Centuries before a Roman Catholic missionary taught Irish pagans about the Holy Trinity with a three-leaf clover, indigenous priests were using that clover for its healing and divine properties. And centuries after that missionary’s canonization as St. Patrick, the same clover became a symbol of Irish nationalism in a fight for independence. To this day, the three roles assumed by that clover – healer, teacher and leader – persist in and beyond Erin (Ireland), and more than just on Lá Fhéile Pádraig (St. Patrick’s Day). That clover is the shamrock, and here is its full profile.
The Real Shamrock: Trifolium vs. Oxalis
The often-cartoonish depiction of the commercialized shamrock belies its profound significance in traditional medicine, Christianization and the Irish people’s socio-political identity in the 20th century. Typically, the lighthearted images substitute the rugged Trifolium shamrock with its prettier distant cousin, the Oxalis, too. Dubbed the “false shamrock” despite being upheld (outside Ireland) as symbolizing the luck o’ the Irish, the Oxalis doesn’t share the shamrock’s biological classification, medicinal application and journey to proxy sainthood.
Ireland’s Agriculture and Food Development Authority, the Teagasc, settled the debate of what the real Irish shamrock is by appointing the Trifolium dubium (aka yellow clover and numerous other aliases) as the national flower. This reflected the Irish people’s plurality vote in multiple studies spanning a century, from the 1890s through the 1980s. Interestingly, although the two largest pluralities went to two Trifolium species (nearly 50% for yellow clover and roughly 33% for white clover) even 100 years apart, the Oxalis (aka wood sorrel) got only a small percentage of the votes – lumped in with many other options in what remained of the votes. So, the Irish aren’t the ones responsible for the confusion; the Brits are. (More on that to come.)

The Oxalis acetosella (aka wood sorrel) is often mistakenly portrayed as the shamrock of Irish fame.Photo credit: Maja Dumast /CC BY 2.0 https://www.flickr.com/photos/blumenbiene/5665776061/

The Trifolium dubium (aka yellow clover) is what the Irish government established as the official shamrock, ending a debate that had spanned the 1890s to the 1980s./Photo by I, Kenraiz, CC BY-SA 3.0 <http://creativecommons.org/licenses/by-sa/3.0/>, via Wikimedia Commons
“Shamrock” is the anglicization of Irish “seamairóg” ([ˈʃamˠɾˠoːɡ]), which is the diminutive form of seamir (“clover” in Gaelic), meaning “little/young clover.” (Compare it to the Spanish diminutive suffix “-ito/-ita,” such as “gatito” deriving from “gato” to mean “small cat/kitten.”) The qualifier “dubium,” paired with “Trifolium” (meaning “three-leaved”) in the scientific classification, renders Latin’s equivalent: “lesser trifolium.”
Although the Oxalis is three-leaved too, it’s not in the Trifolium plant family, as it is not a legume like the Trifolium species are. Ironically, although legumes (e.g., peanuts, peas, soybeans) are common in the human diet, the shamrock is unsafe for humans to eat, whereas the Oxalis is safe to eat.
In fact, that quality of the Oxalis is what contributed to the confusion (outside Ireland) over what constitutes the real shamrock. British herbalist John Gerard was chronicling the plants of Ireland for his book “General History of Plants” (1596), and he thought that what the Irish people were eating were bits of seamairóg. However, the Irish people were actually eating seamsóg, which is the Oxalis plant. Gerard’s book put that case of mistaken identity into circulation in perpetuity.

Why eat false shamrocks when raw cannabis offers so much more? Look at what you’re missing out on in Why Raw Cannabis Is a Thanksgiving Must-Have. Photo by Kindel Media/ pexels.com
Shamrock the Healer: Mystically Medicinal
The healing properties of shamrocks, which date back to at least the 1500s, apply to many life-critical functions, from blood to bones to skin. They’re rich in isoflavones, a phytoestrogen compound that is structurally similar to estrogen. These have been proven to improve bone mineral density, helping with such ailments as osteoporosis and menopause. Also, because they’re an antioxidant, they neutralize free radicals in the body, aiding in prevention of premature aging.
