# Turing Patterns: What do a leopard’s spots, vegetation in arid zones, and the formation of fingers have in common?

Please excuse my inconsistent posting of late, I have been deep down the rabbit hole of science. Last week, I attended the Society of Industrial and Applied Math (SIAM) dynamical systems conference. What fun!

I learned about Turing Patterns, named for mathematician Alan Turing. Complex patterns can arise from the balance between the diffusion of chemicals and the reaction of those chemicals. For this reason, Turing’s model is also called the Reaction-Diffusion model. In general, these kinds of patterns can arise when there’s some kind of competition.

This sounds abstract, but suspected examples in nature abound. Have you ever wondered how the leopard got his spots or what’s behind the patterns on seashells? We often don’t know the chemical mechanisms that produce the patterns, but we can mathematically reproduce them with generic models.

Image from wired.com discussion of Turing patterns.

Mary Silber and her grad student Karna Gowda presented research on Turing patterns in the vegetation of arid regions. When there isn’t enough precipitation to support uniform vegetation, what vegetation will you observe? If there’s too little water, their model yields a vegetation-free desert. Between “not enough” and “plenty” the model generates patterns, from spots to labyrinths to gaps. Their work expands at least two decades worth of study of Turing patterns in vegetation.

Silber and Gowda considered an area in the Horn of Africa (the bit that juts east below the Middle East). Here, stable patterns in the vegetation have been documented since the 1950s. They wanted to know how the patterns have changed with time. Have the wavelengths between vegetation bands changed? Are there signs of distress due to climate change? By comparing pictures taken by the RAF in the 1950s to recent satellite images, they found that the pattern were remarkably stable. The bands slowly travelled uphill, but they had the same wavelength and the same pattern. They only observed damage in areas with lots of new roads.

From google maps of the Horn of Africa! I screen-capped this from here.

Turing patterns have even been studied experimentally in zebrafish. Zebrafish stripes might appear stationary, but they will slowly change in response to perturbations. So scientists did just. Below is a figure from the paper. The left shows the pattern on the zebrafish, the right shows the predictions of the model.

Experimental perturbations to the patterns of zebrafish are well-predicted by the Turing model. Read more in this excellent Science paper.

The model has been used to explain the distribution of feather buds in chicks and hair follicles in mice. Turing’s equations have even been used to explain how fingers form.

If you want to learn more, the links above are a great start. And if you want to play with the patterns yourself, check out this super fun interactive. These waves aren’t stationary like the Turing patterns I described here, but they arise from similar mathematics. The interactive can make your computer work, fyi.

Reaction-diffusion pattern I generated with this online interactive. It’s super fun!

# The FODMAP Diet: An IBS diet based upon peer-reviewed science

I’m extremely lactose intolerant. What this means, biologically, is that I no longer produce enough lactase to process lactose sugar. Because I can’t process lactose in my small intestine, it moves on intact to my large intestine where bacteria eat the sugar. The byproduct of their digestion, gas, causes bloating, pain, cramping and, well, you know the rest.

#### What is IBS and what causes it?

Irritable Bowel Syndrome (IBS) is an incredibly common malady, affecting 6-46% of the population, depending upon the study. It’s a diagnosis resulting from the lack of a diagnosis; it’s diarrhea, bloating, stomach pain, and cramping that can’t be explained by celiac disease, lactose intolerance, fructose intolerance, or other understood gut disorders.

IBS is thought to be caused by visceral hypersensitivity, or over-sensitivity to pressure on the intestines. Imagine two people eat broccoli and get a bit gassy: the person with IBS would feel pain and discomfort while the other person might be bloated but otherwise fine.

It’s often implied that IBS is psychological as much as physiological. Anxiety and depression are common in people with IBS. In my experience, the perceived psychological component, the lack of simple treatments, and the lack of life-threatening consequences can lead doctors to be blasé about IBS. They recommend fiber, exercise, and routine, and shrug if that does little. Small wonder that people might feel blue. But gut science is improving, and the FODMAP approach is a new and widely successful strategy for reducing the symptoms of IBS.

#### What is the FODMAP approach, and what is different about it?

The FODMAP diet is based upon known biochemistry and the hypothesis that visceral hypersensitivity causes IBS. There are many molecules that, like my undigested lactose, tend to be digested in the large intestine and produce gas. The FODMAP diet eliminates a wide range of such molecules.

