Category Archives: Science

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 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.


Figure by Karna Gowda, see the full article at SIAM news.

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!

#Trypod: Favorite podcasts

March is “Trypod” Month, where podcasts are asking enthusiasts to recommend their favorites. I only started listening to podcasts last summer, but I already have several favorites. One of the reasons I took so long to try podcasts was that I hadn’t heard of many. I tried out my first podcast after reading an interesting episode, and now I’m hooked.

Podcasts are great companions to life’s chores that occupy the hands but not the brain. I listen to podcasts when I do the dishes, when I fold clothes, and when I work in the garden. I love to learn, and this way I can learn at times I couldn’t before.

I listen to quite a range of stuff, as my favorites list will show. I’m also eager for new oddball recommendations.

BackStory: American history from the experts

On BackStory, three University of Virginia professors of history discuss a topic as it has played out through American history. (In 2017, they switched to four professors.) Topics include the history of church and state in America, the history of scandal, and the history of infrastructure, among others. Backstory delights in illuminating the bizarre and exciting about history, while connecting these topics to the present day. And with professors of history, you know you’re listening to real, researched history. Hooray!

Myths and Legends Podcast: Delightful myths from around the world

Narrator Jason brings good cheer to myths, legends, and fairy tales from around the world. Whether it’s the Norse Volsung Saga, Native American stories about giant skunks that can fart you to death, or Russia’s Baba Yaga, who’s home stands on chicken legs, Myths and Legends is guaranteed fun once a week. And that doesn’t even get into the weekly creature segments, like the butter cat, who steals butter from the neighbors for his master.

Russian Rulers History Podcast: Russian rulers, history, and culture

I’m a long-time Russian history enthusiast; if you aren’t this might not be your cup of tea, but it’s one of my favorites. The host isn’t a historian, he just likes Russian history, and does a good job telling it. Nothing flashy, just the history of this massive and enigmatic country, from the time of the Kievan Rus through the present day. The first ~130 episodes cover the Russian rulers, but from there it branches out. There is a massive archive for this podcast, and it’s one of my favorites for doing chores.

Science Magazine Podcast: The week in Science from America’s premier science publication

It’s hard to find good science journalism. That’s why the Science Magazine podcast is so spectacular. Beyond being informative, Science Podcast is fun. I understand my corner of science well enough, but I didn’t have a good insight into advancements in biological studies, for example. Everyone’s read about hair-brained sounding science studies, like making shrimp walk on treadmills (yes, this is real!); the podcast reveals how these strange studies are often really clever ways to answer tough questions. Science Magazine is a product of AAAS (the American Association for the Advancement of Science), of which I am a member and highly recommend.

Stuff You Missed in History Class: Miscellaneous history from around the world

My gateway podcast. Missed in History focuses on the topics given short shrift, often focusing on women, people of color and history from Asia and Africa. Everything that isn’t commonly taught history is fair game, from the Montgolfier brothers who invented the first hot air balloon, to Maria Montessori, founder of the Montessori school, to a history of Rhodesia. This means the podcast leaps around from week to week, but it also means that if one topic doesn’t suit your fancy, another will. Missed in History also has years of archived episodes.

Nature Podcast: the week in science from the UK’s premier science publication

Science and Nature are the top publication venues in the physical sciences. And Nature has a podcast as well! Nature does a wider variety of podcasts within the main podcast–it features a monthly science fiction story and a monthly roundtable discussion, in addition to the weekly review. Nature also did a series called PastCast that discussed historical publications in the journal. The journal goes back to 1869, so there’s a lot to work with. Nature also focuses more on science in the international community.


If you haven’t heard already, today is a “supermoon.” Today, the moon is closer to the Earth than it has been since 1948. Visually, that means it will be bigger and brighter than usual. Intellectually, it’s gratifying to watch the cosmic ballet go on. Our solar system is like a Swiss clock, all the parts proceeding and, for the most part, fitting together perfectly. Winter (northern hemisphere) supermoons are slightly bigger because the Earth is closer to the sun; the sun’s gravitational power pulls the moon slightly, such that the supermoon is bigger. Astrobob explains it better here.

For more pontifications on the moon, check out What If the Moon Didn’t Exist, which I reviewed here. Below are some of my favorite photos of the moon, and a moonrise video over Chaco Canyon, New Mexico.

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Chaco Canyon moon, stars, and clouds

Fractal Art

Here in Albuquerque, mathematical art adorns the schools. We are the Fractal Capital of the World. Fractals are a kind of math that considers the multi-scale aspects of nature. In school, we learn about rectangles, circles, and triangles, but which of these shapes best represents the coastline of Great Britain?

And even if learning fractal math isn’t your path, you probably appreciate what others have done with it.  This documentary describes how lava in Star Wars was simulated using fractal approaches. Many natural objects have fractal aspects, and CGI versions of these objects utilize this approach.

I do research in nonlinear dynamics, which is a cousin to chaos theory and fractal math. Fractal math first emerged as a visual wonder with Benoit Mandelbrot; as a scientist and artist, fractals inspire me in multiple ways. I hope my forays into fractals might inspire, too!

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Surprises out west: Florissant Fossil Beds National Monument

Last week, I traveled through eastern Colorado, hitting Pike’s Peak, Rocky Mountain National Park, and the Great Sand Dunes. But the biggest surprise was a tiny national monument in central Colorado—Florissant Fossil Beds National Monument. Florissant Fossil Beds has provided fossils to the scientific community for over 100 years; an estimated 40,000-50,000 specimens of some 1500 species. As a visitor, you learn about how the fossils at Florissant formed and the era from which they came. The visitor center is full of great science and amazing fossils. A fossil learning lab is open from 1PM to 3PM. The most impressive part, though, are the massive petrified redwood stumps. The largest is 41 feet in circumference and about 10 feet high.

