Cargo ID: 1150872

Turing Type is a gathering of short texts and a collection of personal photographs. (As well, there is an appendix for additional information.) The common thread for all, is the presence of Turing type conceptions, that is, thoughts based on or related to certain discoveries of Alan Turing. Although Turing is well known and contemporarily celebrated as the father of modern computing — he was also the progenitor of a type of mathematical biology focusing on pattern formation, which he collected and published in his Chemical Basis of Morphogenesis. Turing Type is mainly concerned with this late work.

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.

Philip Ball

Forging patterns and making waves from biology to geology

The Royal Society
April 19 2015

(Text is paraphrased)
1.            The spontaneous appearance of pattern and form in a system occurs in many types of natural process, as well as in other areas as disparate as geomorphology and criminology. Alan Turing’s stripe patterns resemble not only the skin of a zebra, tiger or angelfish, but also patterns in inanimate nature, such as the ripples in wind-blown sand. The formation of these patterns is akin to a reaction–diffusion system, which appears to have relevance not just for developmental biology but for chemistry, geomorphology, plant biology, ecology, sociology and perhaps even astrophysics; a reaction–diffusion mechanism has, for example, been suggested as the origin of spiral galaxies.


Greg Egan

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.


Manuel De Landa

A Thousand Years of Nonlinear History

Zone Books
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.


Alan Turing

The Chemical Basis of Morphogenesis

University of Manchester
Link [PDF]
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.


Hans Jenny

Cymatics — A Study of Wave Phenomena and Vibration

Link [PDF]
Cymatics (Wiki)

(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.

Stars as atoms; atoms as stars.

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.
Cosmic Filaments

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)

Roger Caillois

The Writing of Stones

University Press of Virginia
Link [PDF]
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.

Additional information:

  1. Link: Fluid simulation with reaction-diffusion patterns
  2. Link: Reaction-diffusion simulator
  3. Link: Fluid dynamics simulation
  4. Link: Fluid dynamics simulation
  5. Link: Jonathan McCabe Vimeo feed
  6. Link: Paul Prudence Twitter feed
  7. Link: Fractal simulation animation
  8. Link: Moiré simulation
  9. Link: Powers of Ten
  10. Link: Cymatics on But Does it Float — 1
  11. Link: Cymatics on But Does it Float — 2
  12. Link: Cymatics on But Does it Float — 3

  13. Book:  Nature’s Patterns — Philip Ball
  14. Book:  Disaspora — Greg Egan
  15. Book: A Thousand Years of Nonlinear History — Manuel De Landa
  16. Book:  Cymatics: A Study of Wave Phenomena & Vibration — Hans Jenny
  17. Book: The Writing of Stones — Roger Caillois (PDF)
  18. PDF: The Chemical Basis of Morphogenesis — Alan Turing
  19. PDF:  Cyclic Symmetric Multi-Scale Turing Patterns by Jonathan McCabe

  20. Video: Metabolizing Complexity — Ben Cerveny
  21. Video: The Augmented World Experience — Ben Cerveny
  22. Video: Documentary: The Secret Life of Chaos
  23. Video: Philip Ball on Alan Turing’s research on morphogenesis
  24. Video:  Reaction-Diffusion-based animation
  25. Video:   Fluid Dynamics Simulation
  26. Video:  Documentary on Cymatics
  27. Video:  Demonstration of Chladni Patterns
  28. Video:  Demonstration of the Belousov-Zhabotinsky reaction
  29. Video:  How Does Life Come From Randomness?
  30. Video:  Belousov-Zhabotinsky reaction in cellular automata