FODMAP, introduced in 2005 by Monash University, is a peer-reviewed diet based upon a concrete biological hypothesis supported and improved by scientific trials. It is not a weight-loss diet. FODMAP stands for Fermentable Oligo- Di- and Mono- Saccharides And Polyols. Catchy, right? But the concept is simple—FODMAPs are short-chain sugars that we know most people digest poorly (meaning bacteria digest them), and you avoid FODMAPs on the FODMAP diet. (For the biochemists, that means avoiding fructans (oligosaccharide), lactose (disaccharide), fructose (monosaccharide), and all sugar alcohols such sorbitol (polyols).)

Many other diets have questionable scientific bases and are profit driven. The Atkins Diet was published by a cardiologist who never published any peer-reviewed work, but several books. The Paleo Diet was published by an “exercise scientist untrained in paleobiology”. This is not to say that these diets cannot be beneficial in any way. But they have not been tested and refined in the way the FODMAP diet has been, and their fundamental science is hazier. Putting the cart before the horse, they have been developed first for profit, and then researched afterwards, often with mixed results. To be fair, the scientific process is slow and contentious and doesn’t always lend itself well to studies as broad and complex as diet. But FODMAP was developed, tested, and improved using the scientific process. If you’re skeptical of diets, as I am, you can read up and convince yourself that this diet has a reasonable basis and good results.

#### What’s a FODMAP diet like?

If you are considering a FODMAP diet, you will have to do some research, and be able to prepare food often from scratch. The internet is a phenomenal tool, and there are even some dieticians you can consult online. FODMAP sensitivity is not the same thing as an allergy. You don’t have to absolutely eliminate FODMAP foods, you simply must aim to minimize them for a period of time.

To follow the FODMAP diet, you avoid FODMAP-laden foods for two weeks to two months (different sources vary in their recommendations, and provide rationales). After this time, you re-introduce foods in a controlled manner to identify trigger foods. Most IBS-sufferers are not sensitive to all FODMAPs. Many people report benefits within a few days of starting the diet, and 70% of IBS patients in peer-reviewed studies reported improvements following the diet. I personally had much less bloating within a few days. Following a FODMAP diet revealed that some of my symptoms are due to gastritis, which I’m now treating. I see now that I’ve had gastritis symptoms for a while, but I was unable to separate various gastrointestinal symptoms before this diet. I remain on the full FODMAP diet after three months, but I have eliminated one side issue.

#### What foods are and aren’t allowed?

Following the most basic level of the FODMAP diet, one avoids all garlic, onion, and gluten-containing foods. It is not a gluten-free diet, but grains containing gluten overlap almost perfectly with grains containing the FODMAP fructan. Beer happily is the major exception; it is FODMAP-free due to the fermentation process.

I consider the FODMAP approach an alternative way of categorizing foods. There is a common perception that vegetables and fruit are healthful, and grains and meat are less healthful. At least from the perspective of IBS, that is not a useful framework. On the FODMAP diet, meats are okay. Roughly half of grains, dairy, vegetables and fruit contain FODMAPs, and these are avoided on the diet. Specifically, greens and squash are okay, but broccoli, leeks, and  brussels sprouts aren’t. Citrus and melon are okay, but peaches, cherries, and figs aren’t. Lactose-free milk and hard cheeses are okay, and ice cream, fresh cheeses, and sour cream aren’t.

For those considering the diet, this is my favorite exhaustive list of allowed and disallowed foods.

#### TL;DR

In short, the FODMAP diet requires research and it’s a pain to follow, but it offers real promise to the numerous people suffering from IBS. If you’re considering the diet yourself, good luck. I hope this provided a better explanation of the topic than the sources I encountered when trying to understand this diet. To others, maybe this will help explain why your friend has such a fiddly diet, and why you should support them.

# Book review: What If the Moon Didn’t Exist? (Neil F. Comins 1993)

What If the Moon Didn’t Exist? is a book that asks just that– what would Earth be like if the ancient collision that led to our present-day moon never happened and the Earth had no moon? Comins, a professor of astronomy and physics at the University of Maine, also asks what if the moon was closer, what if the Earth was smaller, what if the Earth was tilted like Uranus, among other questions.

This book is a must-have for science fiction writers interested in writing about other planets. Comins follows through on his initial questions in a way that science fiction enthusiasts will appreciate. If the moon didn’t exist, the moon’s tidal pull wouldn’t exist. Due to the lack of that tidal pull, Earth’s day would be 8 hours long, not 24. Which would cause much stronger winds and storms. And the tides would be lower. Which would impede the transition of  life from water to land. And that life would have to adapt to the windy, stormy short days. Would that life develop hearing, with all that wind? Would plants opt for low-surface-area needles instead of broad leaves? Assuming humans developed, how would early man tell time without a lunar cycle? Would this influence man’s scientific development? Comins asks and suggests answers to all of these questions. It’s exciting food for thought, and it made me want to go dream up worlds of my own.

