Cargo ID: 1150872
Around a decade ago I was introduced to Turing’s reaction-diffusion theories through the writing of Philip Ball. Ball’s expositions of these Turing Patterns completely seeped into my thinking; they became a chief filter through which I saw the world. I started to detect exquisite examples of these traveling waves and self-organizing systems everywhere. I tried to document them with a camera; an archive of these recordings is collected on this site.
Thanks to Ben for the education and Matt for the organization.
Forging patterns and making waves from biology to geology
The Royal Society
April 19 2015
(Text is paraphrased)
Orphanogenesis, an excerpt from the novel Diaspora
2. A second wave was added — running askew to the first, modulated with a slow steady rise — carving each ridge into a series of ascending mounds. Then a third, and a fourth, each successive wave enriching the pattern, complicating and fracturing its symmetries: defining directions, building up gradients, establishing a hierarchy of scales. The fortieth wave ploughed through an abstract topography bearing no trace of the crystalline regularity of its origins, with ridges and furrows as convoluted as the whorls of a fingerprint. Not every point had been rendered unique — but enough structure had been created to act as the framework for everything to come. So the seed gave instructions for a hundred copies of itself to be scattered across the freshly calibrated landscape.
A Thousand Years of Nonlinear History
3. Despite the many differences between them, living creatures and their inorganic counterparts share a crucial dependence on intense flows of energy and materials. In many respects the circulation is what matters, not the particular forms that it causes to emerge. As the biogeographer Ian G. Simmons puts it, “The flows of energy and mineral nutrients through an ecosystem manifest themselves as actual animals and plants of a particular species.” Our organic bodies are, in this sense, nothing but temporary coagulations in these flows: we capture in our bodies a certain portion of the flow at birth, then release it again when we die and microorganisms transform us into a new batch of raw materials.
The Chemical Basis of Morphogenesis
University of Manchester
4. It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. ( ) Such reaction-diffusion systems are considered in some detail ( ). It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. ( ) Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis.
Cymatics — A Study of Wave Phenomena and Vibration
(Text is paraphrased)
5. Whenever we look in nature, animate or inanimate, we see widespread evidence of periodic systems. Events do not take place in a continuous sequence, but are in a state of constant vibration, oscillation, undulation and pulsation. On the largest and smallest scale we find repetitive patterns: from the space lattices of mineralogy to cosmic systems — rotations, pulsations, turbulences, circulations, plasma oscillations — down to the world of atomic or even nuclear physics. Periodicity also expands to include the oceans, and the fault systems of geographical formations that affect immense areas of rock.
iPhone video of fluid dynamics in a body of water; a web of crests and troughs forms a lattice of refracted light. The dispersion of waves looks like a sped-up version of the Universe simulation on the right.
Simulation of a section of the Universe at its largest scale; a web of cosmic filaments forms a lattice of matter. These filaments are massive thread-like formations comprised of huge amounts of galaxies, gas and ‘dark matter.’ (Image: Greg Poole)
The Writing of Stones
University Press of Virginia
6. Life appears: a complex dampness, destined to an intricate future and charged with secret virtues, capable of challenge and creation. A kind of precarious slime, of surface mildew, in which a ferment is already working. A turbulent, spasmodic sap, a presage and expectation of a new way of being, breaking with mineral perpetuity and boldly exchanging it for the doubtful privilege of being able to tremble, decay, and multiply. ( ) The tissue of the universe is continuous ( ) I can scarcely refrain from suspecting some ancient, diffused magnetism; a call from the center of things; a dim, almost lost memory, or perhaps a presentiment, pointless in so puny a being, of a universal syntax.
- Link: Fluid simulation with reaction-diffusion patterns
- Link: Reaction-diffusion simulator
- Link: Fluid dynamics simulation
- Link: Fluid dynamics simulation
- Link: Jonathan McCabe Vimeo feed
- Link: Paul Prudence Twitter feed
- Link: Fractal simulation animation
- Link: Moiré simulation
- Link: Powers of Ten
- Link: Cymatics on But Does it Float — 1
- Link: Cymatics on But Does it Float — 2
- Link: Cymatics on But Does it Float — 3
- Book: Nature’s Patterns — Philip Ball
- Book: Disaspora — Greg Egan
- Book: A Thousand Years of Nonlinear History — Manuel De Landa
- Book: Cymatics: A Study of Wave Phenomena & Vibration — Hans Jenny
- Book: The Writing of Stones — Roger Caillois (PDF)
- PDF: The Chemical Basis of Morphogenesis — Alan Turing
- PDF: Cyclic Symmetric Multi-Scale Turing Patterns by Jonathan McCabe
- Video: Metabolizing Complexity — Ben Cerveny
- Video: The Augmented World Experience — Ben Cerveny
- Video: Documentary: The Secret Life of Chaos
- Video: Philip Ball on Alan Turing’s research on morphogenesis
- Video: Reaction-Diffusion-based animation
- Video: Fluid Dynamics Simulation
- Video: Documentary on Cymatics
- Video: Demonstration of Chladni Patterns
- Video: Demonstration of the Belousov-Zhabotinsky reaction
- Video: How Does Life Come From Randomness?
- Video: Belousov-Zhabotinsky reaction in cellular automata