Nature indeed has favorite patterns of propagation, from sound waves to cell division — and the reproductive foundation is “self-similarity,” copying and varying the self, which encapsulates logarithms, fractals, spirals/chirals and the exemplary patterns described below. Understanding and being able to analyze the patterns that repeat across different orders of magnitude and scale will help continue to unlock meaningful and sustainable advancements in technology and consciousness. All of the patterns mentioned here product of field dynamics made visible, and they exhibit self-similarity, aka cloning or parthenogenesis, in propagation.
Bifurcation <- Branching shapes <- Linear travel
Bifurcation, like the other patterns mentioned here, is a naturally occurring phenomenon, that seems to exist to explore channels of possibility in nature, math and computing. The appearance is branching or splitting that leads to complex structures and their emergent properties. This can be viewed through both linear and non-linear lenses; linear in the computing and diagrammatic view, and non linear in nature. A beautiful example is the “dielectric breakdown” of lightning with its rapid ionization of the air and thus conductive pathways.
The photo above of the sand illustrates change or energy transfer/exchange within the sort of dynamic equilibrium in an open system, that includes the interaction of fluid or hydrodynamics with the sediment.
The behavior of bifurcation, the traveling tree!, can be mathematically described and calculated with integral calculus, or families of differential equations. And machine learning is beginning to prove extremely useful for such predictions.
Phyllotaxis ~ Radial, Axial, Spiral ~ Distribution, Light Diffraction
Related, is Phyllotaxis, a spiral or radial regular arrangement readily demonstrated by plants, is much easier to predict, based on discrete patterns or sequences. One could even say spiral phyllotaxis encompasses DNA:
DNA measures 34 angstroms long by 21 angstroms wide for each cycle of its double helix spiral. These numbers, 34 and 21, are numbers in the Fibonacci series, and their ‘golden ratio’ closely approximates phi, or 𝛷 . (1)
And a favored or ‘golden’ angle is 137.5 (2), related to optimal absorption of light and the interacting diffraction patterns involved in shaping matter.
Turing Pattern / Oscillation, Gyrification / interference, communication, growth
Next, here’s an interesting one: A ‘Turing’ pattern related to “reaction-diffusion” and producing stability or homogeneity from ‘chaos’ or uneven distribution. The ripples could be said to be a materialization of harmonics or “flow-distributed oscillation.” (3) The brain is a fascinating example of this gyrification to enhance and accommodate functionality, level of complexity and communication. And so is the developing technology of microchips and lithography – so much potential!
These three patterns are a few ways the forces of nature move for optimization, and reflect the propagation of light and sound. Our marvelous universe straddles the seemingly mysterious line between organization and primordial chaos, and all in nature reveals a purpose. Parallel advancements in computing promise to continue illuminating this and other grand designs.
1. https://www.mdpi.com/2073-8994/13/10/1949
2. https://royalsocietypublishing.org/doi/10.1098/rsif.2018.0850