What If the Moon Didn’t Exist? is over twenty years old now. I expect some of the science in it may be outdated (none that I actually noticed, but given the advances in planetary science since 1993, it seems likely). However, the logic the book employs is sound, and I still found it very stimulating. And in researching this post, I discovered two more recent books my Comins: What If the Earth Had Two Moons? written in 2011 and The Hazards of Space Travel: A Tourist’s Guide written in 2007. They seem similar in tenor and I expect to like them too.

# Fun Science: Two metals in contact do fun stuff

Have you ever made lasagna, and later discovered black spots or holes on the tin foil you used to cover it? Those spots are due to bimetallic or galvanic corrosion. Galvanic corrosion is an electrochemical process that occurs when two different metals contact through an electrolyte. Any two metals or alloys can experience galvanic corrosion, but pairs with dissimilar potentials will experience more. The potential of a metal is an inherent property of that metal, like density or hardness. Galvanic corrosion can be a very destructive force, or it can be exploited to make electrical current in a battery. In the case of the lasagna, the lasagna functions as the electrolyte, the pan as one metal, and the tin foil as the second metal.

### How to make a simple battery at home

The first battery was invented in 1800 by Alessandro Volta. It was called the voltaic pile, and it was composed of a stack of zinc and copper disks.

A voltaic pile, the earliest kind of battery. Voltaic piles were used to discover many elements and to study electricity (credit: wikimedia commons)

If you have coins, you can make a battery. US pennies are zinc coated with pure copper and US nickels are 75% copper.

Battery 1 (weak, but easy): You can make a weak battery by stacking pennies alternated with nickels. Just separate the coins with paper towels soaked in vinegar, which will serve as the electrolyte. Here’s a great summary of some experiments you can do with this system. If you have a multimeter, you can measure the voltage of your system; the more alternating sets of coins, the higher the voltage. This battery won’t be powerful enough to light an LED, but if you keep it wet for a few days, you will be able to see the effects of the corrosion on the coins.

Battery 2 (strong, but more work): If you’re more ambitious, you can sand the copper off one side of the pennies, and create a battery from just pennies. A few pennies like this can easily light LEDs.The video below shows how to make battery 2.

Battery 2 is much more powerful because the metals in battery 2 (the zinc of the penny’s core and the copper of the penny’s surface) have a higher difference in potential than those in battery 1 (the 75% copper of the 5 cent coin and the pure copper of the penny surface). The farther apart two substances are on the galvanic series, the more voltage there will be.

### Galvanic corrosion and the Statue of Liberty

The Statue of Liberty has an iron skeleton covered by a thin layer of copper. It was built with insulators between the copper and iron to prevent corrosion, but these insulators broke down. The Statue of Liberty was extensively renovated in the 1980s to repair damage from this corrosion.

Galvanic corrosion occurs in a lot of systems. If you use washers that are a different kind of metal than your screw, galvanic corrosion will occur. Galvanic corrosion can get even trickier: alloys that contain more than one kind of metal are composed of crystal grains that may vary slightly in composition. Galvanic corrosion can occur in an alloy between grain boundaries!

The bolts are a different kind of stainless steel, which has led to corrosion (credit: wikimedia commons)

Fortunately, we have methods for combatting corrosion. Corrosion only eats away at the lower potential metal. So engineers often design less critical pieces out of lower potential metals, so that they are sacrificial. Galvanic and other kinds of corrosion are major topics of research, relevant to boat construction, bridges, high temperature processing, and more. And thanks to galvanic corrosion, you can power a light with just pennies.

# Fun science: An easy fractal to make at home

Viscous fingering is a fractal pattern that occurs when a less viscous (or thick) fluid spreads through a more viscous (or thick) fluid. Such systems are present in oil extraction, when we pump one fluid underground to push another one out. Fractals are common in nature even though they’re new to our mathematics, and they are beautiful.

The pictures in this post were created with basic watercolor paints using one simple principle: water containing paint is more viscous than regular water. It’s easy to try at home!

For the top picture, I laid down red paint. Before the paint dried, I added salt, then let the square dry. Water from the still-damp paper rushed to the salt (because of entropy, systems tend towards uniform distributions of things if they can help it– in this case, the lowest energy state is to have a uniform distribution of salt). But because paint molecules are larger than water molecules, they don’t move as well. The water that accumulates around the salt has less paint than the water in the rest of the paper, and thus we have a less viscous fluid spreading into a more viscous one. Try it at home! If the paint is too wet or too dry when you add the salt, the results won’t be as dramatic, so play around a bit. Larger salt crystals can be especially fun.