When consumed in teas or decoctions, shamrocks act as an anti-inflammatory to ease pain, calm sore throats and mouth ulcers, treat diarrhea and abdominal pain, hinder plaque accumulation on the arteries, reduce fever, and treat upper respiratory conditions (coughing, etc.). When chopped up and prepared as a poultice, they stem bleeding from cuts, while also serving as an antiseptic, and can even treat skin conditions (eczema, psoriasis, etc.). Also, the leaves of a shamrock plant contain potassium binoxalate, which can prevent or cure scurvy.

Shamrocks aren’t the only potent medicinal plant native to Ireland. The Irish flower duán ceannchosach, covered in Ireland’s Miracle Flower Is Cannabis’s Sister From Another Mother, will amaze you too.
Pagan Irish priests (Druids) attributed these healing properties to the clover’s divinity, which they deduced from the plant’s incorporation of their sacred number, 3. This number represented the three branches of life – past, present and future – and the three elements of the earth: sky, ground and underground. Also, pagan Celtic society had three classes and three main gods (Maiden, Mother and Crone), and used trio designs in stone and metal artwork. One spectacular example of these is the megalith engraved on the entrance stones at Newgrange. The ancient Celts were animists, so their worldview recognized influences from non-human entities, including plants, which they believed possessed a spiritual essence. Druids believed the shamrock could ward off evil spirits and bring good luck.

Shamrocks were just one of the many plants that Druids used for their spiritual properties. Look at what other things they achieved through herbal inspiration in Why Did the Ancient Celts Get High on Halloween? / Photo of mugwort by Carola68 Die Welt ist bunt from Pixabay
Shamrock the Teacher: St. Patrick’s Key Visual Aid
Given that triads were central to pre-Christian Celtic religious traditions, and especially since elements of nature took on godlike auras, the shamrock was an ideal way to explain Christianity’s Holy Trinity. So goes the legend of what resulted in St. Patrick’s Day.
While in Ireland in A.D. 432 as a missionary, Patrick (not yet canonized) was giving an impromptu sermon at the Rock of Cashel, when he plucked a shamrock to use as a visual aid. This is described by the 18th-century dissenting minister Caleb Threlkeld – hardly an eye witness, but the earliest source nonetheless – in his book on Irish native plants.
With the shamrock, Patrick explained how the Father, Son and Holy Spirit could exist as three distinct aspects of one divine essence, just as the three leaves of the clover were united on one stalk. In 1727, Threlkeld wrote, “This plant [white clover] is worn by the people in their hats upon the 17th day of March yearly, which is called St Patrick’s Day, it being a current tradition that by this Three-Leafed Grass he emblematically set forth to them the Mystery of the Holy Trinity.”
Patrick had grown up in Ireland after being kidnapped by Irish pirates when he was 16. (Read his autobiography, “Confessio,” for all the details.) After escaping and returning home to Britannia, he became an ordained bishop. Then, he answered a calling he received in a vision and returned to Ireland to preach the Gospel there. He had two unique advantages: he was fluent in the native language, and he had a firm grasp of the Celtic worldview. He carried out his missionary work for nearly 30 years and died in modern-day Downpatrick (Northern Ireland) on March 17, 461.

The simultaneous existence of three persons in one divine being was illustrated in nature through a three-leaved plant, whose leaves and stalk served as the ideal analogy./Image Credit:Original: George McFinnigan Vector: Vitaium, CC BY 3.0 <https://creativecommons.org/licenses/by/3.0>, via Wikimedia Commons
Shamrock the Leader: Éirinn go Brách!
In 1800, the Act of Union (Ireland) brought Ireland under British rule, and the shamrock became Ireland’s symbol. (Wales and Scotland had their own symbols too: the leek and the thistle, respectively.) From that point forward, the shamrock became increasingly popular in Irish music, art, architecture and governmental bodies. The government even trademarked the shamrock symbol due to its compelling place in ancient and contemporary Irish lore. By law, the symbol is allowed only for goods and services of Irish origin, and its use must be approved by the Irish government.
In the early 1900s, a political debate in Ireland was heating up between those who wanted independence and those who wanted to remain in the union with Britain. Those in the former camp adopted the shamrock as their symbol, and it was donned on the uniforms of the Limerick Volunteers, Braid Volunteers and United Irishmen, among other groups. The ensuing violence in the Easter Rising of 1916, and the visibility it gained Ireland worldwide, cemented the shamrock’s visual association with Ireland internationally. (More importantly, it paved the way for Ireland’s independence, granted in 1922.) Over time, it lost its political innuendo and ceased to be regarded as a militant symbol.

