Getting trippy with simulated chemicals
October 15, 2013 9:14 AM Subscribe
Alan Turing's paper The Chemical Basis of Morphogenesis described reaction-diffusion systems. Jonathan McCabe writes about adapting Turing's math to generate trippy images and videos.
Play with Turing-McCabe patterns and reaction-diffusion systems.
Play with Turing-McCabe patterns and reaction-diffusion systems.
Turing reaction-diffusion is used to explain "how the leopard got its spots".
Here's a nifty animal coat toy (java).
posted by bonehead at 9:23 AM on October 15, 2013
Here's a nifty animal coat toy (java).
posted by bonehead at 9:23 AM on October 15, 2013
Robert Munfo has an interesting page about the Gray-Scott reaction-diffusion system (following on from Roy David Williams' Xmorphia), which links to various software simulations and screensavers.
posted by James Scott-Brown at 9:59 AM on October 15, 2013 [3 favorites]
posted by James Scott-Brown at 9:59 AM on October 15, 2013 [3 favorites]
These of course are all numerical simulations, but it should be pointed out that it works with real chemicals, too.
posted by mr_roboto at 10:46 AM on October 15, 2013 [1 favorite]
posted by mr_roboto at 10:46 AM on October 15, 2013 [1 favorite]
Not fair that so many brains were given to one guy. I WANT MY SHARE!!!!
posted by Mental Wimp at 12:01 PM on October 15, 2013
posted by Mental Wimp at 12:01 PM on October 15, 2013
I'm pretty sure this is what triggers CASE NIGHTMARE GREEN.
posted by Static Vagabond at 12:49 PM on October 15, 2013
posted by Static Vagabond at 12:49 PM on October 15, 2013
These of course are all numerical simulations, but it should be pointed out that it works with real chemicals, too.
I'm pretty sure you and I are also evidence it works with real chemicals, too. Unless you fail the Turing test, of course.
posted by Mental Wimp at 12:52 PM on October 15, 2013 [1 favorite]
I'm pretty sure you and I are also evidence it works with real chemicals, too. Unless you fail the Turing test, of course.
posted by Mental Wimp at 12:52 PM on October 15, 2013 [1 favorite]
James Scott-Brown, I am in awe of that map!
posted by a snickering nuthatch at 1:18 PM on October 15, 2013
posted by a snickering nuthatch at 1:18 PM on October 15, 2013
I am going to have to spend some time with this new material.
The Chemical Basis of Morphogenesis
Oh I love this paper to death. I have read it over and over and each time I follow the math, I rise a little higher before I fall flat on my face.
I particularly like how Turing writes a preface:
The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading.
Elementary facts indeed.
This paper is some of Turing's last work. It shows exactly how brilliant his work was, and how misunderstood it was at the time. Today we would do this work as a cellular automatons in a digital simulation. But Turing does them all with functions, transforming infinite sets of numbers like he was flipping a bit.
If you enjoyed this, you should visit the Turing Archive and read his later works that evolved from it. For example manuscripts with Turing's notes:
A diffusion reaction theory of morphogenesis in plants
Morphogen theory of phyllotaxis. Part I. Geometrical and descriptive phyllotaxis.
Part II
Part III
But this is my favorite, handmade diagrams of morphogenetic patterns.
I particularly recommend zooming in to maximum on one of the final two diagrams. You can see the grid of his calculated diffusion reactions, and his drawings delineating the field intensities.
OMFG. There is a paper that explains these diagrams, it has been offline for years. I have just discovered, it's back online, read it: Watching the Daisies Grow: Turing and Fibbonacci Phyllotaxis. This guy had a whole site about morphogenesis, but this is the only bit that remains. And it's a really really good bit.
posted by charlie don't surf at 4:22 PM on October 15, 2013 [5 favorites]
The Chemical Basis of Morphogenesis
Oh I love this paper to death. I have read it over and over and each time I follow the math, I rise a little higher before I fall flat on my face.
I particularly like how Turing writes a preface:
The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading.
Elementary facts indeed.
