Superlattice Turing Patterns

Quite extraordinary!

"The study of pattern formation in nonequilibrium reaction-diffusion systems began with the theoretical analysis of Turing structures, which are stationary, spatially periodic patterns resulting from the interplay between pure diffusion and nonlinear reaction kinetics. Turing suggested that such structures could play a role in morphogenesis, and his point of view has gradually become prominent. The first experimental observation of Turing patterns occurred nearly 40 years after Turing's work, in a chemical reaction-diffusion system. Later, Kondo and collaborators showed that skin patterns in various small fish also develop according to the Turing mechanism."

- Dr. Lingfa Yang

http://hopf.chem.brandeis.edu/yanglingfa/pattern/ptn.html

Pattern in a Pattern

The sephirot pattern fits beautifully inside the Flower of Life pattern. Coincidence? I think, most likely, not.

Transient Equilibrium

Everything around us, and everything inside of us, is always moving, transitioning from one state to another. A steady-state is reached, and then another transition is underway, striving towards yet another steady-state, and yet another state of transient equilibrium. It continues. Life evolving.

My recent studies of sacred geometry (The Flower of Life) have me considering geometric structures as patterns of equilibrium that are never quite reached or held for long in a world that is always shimmering with movement. It's as if physical matter aspires to realize these configurations, perhaps because they are economical, and cost the least amount of energy.

There are certain arrangements, certain configurations that are more optimal for the form of physical structures. Why? Because they represent a state of equilibrium that is balanced amongst oppositional forces? This is beginning to sound very much like chemistry...

Flower of Life 6 shown above is by Peter W. Michel

http://www.petermichel.com/About.html

Rules: Paths Across Mountains of Data

This morning, I started thinking about Rules as Patterns of High Probability, like tributaries that stretch out across a vast landscape of information, as well-trodden paths across mountains of data.

How is a Rule formed? And how does one Rule become the rule of "best practice"?

In the beginning, there are no rules, just an information landscape to traverse. Over time, a path forms, based on trial and error. A Rule acts as an averaging principle that only evolves after repeatedly confronting similar situations, dynamics and consequences. A well-tested Rule could evolve into a Law, to embody a pattern with an extremely high level of persistent probability, within a broad range of contexts.