Scientists started coming to Florissant to document fossils in the 1870s. Unfortunately, tourists flocked to the site as well, fascinated by the redwood stumps and petrified wood. Once upon a time, petrified wood littered the landscape. Now, visitors take in the big stumps alone. The biggest stump has two blades still embedded in it, remnant of when someone tried to chop it up to sell pieces out east. Two tourist companies staked out the site and competed bitterly over traffic. One left nails at the other’s entrance; they also literally got into a shooting match.

Federal protection came very late for Florissant. Despite calls for conservation going back at least to the 1890s, it took until the 1969 for the site to gain national monument status. Before that, people wanted to divide the site up for houses. Environmentalists faced down bulldozers. Standing in the empty fields of Florissant, over an hour west of Colorado Springs and really in the middle of nowhere, it was hard to imagine why the area needed more houses. By contrast, Petrified Forest National Park gained National Monument status in 1906. When you visit Arizona’s Petrified Forest, they will tell you how much petrified wood has left the park through tourism—Petrified Forest is still littered with petrified wood while Florissant is not.

I learned a lot about fossils and fossil formation at Florissant Fossil Beds. I marveled at the great tree trunks, wondering how many more must lay still buried around me. But I think I was most struck by the story of conservation at Florissant Fossil Beds. The monument covers the fight to preserve Florissant, but it can’t editorialize. Florissant is a microcosm of when capitalism and general human interest don’t align. Many of our national lands tell the story of where the human interests won. Florissant tells a story where that interest emerged on top at the very last possible moment; I felt wistful wondering how many marvels wandered away with all the care of a tourist buying a souvenir shot glass.

If you find yourself in central Colorado, stop by Florissant for a visit. The stumps are truly other-worldly. I learned a lot about fossils. And I took a pleasant hike through an alpine meadow in the shadow of Pike’s Peak. The park implores us to imagine what the meadow was like 30 million years ago when the valley was in the flow path of a volcano. I also found myself imagining the place as a virgin bed of paleontology 150 years ago.


41 foot circumference petrified tree stump


Pike’s Peak!

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The impermanence of color: the treachery of entropy

Color seems like an easy, marvelous thing when you get that 64 color box of Crayolas as a kid. 64 sticks of pure color. But, of course, color is complicated. It can be impermanent, difficult to obtain, and toxic. To understand the life and chemistry of colors is to peek under the hood. It’s not what catches your eye, but it’s the heart of the drama.

Many paintings are known to be fading; it’s the newer paintings that draw the most concern. To some extent, the older paintings had probably already faded, but the older paintings also used old tried-and-true methods. The works of Jan van Eyck (1390-1441) are considered to be about as colorful today as when they were painted. Van Gogh’s daisies are fading. Renoir’s red has been digitally re-envisioned to show its pre-faded look.

The 1800s were a boom time of chemistry and industrialization, and the art world participated in this expansion too. 12 elements, including sodium and potassium, were discovered between 1800 and 1810. As Chemistry exploded, and new colors exploded. Mauve, the first synthetic dye, was produced in 1856 from coal tar. Renaissance painters (or their apprentices) prepared their own dyes and pigments (think of those scenes from “The Girl with the Pearl Earring” where Scarlett Johansson is grinding various things); 19th century painters bought paint from chemists. Like the disintegrating trade paperbacks of the early 1900s, when industrialization took over an old process, it was faster and cheaper, but took a while to match other characteristics. Books from the early 1800s are often far more intact than the wood-pulp books that followed them.

Artists like Van Gogh knew the strengths and limitations of their new tools. Van Gogh wrote to his brother, noting that the Impressionist paints “fade like flowers,” so he used the brightest colors he could, doing what he could to counteract impermanence. Even now, not all paints are equally durable; here’s a table for watercolors including such measures.

Today, scientists are studying the precise chemistry that causes fading using X-rays. So far, nothing can be done to stop or reverse the fading; they can only be kept away from light. At least we have the tools to imagine their former glory.

Further reading: Victoria Finlay’s Color is a great read on the chemistry of color without diving too deep technically. I reviewed it on this blog a couple of years ago. This article about the history of oil colors is also really fascinating. And finally, if you’re a chemistry buff, the scientific article about Van Gogh’s fading yellow is open source, and available to the public here.



More Awesome NASA Space Travel Posters

Thinking about a trip to Mars or Ceres? Book today! Don’t forget to ask about your Pi Day discount.

NASA is in the travel agent business again! JPL released travel posters for Mars, Venus, Jupiter, and several moons. They explore some different styles from the first set, and are cool as hell. Below are some of the preview sizes. They are available to download free at high res, suitable for printing up to 20″ x 30″.

And if you’re a vintage poster enthusiast like me, also check out the Library of Congress site. Tons of WPA posters are available free at high res, among other historical documents. (Beware, though, their site requires patience. It’s not organized for quick browsing, but there are some real gems in their collection. I linked to some of my favorites in this old post. I decorated my bathroom with them. Yes, I have a poster about syphilis in my bathroom.)  And finally, the National Parks posters are amazing vintage posters, though they aren’t free. I just made a few of my own last week.

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Proof! I did indeed print and hang the travel posters. Also in this room: a tea towel with a graphic of the Very Large Array (VLA). Nerd factor infinity!