Fractals and Cascades of !Nonlinear Bifurcations

The Theory of !resonances views the environment (!reality) not through the customary prism of linear time, but through the dynamics of cycles.

Hierarchy of Cycles and Harmonics in T!R

In t!r, 1 Saros is taken as the base unit of reference for a !time slot — a draconian astronomical cycle lasting ~18 years and 11 days (6585.32 days), after which the sequence of Lunar and Solar eclipses repeats. Analysis of event !flows shows that it is precisely along the Saros that large fractal patterns with a scale of 50–100 years (planetary-level events) can be traced.

Structuring processes in t!r relies on a system of harmonic oscillations:

• Minor cycle (1/16 of Saros — i!l): Inter-!librational harmonic oscillation lasting ~14 lunar months (the intersection point of eclipses with a new moon). The superposition of frequencies in these slots creates an increased event density.

• Medium cycle (Saros * 16): An interval of approximately ~288 years for tracking large-scale historical patterns.

• Ultimate cycle (Saros * 16^2): A period of ~4608 years — the technological limit of fractal dimensionality with which practical work is possible.

Note: For intervals smaller than 1/16 of a Saros, standard lunar days are used in practice instead of further division into 16 harmonics.

In the Theory of !resonances itself, linear time does not exist — it is applied exclusively to convert cycles into a familiar calendar format.

Event !flows are synchronized by waves of varying lengths, but the physics of the process is identical. This creates a strict fractal correspondence between a 2-week cycle (New Moon — Full Moon) and an 18-year Saros.

Fractality of Cycles vs. Event !Cascades

It is important to distinguish between the large-scale fractality of cycles and local !cascades within the !flow itself:

• !Libration cycles demarcate !time slots and are responsible for synchronization, !resonance, and navigation of the event !flow.

• An event !cascade is the internal structure of the !flow itself. It represents a chain of three consecutive !nonlinear bifurcations. Similar chains repeating from cycle to cycle within a single theme are linked together into a single end-to-end !cascade.

Example of an End-to-End !Cascade

Consider a destructive !flow associated with a car breakdown: