Order behind chaos in the fractal build up of a vortex

The filaments and the vortices, forming the geometric pattern, evolve constantly with the passage of time, and create ever changing fluctuations of motions through out the entire pattern.

Though the individual filaments and vortices undergo constant evolutions with time, the directions of average flow of fluid through the geometric element remain predictable. The evolutions of the vortices, which are entangled in the network, create fluctuations throughout the pattern. In spite of these fluctuations, there exists clear directions along which inflows and outflows should occur. The ways the outflowing streams embolden the inflowing streams and, in turn, inflowing streams split to join the outflowing streams follow a universal rule. This rule repeats in all vortices which create the same geometric pattern. Though the path of a test particle, moving in the vortex, can not be predicted beyond a very short time, the global movements of the streams follow rather predictable paths. One can predict the way the vortices and the filaments will entangle, and the average motions of flow at different parts of the geometric element by studying the geometry alone. Thus there exists a predictable global order behind an unpredictable local chaos.

A whirlpool in sea

The ejections and infall in a whirlpool

The complex structure of the vortex formed by entanglement of filaments: The filaments constantly split, join. form loops and knots and break away from knotty structures again and again while creating an ever fluctuating world, which maintains a geometric design involving interactions of two spirals.

The vortices are made of innumerable smaller vortices which seem to follow a fractal arrangement, which intertwine two spiral structures. In such a vortex universe what may stream out of it will always return towards it.

When two spiral vortices merge they generate a structure with two envelopes, which are stacked inside each other in a hierarchical manner. The fractal stacking of such dual envelopes are very often seen in cosmic structures.

A three armed spiral inside the vortex wall of an atmospheric vortex. Such three armed spiral can be seen in the core of whirlpool galaxy.

A spiral at the heart of an intense atmospheric vortex. Such structure can be found at the heart of our own Milky Way galaxy.

SEE the resemblances with galactic structures