From Ireland’s strained hemp supply, cannabis was emblematic of another struggle between the Irish and the British, one that culminated in the Anglo-Spanish War (1587-1604). Read what happened in Light Me Up – I’m Irish: Ireland’s Secret Cannabis History. Photo de Kiffcowboy en seedfinder.eu/Creative Commons/
As an interesting aside, well before the shamrock took on the potency of a military insurgence, it bore the rebellious spirit of the Irish. In the 17th century, when the feast of St. Patrick had become commonplace in honor of Ireland’s patron saint, it was customary to wear St. Patrick’s cross. However, rural folk played by their own rules. In addition to wearing a shamrock instead of the saint’s cross, they got away with suspending all Lenten restrictions on March 17. The National Museum of Ireland explains:
“On [St. Patrick’s] feastday, a meal containing meat was usually eaten after Mass. This was sometimes called ‘Lenten Fish’ as Patrick was believed to have eaten meat during Lent and was filled with remorse. An angel told him to put the remains of the meat he had eaten in water, upon which they turned to fish. It seems that on his feast day, once meat was dipped in water, people could eat itas ‘St. Patrick’s Fish’. ‘St. Patrick’s Pot’ or Póta Phádraig was a common term for the alcoholic drink consumed to ‘the drown the shamrock’. After a toast to St. Patrick, the shamrock was thrown over the shoulder for luck.”
Aforementioned minister and de facto historian Threlkeld, when writing about the Irish people wearing shamrocks on St. Patrick’s Day, added: “However that be, when they wet their Seamar-oge, they often commit Excess in Liquor, which is not a right keeping of a Day to the Lord … generally leading to debauchery.”

Conclusion
The shamrock, then and now, is greater than the sum of its parts. It is endowed with healing properties, has a starring role alongside an immortal legend, and places a chip on the shoulder of anyone wearing one. (For a variety of Gaelic idiomatic equivalents of “FAFO,” read this Reddit thread.)
Three roles in three leaves, as if divinely orchestrated, the shamrock has earned its timeless adoration.
May your blessings outnumber
the shamrocks that grow,
and may trouble avoid you,
wherever you go.
The information in this article and any included images are for educational purposes only. This information is neither a substitute for, nor does it replace, professional legal advice or medical advice, diagnosis or treatment. If you have any concerns or questions about laws, regulations or your health, you should always consult an attorney, physician or other licensed professional.
Kathleen Hearons is a writer, editor, linguist and voice over actor from Los Angeles. She specializes in creative writing and research-intensive analysis and reporting.
Sources and Suggested Reading
Act of Union (Ireland), Acts of the Old Irish Parliament. Accessed March 2, 2025. https://www.legislation.gov.uk/aip/Geo3/40/38/contents.
Alexis, Amber Charles. “Is Clover Edible? Nutrients, Benefits, and Downsides.” Healthline. Feb. 15, 2022. Accessed March 1, 2025. https://www.healthline.com/nutrition/is-clover-edible.
“Blue Wiss.” Lovetofeel (United Kingdom). Accessed March 1, 2025. https://lovetofeel.com/pages/blue-wiss.
“clover.” Britannica. Last updated Jan. 20, 2025. Accessed March 1, 2025. https://www.britannica.com/plant/clover-plant.
“Clover: Gardener’s Guide and Plant Profile.” Spoken Garden (United Kingdom). Accessed March 1, 2025. https://www.spokengarden.com/clover-gardeners-guide-and-plant-profile/?srsltid=AfmBOooxInzWW08jcFriZWN0aYoy_W-wHAT-PJDuc4JqshAqmiDc2yR2.
“Clover Health Benefits.” WebMD. Sept. 1, 2023. Accessed March 1, 2025. https://www.webmd.com/diet/health-benefits-clover.
Cox, Sally. “Clover the Medicinal Benefits, Not just a Lucky Charm.” Pharmacy Consulting Limited (UK). March 17, 2022. Accessed March 1, 2025. https://pharmacyconsulting.co.uk/blog/not-just-a-lucky-charm-the-medicinal-benefits-of-clover/.