This paper is some of Turing's last work. It shows exactly how brilliant his work was, and how misunderstood it was at the time. Today we would do this work as a cellular automatons in a digital simulation. But Turing does them all with functions, transforming infinite sets of numbers like he was flipping a bit.
If you enjoyed this, you should visit the Turing Archive and read his later works that evolved from it. For example manuscripts with Turing's notes:
A diffusion reaction theory of morphogenesis in plants
Morphogen theory of phyllotaxis. Part I. Geometrical and descriptive phyllotaxis.
Part II
Part III
But this is my favorite, handmade diagrams of morphogenetic patterns.
I particularly recommend zooming in to maximum on one of the final two diagrams. You can see the grid of his calculated diffusion reactions, and his drawings delineating the field intensities.
OMFG. There is a paper that explains these diagrams, it has been offline for years. I have just discovered, it's back online, read it: Watching the Daisies Grow: Turing and Fibbonacci Phyllotaxis. This guy had a whole site about morphogenesis, but this is the only bit that remains. And it's a really really good bit.
posted by charlie don't surf at 4:22 PM on October 15, 2013 [5 favorites]
Turing: The Final Years
Among his collected works, in the few, short years before mathematician Alan Turing was driven to suicide, he published "The Chemical Basis of Morphogenesis", theorizing how a standing wave-like distribution of "cannibal" and "missionary" chemicals might explain how plants and animals develop their shape and pigmentation. Blogger Jonathan Swinton focuses on this more obscure aspect of Turing's research, and reviews some of his posthumous and unpublished efforts — including one of the earliest known examples of digital computation applied to the field of biology.
posted by Blazecock Pileon at 4:29 PM on October 15, 2013
Among his collected works, in the few, short years before mathematician Alan Turing was driven to suicide, he published "The Chemical Basis of Morphogenesis", theorizing how a standing wave-like distribution of "cannibal" and "missionary" chemicals might explain how plants and animals develop their shape and pigmentation. Blogger Jonathan Swinton focuses on this more obscure aspect of Turing's research, and reviews some of his posthumous and unpublished efforts — including one of the earliest known examples of digital computation applied to the field of biology.
posted by Blazecock Pileon at 4:29 PM on October 15, 2013
The patterns are strikingly similar to things you see in nature, but it's been surprisingly hard to find reaction-diffusion happening in living things. Apparently someone finally found a real world example a couple years ago, but nobody really knows how the leopard gets its spots.
posted by nixt at 7:32 PM on October 15, 2013 [1 favorite]
posted by nixt at 7:32 PM on October 15, 2013 [1 favorite]
it's been surprisingly hard to find reaction-diffusion happening in living things
[facepalm]
Look at your fingertip.
posted by charlie don't surf at 7:44 PM on October 15, 2013 [1 favorite]
[facepalm]
Look at your fingertip.
posted by charlie don't surf at 7:44 PM on October 15, 2013 [1 favorite]
Actually, both reaction-diffusion and cell-movement models (governed by mechanical as well as chemical cues) can account for morphogenesis and animal-coat patterns. There's good reason to believe that these models act in concert to produce observed patterns that are beyond the range of either model acting alone: Bones, feathers, teeth and coat marking: a unified model.
Very different mechanisms can produce similar patterns. "How the leopard gets its spots" shows examples of Chladni patterns produced by the vibration of metal plates shaped like animal coats: Holographic interferometry used to demonstrate a theory of pattern formation in animal coats.
posted by 0rison at 9:21 PM on October 15, 2013 [3 favorites]
Very different mechanisms can produce similar patterns. "How the leopard gets its spots" shows examples of Chladni patterns produced by the vibration of metal plates shaped like animal coats: Holographic interferometry used to demonstrate a theory of pattern formation in animal coats.
posted by 0rison at 9:21 PM on October 15, 2013 [3 favorites]
Charlie, that's why I used the word "surprisingly".
Yes, RD (or resonating plates, or windblown sand) can produce fingerprint-like patterns. No, that doesn't imply that fingerprints are formed by RD (or resonance, or wind). And in fact the biologists looking for in vivo evidence for the RD theory have not found much yet, though you wouldn't know it from most of the writing on this subject.
