News
Sunflowers make small moves to maximize their Sun exposure – physicists can model them to predict how they grow
Charles Darwin’s detailed observations of plant movements, such as sunflower circumnutation and self-organization, reveal how randomness helps plants optimize growth and adapt to their environments. Sunflowers!
Last Updated on March 6, 2026 by Daily News Staff
Chantal Nguyen, University of Colorado Boulder
Sunflowers make small moves to maximize their Sun exposure – physicists can model them to predict how they grow
Most of us aren’t spending our days watching our houseplants grow. We see their signs of life only occasionally – a new leaf unfurled, a stem leaning toward the window.
But in the summer of 1863, Charles Darwin lay ill in bed, with nothing to do but watch his plants so closely that he could detect their small movements to and fro. The tendrils from his cucumber plants swept in circles until they encountered a stick, which they proceeded to twine around.
“I am getting very much amused by my tendrils,” he wrote.
This amusement blossomed into a decadeslong fascination with the little-noticed world of plant movements. He compiled his detailed observations and experiments in a 1880 book called “The Power of Movement in Plants.”
In one study, he traced the motion of a carnation leaf every few hours over the course of three days, revealing an irregular looping, jagged path. The swoops of cucumber tendrils and the zags of carnation leaves are examples of inherent, ubiquitous plant movements called circumnutations – from the Latin circum, meaning circle, and nutare, meaning to nod.
Circumnutations vary in size, regularity and timescale across plant species. But their exact function remains unclear.
I’m a physicist interested in understanding collective behavior in living systems. Like Darwin, I’m captivated by circumnutations, since they may underlie more complex phenomena in groups of plants.
Sunflower patterns
A 2017 study revealed a fascinating observation that got my colleagues and me wondering about the role circumnutations could play in plant growth patterns. In this study, researchers found that sunflowers grown in a dense row naturally formed a near-perfect zigzag pattern, with each plant leaning away from the row in alternating directions.
This pattern allowed the plants to avoid shade from their neighbors and maximize their exposure to sunlight. These sunflowers flourished.
Researchers then planted some plants at the same density but constrained them so that they could grow only upright without leaning. These constrained plants produced less oil than the plants that could lean and get the maximum amount of sun.
While farmers can’t grow their sunflowers quite this close together due to the potential for disease spread, in the future they may be able to use these patterns to come up with new planting strategies.
Self-organization and randomness
This spontaneous pattern formation is a neat example of self-organization in nature. Self-organization refers to when initially disordered systems, such as a jungle of plants or a swarm of bees, achieve order without anything controlling them. Order emerges from the interactions between individual members of the system and their interactions with the environment.
Somewhat counterintuitively, noise – also called randomness – facilitates self-organization. Consider a colony of ants.
Ants secrete pheromones behind them as they crawl toward a food source. Other ants find this food source by following the pheromone trails, and they further reinforce the trail they took by secreting their own pheromones in turn. Over time, the ants converge on the best path to the food, and a single trail prevails.
But if a shorter path were to become possible, the ants would not necessarily find this path just by following the existing trail.
If a few ants were to randomly deviate from the trail, though, they might stumble onto the shorter path and create a new trail. So this randomness injects a spontaneous change into the ants’ system that allows them to explore alternative scenarios.
Eventually, more ants would follow the new trail, and soon the shorter path would prevail. This randomness helps the ants adapt to changes in the environment, as a few ants spontaneously seek out more direct ways to their food source.
In biology, self-organized systems can be found at a range of scales, from the patterns of proteins inside cells to the socially complex colonies of honeybees that collectively build nests and forage for nectar.
Randomness in sunflower self-organization
So, could random, irregular circumnutations underpin the sunflowers’ self-organization?
My colleagues and I set out to explore this question by following the growth of young sunflowers we planted in the lab. Using cameras that imaged the plants every five minutes, we tracked the movement of the plants to see their circumnutatory paths.
We saw some loops and spirals, and lots of jagged movements. These ultimately appeared largely random, much like Darwin’s carnation. But when we placed the plants together in rows, they began to move away from one another, forming the same zigzag configurations that we’d seen in the previous study.