Darabi, Dina Mirsadeghi, Peiman Ariaii, Reza Safari and Mohammad Ahmadi. “Effect of clover sprouts protein hydrolysates as an egg substitute on physicochemical and sensory properties of mayonnaise.” Food Science & Nutrition, Vol. 10, Issue 1 (December 2021): 253-263. doi:10.1002/fsn3.2665. Accessed March 1, 2025. https://pubmed.ncbi.nlm.nih.gov/35035926/.
de Rijke, Eva, Herman Zappey, Freek Ariese and Udo A. T. Brinkman. “Flavonoids in Leguminosae: Analysis of extracts of T. pratense L., T. dubium L., T. repens L., and L. corniculatus L. leaves using liquid chromatography with UV, mass spectrometric and fluorescence detection.” Analytical and Bioanalytical Chemistry, Vol. 378 (2004): 995-1006. doi:10.1007/s00216-003-2310-6. Accessed March 1, 2025. https://link.springer.com/article/10.1007/s00216-003-2310-6.
Downey, Ashleigh. “The Humble Shamrock.” Green Sod Ireland (Ireland). March 17, 2021. Accessed March 1, 2025. https://greensodireland.ie/2021/03/17/the-humble-shamrock/.
Doyle, Clodagh. “St. Patrick.” National Museum of Ireland (Ireland). Accessed March 1, 2025. https://www.museum.ie/en-IE/Collections-Research/Folklife-Collections/Folklife-Collections-List-(1)/Religion-and-Calendar-Customs/St-Patrick.
“Easter Rising.” National Army Museum (United Kingdom). Accessed March 2, 2025. https://www.nam.ac.uk/explore/easter-rising.
Fiorello, Sarah. “Which Plant Is the Real Shamrock?.” Cornell University. March 16, 2023. Accessed March 1, 2025. https://cornellbotanicgardens.org/which-plant-is-the-real-shamrock/.
Gervais, Michelle. “The History of the Shamrock.” Fine Gardening. Accessed March 1, 2025. https://www.finegardening.com/article/the-history-of-the-shamrock.
Gounden, Thaveshan, Roshila Moodley and Sreekantha Babu Jonnalagadda. “Distribution and Assessment of Heavy Metals in Trifolium dubium (Little Hop Clover) and the Impact of Soil Quality.” Analytical Letters, Vol. 52, Issue 2 (October 2018): 1-12. doi:10.1080/00032719.2018.1523912. Accessed March 1, 2025. https://www.researchgate.net/publication/328520678_Distribution_and_Assessment_of_Heavy_Metals_in_Trifolium_dubium_Little_Hop_Clover_and_the_Impact_of_Soil_Quality.
Gounden, Thaveshan, Roshila Moodley and Sreekantha B. Jonnalagadda. “Elemental analysis and nutritional value of edible Trifolium (clover) species.” Journal of Environmental Science and Health, Part. B: Pesticides, Food Contaminants, and Agricultural Wastes, Vol. 53, Issue 8 (2018): 487-492. doi:10.1080/03601234.2018.1462923. Accessed March 1, 2025. https://pubmed.ncbi.nlm.nih.gov/29708825/.
Hayden, David. “The History of the Shamrock – From Saint Patrick to Campion’s ‘Wild Irish’ to Rebellion and Nationhood.” Green News (Ireland). March 16, 2017. Accessed March 1, 2025. https://greennews.ie/the-history-of-the-shamrock-from-saint-patrick-to-campions-wild-irish-to-rebellion-and-nationhood/.
Hearons, Kathleen. “Ireland’s Miracle Flower Is Cannabis’s Sister From Another Mother.” Head Magazine. Accessed March 2, 2025. https://headmagazine.com/irelands-miracle-flower-is-cannabiss-sister-from-another-mother/.
Hearons, Kathleen. “Light Me Up – I’m Irish: Ireland’s Secret Cannabis History.” Head Magazine. Accessed March 2, 2025. https://headmagazine.com/light-me-up-im-irish/.
Hearons, Kathleen. “Why Did the Ancient Celts Get High on Halloween?.” Head Magazine. Accessed March 2, 2025. https://headmagazine.com/why-did-the-ancient-celts-get-high-on-halloween/.
Hearons, Kathleen. “Why Raw Cannabis Is a Thanksgiving Must-Have.” Head Magazine. Accessed March 2, 2025. https://headmagazine.com/why-raw-cannabis-is-a-thanksgiving-must-have/.