Philip Ball's Shapes is good if you like this sort of thing.
posted by nixt at 1:27 AM on October 16, 2013 [4 favorites]
Yes, RD (or resonating plates, or windblown sand) can produce fingerprint-like patterns. No, that doesn't imply that fingerprints are formed by RD (or resonance, or wind). And in fact the biologists looking for in vivo evidence for the RD theory have not found much yet, though you wouldn't know it from most of the writing on this subject.
Philip Ball's Shapes is good if you like this sort of thing.
posted by nixt at 1:27 AM on October 16, 2013 [4 favorites]
it's been surprisingly hard to find reaction-diffusion happening in living things
[facepalm]
Look at your fingertip.
Look at your whole body.
posted by Mental Wimp at 8:21 AM on October 16, 2013
[facepalm]
Look at your fingertip.
Look at your whole body.
posted by Mental Wimp at 8:21 AM on October 16, 2013
Now look away.
posted by Joe in Australia at 6:32 PM on October 16, 2013 [3 favorites]
posted by Joe in Australia at 6:32 PM on October 16, 2013 [3 favorites]
Only vaguely related, this very interesting paper was published a few days ago.
A Turing test for free will
Before Alan Turing made his crucial contributions to the theory of computation, he studied the question of whether quantum mechanics could throw light on the nature of free will. This article investigates the roles of quantum mechanics and computation in free will. Although quantum mechanics implies that events are intrinsically unpredictable, the `pure stochasticity' of quantum mechanics adds only randomness to decision making processes, not freedom. By contrast, the theory of computation implies that even when our decisions arise from a completely deterministic decision-making process, the outcomes of that process can be intrinsically unpredictable, even to -- especially to -- ourselves. I argue that this intrinsic computational unpredictability of the decision making process is what give rise to our impression that we possess free will. Finally, I propose a `Turing test' for free will: a decision maker who passes this test will tend to believe that he, she, or it possesses free will, whether the world is deterministic or not.
I am currently tracking down some of the sources, which seem to primarily revolve around the Conway-Kochen theorem. I do not like this line of argument at all.
posted by charlie don't surf at 8:53 PM on October 21, 2013 [1 favorite]
A Turing test for free will
Before Alan Turing made his crucial contributions to the theory of computation, he studied the question of whether quantum mechanics could throw light on the nature of free will. This article investigates the roles of quantum mechanics and computation in free will. Although quantum mechanics implies that events are intrinsically unpredictable, the `pure stochasticity' of quantum mechanics adds only randomness to decision making processes, not freedom. By contrast, the theory of computation implies that even when our decisions arise from a completely deterministic decision-making process, the outcomes of that process can be intrinsically unpredictable, even to -- especially to -- ourselves. I argue that this intrinsic computational unpredictability of the decision making process is what give rise to our impression that we possess free will. Finally, I propose a `Turing test' for free will: a decision maker who passes this test will tend to believe that he, she, or it possesses free will, whether the world is deterministic or not.
I am currently tracking down some of the sources, which seem to primarily revolve around the Conway-Kochen theorem. I do not like this line of argument at all.
posted by charlie don't surf at 8:53 PM on October 21, 2013 [1 favorite]
In case there is anyone still monitoring this thread..
I was cleaning my hard drive today and I found this very interesting reprint from Scientific American on Turing's work, I will make it available for download:
How the Leopard Gets Its Spots
It discusses Turing's reaction-diffusion systems and compares them to standing wave patterns. The paper is undated but my file stamp says January 2006 so it certainly predates that.
posted by charlie don't surf at 7:30 AM on November 10, 2013 [1 favorite]
I was cleaning my hard drive today and I found this very interesting reprint from Scientific American on Turing's work, I will make it available for download:
How the Leopard Gets Its Spots
It discusses Turing's reaction-diffusion systems and compares them to standing wave patterns. The paper is undated but my file stamp says January 2006 so it certainly predates that.
posted by charlie don't surf at 7:30 AM on November 10, 2013 [1 favorite]
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