We analyzed the plants’ circumnutations and found that at any given time, the direction of the plant’s motion appeared completely independent of how it was moving about half an hour earlier. If you measured a plant’s motion once every 30 minutes, it would appear to be moving in a completely random way.
We also measured how much the plant’s leaves grew over the course of two weeks. By putting all of these results together, we sketched a picture of how a plant moved and grew on its own. This information allowed us to computationally model a sunflower and simulate how it behaves over the course of its growth.
A sunflower model
We modeled each plant simply as a circular crown on a stem, with the crown expanding according to the growth rate we measured experimentally. The simulated plant moved in a completely random way, taking a “step” every half hour.
We created the model sunflowers with circumnutations of lower or higher intensity by tweaking the step sizes. At one end of the spectrum, sunflowers were much more likely to take tiny steps than big ones, leading to slow, minimal movement on average. At the other end were sunflowers that are equally as likely to take large steps as small steps, resulting in highly irregular movement. The real sunflowers we observed in our experiment were somewhere in the middle.
Plants require light to grow and have evolved the ability to detect shade and alter the direction of their growth in response.
We wanted our model sunflowers to do the same thing. So, we made it so that two plants that get too close to each other’s shade begin to lean away in opposite directions.
Finally, we wanted to see whether we could replicate the zigzag pattern we’d observed with the real sunflowers in our model.
First, we set the model sunflowers to make small circumnutations. Their shade avoidance responses pushed them away from each other, but that wasn’t enough to produce the zigzag – the model plants stayed stuck in a line. In physics, we would call this a “frustrated” system.
Then, we set the plants to make large circumnutations. The plants started moving in random patterns that often brought the plants closer together rather than farther apart. Again, no zigzag pattern like we’d seen in the field.
But when we set the model plants to make moderately large movements, similar to our experimental measurements, the plants could self-organize into a zigzag pattern that gave each sunflower optimal exposure to light.
So, we showed that these random, irregular movements helped the plants explore their surroundings to find desirable arrangements that benefited their growth.
Plants are much more dynamic than people give them credit for. By taking the time to follow them, scientists and farmers can unlock their secrets and use plants’ movement to their advantage.
Chantal Nguyen, Postdoctoral Associate at the BioFrontiers Institute, University of Colorado Boulder
This article is republished from The Conversation under a Creative Commons license. Read the original article.
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Every year on the first Friday in August, beer lovers around the world come together to celebrate International Beer Day. In 2026, the celebration falls on Friday, August 7, offering the perfect opportunity to discover new brews, support local breweries, and enjoy time with friends.
Founded in 2007 in Santa Cruz, California, International Beer Day has grown into a global event observed in dozens of countries. The celebration recognizes not only the beverage itself but also the brewers, bartenders, servers, and everyone who helps bring beer from the brewery to your glass.
Whether you’re a fan of crisp lagers, hoppy IPAs, rich stouts, refreshing wheat beers, or adventurous sour ales, International Beer Day is a great excuse to step outside your comfort zone and sample something new. Many breweries and pubs celebrate with special releases, tasting flights, live entertainment, brewery tours, and food pairings.
As the craft beer movement continues to flourish across the United States, this annual celebration is also a reminder of the creativity and community that local breweries bring to neighborhoods large and small.
If you decide to celebrate, remember to drink responsibly, arrange for a designated driver or rideshare if needed, and support your favorite local brewery.
Cheers to International Beer Day!
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From celebratory parties to casual get-togethers, hosting is a wonderful way to bring people together, share laughs and make memories. Of course, planning and hosting can be quite a bit of work, so a little preparation can go a long way to ensure an enjoyable time for everyone, including the host. - The Nutrient-Packed Fruit Families are Adding to Their Fruit Bowls
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Economy
Donor States vs. Recipient States: Where Does Your Federal Tax Dollar Go?
Some states send Washington more money than they receive, while others receive considerably more federal spending. Here’s what “donor state” really means—and why the numbers don’t necessarily measure government dependency.
