutual cybernetic information . In other words, system activities are superpositions of dampening responses to time dependent external perturbing fields. Responses are coupled to effective fields via emergent (average) interactions between response superpositions and effective fields.

The simulation demonstrates this local strategy resulting in emergent system level properties such as:

Initially only two-dimensional cybernetic system (in blue and brown) driven by two-dimensional resource samples (light dots) are shown. Resource samples are attenuated (light lines) by implicit resource use, which gives an estimate (black circle) of the current resource (black disks at mouse position). The systems interact only via their environment, but still as a whole enact functionally interesting structures. See “controls” tab and more animations below the demo to learn more.

Explore the Interactive Demo

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Higher-Dimensional Examples

The simulation presents only 1–5 models in a 2–5-dimensional resource space. Useful results are obtained in higher-dimensional spaces. The spaces can be composed of any kind of finite data (for example, augmented with delayed, combined, and otherwise transformed resources), but perhaps it is most illustrative to present a few examples where the structure of the resource space is intuitively clear: using images as multidimensional resources. Each example below is initiated with random models in the resource space that is determined by image data.

In addition, among recent developments is to use complex values for representing resource magnitude and phase together, allowing modeling of resource space change tensions in the same framework.

Update: Now you can test run the algorithm in R environment for statistical computing: eca.r. A more thorough tutorial may be prepared later. In the meantime, lectures on elementary cybernetics, especially lecture 4 and later, discusses emergent linear models, and some summaries and detailed analyses are available too.


Neocybernetics may offer new possibilities for research and development of complex systems, i.a. bioinspired and hyperdimensional computing. See lectures and publications elsewhere on this site for examples on:

Neocybernetic Proposal

As a summary, studies on neocybernetics suggest that mostly everything is information (covariation) – the essence of perceived stable structures consists of patterns of dynamic processes governed by modeling and entropy pursuit in the resource space. Life could then be characterized – in a more general way than the common understanding as the germline – as the drive towards fractal balance of functions in various environments.