For the three pictures below, I simply placed a drop of water into a damp square of paint. The patterns vary depending upon the size of my drop, the wetness of the paint, and the paint color (the chemistry of which influences the viscosity of the paint).

Below are a couple of examples from the University of Alberta of viscous fingering with pentane into oil and water into oil. This particular research aims to improve the flow rate of oil during extraction. And it looks pretty similar to some humble watercolors.

Left: pentane displacing mineral oil. Right: Water displacing mineral oil (University of Alberta).

# Food and science: Why are peppers hot?

Chili peppers, such as jalapeños and serranos and habañeros, are hot because they contain a chemical called capsaicin, which is an irritant to humans.

Why capsaicin?

If it is advantageous to plants to spread their seeds, why do the fruits (peppers) contain a chemical that repels animals? It turns out that birds are not sensitive to the effects of capsaicin. Thus, capsaicin repels animals whose chewing action may destroy the seed while not repelling birds. Additionally, capsaicin may function as a antifungal.

What does capsaicin do, chemically?

Capsaicin binds to receptors for heat and pain called vanilloid receptors. Capsaicin causes the receptor’s neuron to fire, which normally occurs at higher temperatures; thus, the brain interprets this neuron signal as sensing heat.

Capsaicin is just one kind of vanilloid compound; vanilla is another member of the vanilloid family, with a similar structure, but it does not act on vanilloid receptors. Now I wonder if peppers taste at all like vanilla to birds. A mystery for the ages.

Capsaicin in peppers

As you may have noticed, some peppers are hotter than others. This is because some contain more capsaicin and related chemicals than others. The relative hotness of peppers is measured by the Scoville scale. According to this scale, habañeros are a few times hotter than ají peppers which are a few times hotter than chipotle peppers. Bell peppers actually don’t contain capsaicin due to a recessive trait.

Contrary to what I learned growing up, the seeds don’t contain capsaicin. However, the pith that surrounds the seeds has the highest concentration. This may be why the hottest peppers look like wrinkly sphinx cats; they are just packed with pith (such as the Carolina Reaper pepper, bottom). You can reduce the hotness of a pepper for cooking by preferentially removing the white spines, which is the pith.

Habañero peppers have a Scoville rating of roughly 500,000. Pure capsaicin has a rating of 16 million. Some chemical called resiniferatoxin found in Moroccan cacti has a rating of 16 billion (1,000 times higher!). 40 grams of the stuff can kill a person.

So, there’s your overview of peppers for this Friday. Don’t consider this a challenge to go find that Moroccan cactus, but when your lips tingle after eating salsa, perhaps think of capsaicin.

Carolina reaper peppers, one of the hottest according to the Scoville Scale. Just look at the wrinkles! (Wikipedia)

# Food and Science: Caramelization and the Maillard Reaction

When we cook food, we want it to be as flavorful as possible. Two types of chemical reactions contribute to browning; both of these reactions create hundreds or thousands of other molecules, which then add aroma and flavor. The higher temperature reaction you may be familiar with: caramelization is the breakdown and reaction of sugars. The Maillard reaction occurs at slightly lower temperatures (still usually above the boiling point of water); this reaction occurs between the amino acids of proteins and sugars.

Both of these reactions are so complex that scientists don’t know everything that occurs during them. We understand the basic nature of each reaction, but any plant or animal food contains literally thousands of different molecules that can all react together. Fortunately, we can still implement the process without a full understanding (and we have been for millennia), and a lot of very nice foods undergo either or both reactions.

The Maillard reaction and caramelization often occur at the same time, and produce similar results visually, so they can be tough to separate. If something contains both proteins and sugars, both reactions can occur with heat. Fortunately, they both taste good. They’re also easy to do at home. If you want to brown your food, get a skillet nice and hot. Make sure you’ve patted the food dry (this allows the surface to get hotter than the boiling point of water, thus allowing the reactions to occur), and sear away.

# Fun science: the smell of lavender

This weekend, I visited a lavender farm, and thus smelled a lot of lavender. The sense of smell is really an amazing thing. Our vision processes light waves, our hearing processes sound waves– but smell processes many kinds of molecules at concentrations down to parts per billion. We tend to think of smell as a less important sense, but from a scientific standpoint, it’s amazing.

How does smell work?