Heberling, Mason. “What’s a Shamrock?.” Carnegie Museum of Natural History. Accessed March 1, 2025. https://carnegiemnh.org/whats-a-shamrock/.
“History of the Irish Volunteers.” The Irish War. Accessed March 2, 2025. https://www.theirishwar.com/history-of-the-irish-volunteers/.
“Hop Clover.” Edible Wild Food. Accessed March 1, 2025. https://www.ediblewildfood.com/hop-clover.aspx.
“How to say F*&k around and find out in Gaelic?.” Reddit thread initiated by Egregious67 in the subreddit r/gaidhlig. January 2025. Accessed March 2, 2025. https://www.reddit.com/r/gaidhlig/comments/1htvfar/how_to_say_fk_around_and_find_out_in_gaelic/?rdt=60652.
“Irish Symbols: The Complete Guide to the Origins and Meanings.” Let’s Go Ireland. Last updated Feb. 23, 2023. Accessed March 1, 2025. https://www.letsgoireland.com/irish-symbols/.
“Irish War of Independence.” National Army Museum (United Kingdom). Accessed March 2, 2025. https://www.nam.ac.uk/explore/irish-war-independence.
Jennings, Abigail. “Our Irish Connection to Shamrocks (aka White Clover) Trifolium repens.” Hugh Torance House and Store. March 23, 2022. Accessed March 1, 2025. https://www.hught.org/post/our-irish-connection-to-shamrocks-aka-white-clover-trifolium-repens.
Judy. “Six Reasons Why Shamrock Plants Are Worth Growing in Your Garden.” Houseplant411. March 24, 2023. Accessed March 1, 2025. https://houseplant411.com/shamrock/six-reasons-why-shamrock-plants-are-worth-growing-in-your-garden/.
Kiss, Kate. “Not just for the Irish; shamrock has medicinal uses.” Wellington Advertiser (Canada). Accessed March 1, 2025. https://www.wellingtonadvertiser.com/not-just-for-the-irish-shamrock-has-medicinal-uses/.
“Lesser trefoil.” Brickfields Country Park (United Kingdom). Last updated May 22, 2023. Accessed March 1, 2025. https://www.brickfieldspark.org/data/lessertrefoil.htm.
“Lesser trefoil.” Wild Flower Web (United Kingdom). Accessed March 1, 2025. http://www.wildflowerweb.co.uk/plant/504/lesser-trefoil.
“Meaning of the Irish blessing ‘May your blessings outnumber the shamrocks that grow.’” Irish Central. April 10, 2023. Accessed March 2, 2025. https://www.irishcentral.com/meaning-irish-blessing-shamrocks.
Miklas, Lois, and Barb Ryan. “The Botany Behind the Shamrock.” PennState Extended. Last updated Feb. 22, 2023. Accessed March 1, 2025. https://extension.psu.edu/the-botany-behind-the-shamrock.
Milmo, Cahal. “St. Patrick’s Day: The legend of the shamrock.” Independent (United Kingdom). March 16, 2006. Accessed March 1, 2025. https://www.the-independent.com/news/uk/this-britain/st-patrick-s-day-the-legend-of-the-shamrock-6106550.html.
Moerman, Daniel E. “Native American Ethnobotany.” Timber Press: 1998. ISBN-10: 0881924539
ISBN-13: 978-0881924534.
Mulvihill, Mary. “Why this plant is a bit of a sham.” The Irish Times. March 15, 2012. Accessed March 1, 2025. https://www.irishtimes.com/news/science/why-this-plant-is-a-bit-of-a-sham-1.482086.
Nelson, E. Charles. “Shamrock: Botany and History of an Irish Myth: a Biography of the Shamrock in History, Literature, Music and Art.” Boethius Press: 1991. ISBN-10: 0863141994.
ISBN-13: 978-0863141997.
Newgrange.com. Accessed March 2, 2025. https://www.newgrange.com/.
Rankel, Kiersten. “10 Benefits of Having a Lesser Hop Clover.” Greg. June 18, 2024. Accessed March 1, 2025. https://greg.app/lesser-hop-clover-benefits/.
Rankel, Kiersten. “Shamrock Is Not Edible.” Gret. Oct. 19, 2024. Accessed March 1, 2025. https://greg.app/shamrock-edible/.