Every year, Americans send trillions of dollars to Washington through income taxes, payroll taxes, corporate taxes and other federal revenues. The federal government then sends trillions back across the country through Social Security, Medicare, Medicaid, military spending, federal salaries, contracts, grants, infrastructure projects and dozens of other programs.
But the money doesn’t necessarily return to the states in the same proportions in which it was collected.
That’s where the terms “donor state” and “recipient state” come in.
What Is a Donor State?
Simply put, a donor state sends more money to the federal government than it receives back in federal spending.
Imagine taxpayers and businesses in a state contribute $100 billion to the federal government during a year. If federal spending within that state totals only $80 billion, the state has effectively contributed $20 billion more to the federal government than it received.
A recipient state experiences the opposite: federal expenditures within the state exceed the amount collected there in federal revenue.
These aren’t official federal government classifications, however. They’re terms commonly used by researchers analyzing the flow of money between individual states and Washington.
Only Three Donor States in 2023?
According to an August 2025 analysis from the Rockefeller Institute of Government using preliminary federal fiscal year 2023 data, only three states had negative balances—meaning they contributed more federal revenue than they received in federal expenditures.
Those states were:
New Jersey: approximately $18.9 billion more contributed than received.
Massachusetts: approximately $6.8 billion more contributed than received.
Washington: approximately $54 million more contributed than received.
At first glance, that might suggest nearly every other state depends financially on those three states.
The reality is considerably more complicated.
COVID Changed the Numbers
Historically, several wealthy states—including California and New York—have frequently appeared on the donor side of the equation.
The enormous federal response to the COVID-19 pandemic disrupted that pattern.
Trillions of dollars in extraordinary federal spending flowed into states through stimulus payments, business assistance, unemployment programs, healthcare funding, state and local government assistance and other programs.
Even after the emergency phase of the pandemic ended, some of those expenditures continued influencing federal balance-of-payments calculations.
That’s one reason examining a single year can produce a misleading picture.
California: Recipient Today, Historical Donor
California provides perhaps the best example.
In fiscal year 2023, California technically received slightly more federal spending than it contributed—approximately $342 more per person.
But look at the longer-term numbers and the picture changes.
Using a nine-year average that excludes COVID-related spending, Rockefeller Institute researchers calculated California’s average balance at approximately negative $29 billion.
In other words, over a more typical period, California has historically contributed substantially more to the federal government than it received.
Its enormous economy, high incomes and large number of taxpayers generate tremendous amounts of federal revenue.
New York Tells a Similar Story
New York has also historically ranked among America’s major donor states.
Yet in 2023, New York had a positive federal balance of approximately $13.3 billion, receiving roughly $1.04 in federal expenditures for every $1 it contributed.
Researchers attributed much of the change from New York’s historical pattern to lingering pandemic-era federal expenditures.
As those programs disappear from the calculations, New York could return to its traditional position as a donor state.
Arizona Is a Net Recipient
Arizona presents a different picture.
Over the Rockefeller Institute’s nine-year analysis, Arizona averaged a positive federal balance of approximately $44.5 billion.
Even after excluding COVID-related spending, Arizona’s average remained positive at roughly $35.3 billion.
That means federal expenditures flowing into Arizona have substantially exceeded federal revenue collected from the state.
But that doesn’t mean Arizona simply receives tens of billions of dollars in “welfare.”
Federal spending includes far more than public assistance.
Arizona hosts military installations, federal lands and agencies, defense and aerospace operations, veterans programs and a significant retiree population receiving Social Security and Medicare.
All of those expenditures count toward the state’s federal balance.
Texas Receives More Than It Sends
Texas also had a substantial positive balance in 2023.
Federal expenditures exceeded revenues collected from Texas by approximately $80 billion, making it one of the country’s largest net recipients in total dollars that year.
Again, the number needs context.
Texas is home to major military installations, NASA operations, defense contractors, federal infrastructure projects and millions of Social Security and Medicare recipients.