The short answer is, we don’t fully know. We know receptors recognize different parts of molecules like ketones, alcohols and aldehydes. We don’t know how the brain assembles all the information from the various receptors. Some studies suggest that groups of neurons synchronize in different ways for different scents, while other studies suggest that the locations of receptors that fire create a spatial pattern for each smell. You can find further reading here, but fair warning, it’s tough material.

How sensitive is smell?

We can detect methyl mercaptan, the scent added to natural gas so that we can smell leaks (also the smell of asparagus pee!), down to parts per billion (ppb).

We can also tell the difference between very similar compounds. Linalool, the primary component of lavender oil, exists in two configurations called enantiomers. Both contain the same elements linked in the same way, but the two are mirror images. The left-handed linalool is the primary component of coriander seed and sweet orange flowers. The right-handed linalool is the primary component of lavender and sweet basil. (L)-linalool is sweeter and detectable to 7.4 ppb while (R)-linalool is woodier and detectable to 0.8 ppb.

Left:Left-handed linalool, the primary smell of coriander seed. Right: right-handed linalool, the primary smell of lavender oil. Image from Wikimedia commons.

Smell and Emotions

Studies suggest that the smell of lavender relieves anxiety and can promote sleep. Smell is strongly tied to emotions; the same parts of the brain that process smell store emotional memories.

I wonder if this connection is partially why we discount smell; smell is at its basic core tied to emotions rather than logic. It’s hard to put a smell into words, and science understands our others senses far better. I stood in the room full of lavender, remembering my last visit to a lavender farm with my family, and thought about how amazingly complex our response to little molecules can be.

# Fun science: how does figure skating work?

How does figure skating work? In short, we don’t fully know. You may have learned in science class that the pressure of the blade causes the ice to melt. Water does have the unusual property that solid ice is less dense than liquid water, and ice will melt under sufficient pressure. The thing is, the weight of a human body on an ice skate isn’t enough pressure to induce that melting.

Phase diagram for water. At normal atmospheric pressure, water freezes (to ice I, or normal ice) at 32 F or 273 K. At higher pressures, the freezing point is suppressed, as shown by the solid black line between the blue and white regions at the bottom. (Figure credit, Wikimedia)

So, if not the weight of the skater, what allows the blade to slide along? Well, there is a layer of liquid at the interface of the blade which allows the skater to glide. Denizens of very cold climates know that at sufficiently cold temperatures, skates do start sticking and catching on the ice (source: my mom’s many winters in Wisconsin, and science). Our best guess right now is that the surface properties of ice differ from the properties of the bulk. Perhaps at the surface of ice, the pressure *is* sufficient to cause melting (at temperatures near enough to freezing).

The difference between bulk properties (the properties of a big chunk of something) and surface and scale-related properties is increasingly studied. Nano-scale gold exhibits a wide variety of properties depending upon particle size, as you can see in the image below. Such colloidal gold is used in a variety of medical applications such as tumor detection and drug delivery.

Solution colors change as the gold particle sizes change. (image source Wikimedia).

When things like water and figure skating are still mysterious, who says science doesn’t leave room for wonder? Given the relatively few forces interacting in such systems, I find the richness of variation we observe entrancing. This Olympics, I’ll watch the athletes skate and consider the angstrom-scale world on which our lives glide.

# Fun science: more crystals!

Months ago, I posted about the collection of crystals and minerals at the Smithsonian Natural History Museum. Well, I went again, this time armed with a nicer (and heavier!) camera, and below are a few of the finds.

Quartz: quartz is a very common type of type of mineral (the second most common after feldspar), made up of silicon and oxygen. This variation is called agate. I used to buy agate slices as a kid, but the Smithsonian’s are slightly fancier.

Another example of quartz. This one arose in a piece of petrified wood. I like this one because it looks like a painting of a setting sun behind a row of pine trees–almost Japanese.

Malachite with azurite: both malachite and azurite are compounds of copper with oxygen, carbon, and hydrogen. The two differ only in the ratios. By geological standards, this rock formed somewhat quickly. We can tell this because the crystals are numerous and small. Single, large crystals form more slowly. This is why you should make ice cream at low temperatures, because when you freeze it quickly, many tiny crystals form, producing a better texture.

Pyrite: As you may see, pyrite, or fool’s gold, has a cubic crystalline structure. Pyrite is composed of iron and sulfur.

Calcite with duftite inclusions: Calcite is known for its optical properties such as birefringence. It was used as a material for gun sights in World War 2. Duftite is a compound of lead, copper, and arsenic. It is the duftite that gives the distinctive green color. I think of this as the kiwi mineral, as it even has the seeds.