Rankel, Kiersten. “What You Should Know About Lesser Trefoil.” Greg. Jan. 10, 2025. Accessed March 1, 2025. https://greg.app/lesser-trefoil-overview/.
“Refresher on the Rules of Fast and Abstinence During Lent 2025.” The Catholic Telegraph. March 1, 2025. Accessed March 2, 2025. https://www.thecatholictelegraph.com/refresher-on-the-rules-of-fast-and-abstinence-during-lent/21603.
Ruhsam, Markus, et al. “The genome sequence of lesser trefoil or Irish shamrock, Trifolium dubium Sibth. (Fabaceae).” Wellcome Open Research, Vol. 9, Article 229 (April 2024). doi:10.12688/wellcomeopenres.21191.1. Accessed March 1, 2025. https://pubmed.ncbi.nlm.nih.gov/39258550/.
“Saint Patrick’s Confessio.” Royal Irish Academy. Accessed March 2, 2025. https://www.confessio.ie/etexts/confessio_english#.
Schillinger, Viola. “Edible plants for rabbits.” How to Rabbit. Accessed March 1, 2025. https://how-to-rabbit.com/list-of-wild-herbs/.
“Shamrock, Irish Heritage and Biodiversity.” Teagasc (Irish Agriculture and Food Development Authority). March 17, 2024. Accessed March 1, 2025. https://www.teagasc.ie/news–events/daily/other/shamrock-irish-heritage-and-biodiversity.php.
“Shamrock Meaning: Delving Into Ireland’s Emblem.” Let’s Go Ireland. Last updated Sept. 28, 2023. Accessed March 1, 2025. https://www.letsgoireland.com/shamrock-meaning/.
“Suckling Clover.” Massey University, University of New Zealand. Accessed March 1, 2025. https://www.massey.ac.nz/about/colleges-schools-and-institutes/college-of-sciences/our-research/themes-and-research-strengths/plant-science-research/new-zealand-weeds-database/suckling-clover/.
“The Real Story of the Shamrock.” Claddagh Design. Dec. 22, 2017. Accessed March 1, 2025. https://www.claddaghdesign.com/blogs/irish-interest/the-real-story-of-the-shamrock.
“The Shamrock Tattoo Meaning: Luck, Culture & Tradition.” Let’s Go Ireland. Last updated May 19, 2023. Accessed March 1, 2025. https://www.letsgoireland.com/shamrock-tattoo-meaning/.
Thompson, Sara. “Benefits of Clover Go Beyond Good Luck.” Explorit Science Center. March 18, 2021. Accessed March 1, 2025. https://www.explorit.org/post/benefits-of-clover-go-beyond-good-luck.
“Trifolium dubium – Sibth.” Plants for a Future (United Kingdom). Accessed March 1, 2025. https://pfaf.org/user/Plant.aspx?LatinName=Trifolium+dubium.
“Use of State Emblems.” Intellectual Property Office of Ireland. Accessed March 2, 2025. https://www.ipoi.gov.ie/en/types-of-ip/trade-marks/understanding-trade-marks/use-of-state-emblems/.
Vishwas, Drishti. “Exploring the Nutritional Benefits and Drawbacks of Clover.” Tasty Pad. February 2025. Accessed March 1, 2025. https://content.tastypad.com/blogs/8193/Exploring-the-Nutritional-Benefits-and-Drawbacks-of-Clover?lang=nl_nl.
Walker, Emer. “Who is St. Patrick: The Man, the Myth, the Legend.” Let’s Go Ireland. Last updated Dec. 25, 2023. Accessed March 1, 2025. https://www.letsgoireland.com/who-is-st-patrick/.
Weber, Jane. “Irish shamrock story.” Citrus County Chronicle (Florida). March 14, 2021. Accessed March 1, 2025. https://www.chronicleonline.com/lifestyle/home/irish-shamrock-story/article_48ec9d1e-82cc-11eb-a1c1-cffc764829e5.html.
Xiao, Jianbo, Tamar S. Muzashvili and Milen I. Georgiev. “Advances in the biotechnological glycosylation of valuable flavonoids.” Biotechnology Advances, Vol. 32, Issue 6 (November 2014): 1145-1156. doi:10.1016/j.biotechadv.2014.04.006. Accessed March 1, 2025. https://www.sciencedirect.com/science/article/abs/pii/S0734975014000536.