Those federal dollars all count as money flowing back into the state.
The Surprising Leader: Virginia
If recipient-state status simply meant dependency on federal welfare programs, Virginia would seem like an unlikely candidate to lead the country.
Yet Virginia recorded the nation’s largest positive federal balance in 2023 at approximately $145.4 billion.
Why?
Location.
Virginia sits next to Washington, D.C., and contains an enormous concentration of federal employees, military installations, government contractors and defense spending.
Neighboring Maryland ranked second with a positive balance of approximately $81.1 billion.
The numbers illustrate why federal balance-of-payments statistics should not automatically be interpreted as measurements of welfare dependency.
A recipient state isn’t necessarily a “welfare state.” Federal expenditures include Social Security, Medicare, military installations, defense contracts, federal salaries, research, infrastructure, grants and other programs.
Where Does the Federal Money Actually Go?
Federal expenditures flowing into a state can include:
- Social Security
- Medicare and Medicaid
- Military bases and personnel
- Defense contracts
- Federal employee salaries
- Highway and transit funding
- Scientific and university research
- Agricultural programs
- Veterans benefits
- Disaster assistance
- Federal grants
- Infrastructure projects
- Federal agency operations
A state containing a large military installation, federal laboratory or government agency can therefore receive billions of federal dollars without that money having anything to do with traditional public assistance programs.
Why Wealthier States Often Become Donors
Federal income taxes are progressive.
People with higher incomes generally pay a larger percentage of their income in federal income taxes.
States containing large concentrations of high-income households and highly profitable companies can consequently generate enormous amounts of federal revenue.
That helps explain why states such as California, New York, New Jersey and Massachusetts have historically appeared frequently among net contributors.
The federal government doesn’t earmark the taxes collected in California exclusively for California.
The money enters the national treasury and helps finance programs throughout the United States.
In that sense, federal taxation intentionally redistributes resources geographically as well as economically.
So Are Donor States “Subsidizing” Recipient States?
In a broad accounting sense, yes.
Federal revenue collected disproportionately from some states helps finance federal expenditures occurring elsewhere.
But describing the relationship simply as one state “paying for” another leaves out important context.
Federal spending follows national priorities rather than state borders.
A Navy base in Virginia protects the entire country. NASA facilities in Texas conduct missions funded by taxpayers nationwide. Social Security benefits paid to a retiree in Arizona may reflect payroll taxes that person paid while working decades earlier in California, Illinois or New York.
Americans and businesses also move between states throughout their lives.
The federal system was never designed to ensure that every dollar collected within a state’s borders would eventually return to that same state.
The Bigger Picture
The donor-state debate is often used as political ammunition, particularly when politicians argue about which parts of the country are supporting others.
The numbers are real, but they require context.
A state can move from donor to recipient status because of a recession, natural disaster, military spending, demographic changes, infrastructure investments or extraordinary events such as the COVID-19 pandemic.
That’s why examining several years of data generally tells us more than looking at a single year.
Ultimately, the donor-versus-recipient calculation reveals something fundamental about the United States:
Federal taxes don’t remain where they’re collected.
They become part of a national pool used to fund programs, obligations and investments across all 50 states.
And depending on where you live, your state may be putting more into that pool—or taking more out—at any particular moment.
Related External Links
- Rockefeller Institute of Government – 2025 Balance of Payments Report
- USAspending.gov – Explore Federal Government Spending
- USAspending.gov – Federal Spending Guide
- IRS – Individual Income Tax Data by State
- IRS – Federal Taxes Collected by State
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Food Truths
The Truth About the “Chemical” in McDonald’s Burger Buns: Should Consumers Be Concerned?
What’s in the Burger Buns:The “yoga mat chemical” controversy changed how consumers view food additives. Here’s what azodicarbonamide is, why McDonald’s removed it, and what the science actually says.
For years, headlines and social media posts have warned consumers about a so-called “yoga mat chemical” found in hamburger buns served by major fast-food chains. The claims sparked widespread concern, prompted petitions, and eventually led several restaurant companies—including McDonald’s—to change their recipes.
But what was the chemical, and is there actually a health risk today?
What Was the Controversial Ingredient?
The ingredient at the center of the controversy was azodicarbonamide (ADA), a chemical used as a dough conditioner. It helped improve the texture of bread, making dough easier to handle and producing softer, more consistent buns.
Ironically, the same compound is also used in manufacturing certain foamed plastics, including some yoga mats and shoe soles. That connection gave rise to the viral nickname, “the yoga mat chemical.”
While the comparison was technically accurate, it also lacked important context. Food-grade azodicarbonamide and industrial applications are very different, and many chemicals have multiple uses across industries.
Why Did People Become Concerned?
The concern wasn’t simply that ADA was used in food. Scientists focused on what happens during baking.
When bread is baked, most azodicarbonamide breaks down into other compounds. Some laboratory studies involving animals raised questions about one of these breakdown products, called semicarbazide (SEM), when administered in high doses.
Those findings prompted some countries to take a more cautious regulatory approach.
Why Is It Banned in Some Countries?
The European Union and Canada do not permit azodicarbonamide as a flour treatment agent. Their food safety policies often follow the precautionary principle, removing ingredients when safer alternatives exist or when scientific uncertainty remains.
In contrast, the U.S. Food and Drug Administration has determined that azodicarbonamide is safe when used within approved limits.
These differing regulations don’t necessarily mean one side believes the ingredient is dangerous while the other believes it is harmless. Instead, they reflect different philosophies about regulating food additives.
Does McDonald’s Still Use It?
No.
McDonald’s removed azodicarbonamide from its U.S. hamburger buns in 2014 following growing consumer demand for simpler ingredient lists.
Today’s buns no longer contain the ingredient, joining a broader trend among food manufacturers to eliminate additives that have become controversial with consumers.
Are There Other Ingredients Consumers Should Know About?
Modern commercial bread still contains ingredients designed to improve freshness, texture, and shelf life.
These may include:
- Calcium propionate to prevent mold
- Ascorbic acid (Vitamin C) as a dough conditioner
- Enzymes that improve consistency
- Emulsifiers that help maintain softness
These ingredients have been evaluated by food safety agencies and are generally recognized as safe when used according to regulations.
The Bigger Health Picture
Nutrition experts generally agree that focusing on one ingredient can distract from the larger issue.
The greatest health risks associated with fast food are more closely linked to:
- High sodium intake
- Excess saturated fat
- Added sugars
- Large portion sizes
- Frequent consumption of ultra-processed foods
An occasional fast-food meal is unlikely to determine someone’s long-term health. Overall dietary patterns, physical activity, sleep, and other lifestyle factors have a much greater impact.
Consumer Awareness Is Changing the Food Industry
Whether or not an ingredient poses a measurable health risk, public concern can influence corporate decisions.
Over the past decade, many food companies have reformulated products to remove controversial ingredients, reduce artificial additives, and simplify ingredient labels. In many cases, those changes have been driven as much by consumer preferences as by regulatory requirements.
The Bottom Line
The “yoga mat chemical” story captured public attention because it combined science, food safety, and memorable marketing. While azodicarbonamide was once used in some hamburger buns, including those supplied to McDonald’s, the company removed it from its U.S. buns years ago.
Current evidence suggests consumers are better served by paying attention to their overall diet rather than worrying about a single ingredient that has already disappeared from many products.
Being an informed consumer means looking beyond the headlines, understanding the science, and recognizing that nutrition is about the complete picture—not just one ingredient.
Related External Links
- U.S. FDA – Food Additives & GRAS Ingredients Information for Consumers
- U.S. FDA – Food Additives and Petitions
- FDA – Azodicarbonamide (ADA) Food Substance Database
- Electronic Code of Federal Regulations – 21 CFR §172.806 (Azodicarbonamide)
- FDA – Types of Food Ingredients and Why They’re Used
- Health Canada – Permitted Flour Treatment Agents
- McDonald’s USA – Nutrition Calculator & Ingredient Information
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