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Harry the tiger shark is quite the traveler
+Sam Andrews reports the results of tracking tiger sharks using satellite technology. Read on to learn about Harry and tracking his movements.

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The travelling life of the tiger shark

At 9 foot long, not including the tail, tiger shark (Galeocerdo cuvier) Harry Lindo is not exactly on the small side.  It’s not Harry’s size that is exciting scientists and shark enthusiasts, nor a photograph taken in 2009 by Ian Card showing a shark – suspected to be Harry, trying to eat a 150 lb juvenile tiger shark off the coast of Bermuda.  Between 2009 and 2012 researchers tagged 24 tiger sharks with satellite transmitters in the Challenger Bank, which lies just off Bermuda in the Atlantic Ocean.  In study lead by James Lea (The Guy Harvey Research Institute, +Nova Southeastern University Oceanographic Center) and team of international collaborators, those shark movements have been compiled and analysed.  Harry, it turns out, is one heck of an ocean wanderer.  In just over 3 years Harry swam over 44,000 kilometres – that’s more than the circumference of the Earth (just over 40,000 kilometres).  Harry’s track is the longest recorded for a tiger shark, and probably the longest ever published for any shark species.  

Unexpected movements
Tiger sharks are often spotted in coastal waters in temperate warm and tropical seas, but they also wander out into the open ocean.  The tagging study is just one of a few multi-year studies tracking individual shark migrations.  The researcher’s hard work was well rewarded when it revealed previously unknown shark movements in the Atlantic.  Most of the sharks in this study were male, but there were a few juvenile and females too.  Adult males, females, and juveniles of both sexes spent the winter months in the Caribbean.  When it came to the summer, all the adult males and just one adult female headed out into the open ocean of the North Atlantic in the summer.  The repeated use of these two vastly different types of habitats up to some 3,500 kilometres or so apart was surprising for a species previously thought to be primarily coastal.  The researchers think that repeated returns to the same sights may be better for the fish than constantly looking for new habitat.  They know where their food is, so why take a risk looking elsewhere only to find none?

How do you track a shark anyway?
Sharks, being a marine species, can’t simply be watched by people.  In this study, the sharks with tagged with something called Argos satellite platform terminal transmitters, also known as PTTs.  Every time a shark goes to the surface, these little tags send location to a receiving satellite.  The researchers can then grab this data from the satellites.  The raw data itself is not 100% usable and goes through processing to ensure that the information is accurate and suitable for analysis.  You can read more about this process in the methods section of the paper (see link below).  As for getting the tags on the shark in the first place, well you have to go fishing.  Once the shark is caught, the tracker device is fixed onto the shark’s fin and then it is released to go about its business.  There is a video showing shark tagging here (start at 1:07 if you don’t want to watch the whole thing)

Why is this work important?
Like many shark species, the tiger shark is an at risk species.  It is currently listed as ‘near threatened’ on the IUCN Red List, primarily threatened because it is targeted by fisheries, and caught as bycatch.  If we want to help look after these sharks, understanding their movement is really useful.  For example, earlier work by the Guy Harvey Research Institute highlighted how important the waters around Bermuda were for the sharks.  The Bahamas government responded by establishing a ‘shark sanctuary’ in 2011, in which all commercial fishing was banned in their territorial waters.  Looking after sharks isn’t just important for the sharks themselves either.  They are an apex predator, and considered to be a ‘keystone’ species, playing an essential role in ecosystem health.  One impact is to alter the predator-prey ratio, with alterations via the food web.  Lose too many predators can cause herbivore populations grow.  If there are too many herbivores, you could lose plant-based habitat, like sea grass beds – and the species that depend on them. 

Read the research for yourself
The paper was published in Nature Scientific Reports, and has been made open access.  You can have a read of the research yourself by heading here 

Fancy following a shark?  
Head over to the Guy Harvey Research Institute Tracking Site where you can see movements of tiger sharks and other species, like blue marlin, sailfish, and mako sharks

Image: This image was published in +National Geographic  and taken by photographer Brian Skerry.  It depicts a tiger shark in the northern Bahamas at a location known as ‘Tiger Beach’.  National Geographic also have an excellent article looking at Brian’s work on sharks which you can read here  To see more of Brian’s work, have a look at his website 

#marinescience #movementecology #marinespatialecology #sciencesunday #sharks #tigersharks
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A Disaster-Response Challenge

In a competition inspired by the Fukushima nuclear meltdown, robots were run through an obstacle course of eight tasks which included driving, going through a door, opening a valve, punching through a wall, and dealing with rubble and stairs. Of the 24 robots to make it to the finals, it was HUBO (HUmanoid roBOT) that won. Read on at the link graciously provided by +Ciro Villa.

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South Koreans triumph in US robot challenge

"South Korean boffins carried home the $2 million top prize Saturday after their robot triumphed in a disaster-response challenge inspired by the 2011 Fukushima nuclear meltdown in Japan.

Team KAIST and its DRC-Hubo robot took the honor ahead of Team IHMC Robotics and Tartan Rescue, both from the United States, at the DARPA Robotics Challenge (DRC) after a two-day competition in California.

The runners-up win $1 million and $500,000 respectively, in a field of more than 20 competitors."

Read more:


Image: The humanoid robot 'DRC-Hubo' developed by Team KAIST from South Korea completes a task before winning the finals of the DARPA Robotics Challenge at the Fairplex complex in Pomona, California on June 6, 2015 
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Floodplain Fundamentals

+Carissa Braun explains why flood prone zones are so important for the health of a river. Also, thanks Carissa, for rescuing that crayfish! ♥

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"The plants in a floodplain slow the floodwaters and prevent much damage downstream. The deep clay soils here store water, reducing flooding. Without intact floodplains, rivers, streams, and the land around them suffer increased erosion and more damaging floods."

Simply put, a floodplain is an area of land prone to flooding. It is often flat with higher elevation on both sides and may be either very small or very large. While it can be a problem for houses build on floodplains, they play an extremely important role. The floods that occur carry sediment rich in nutrients past banks and into surrounding areas. This in turn makes for fertile land ripe for agriculture and is where some of the world's earliest civilizations arose. 

Rather than be labeled as an aquatic or terrestrial ecosystem, some ecologist label floodplains as "pulsed" ecosystems - an intermediate habitat. With exception to extreme events, the "pulse" and reach of a floodplain can be predicted. The flat, fertile, predictable land is therefore considered ideal for building, but often at the cost of the health of the floodplain.

There are six criteria used to determine floodplain health:
1. The ecosystem supports habitats and viable native animal and plant populations similar to those present prior to any disturbances.
2. The ecosystem is able to return to its pre-existing condition after a disturbance, whether natural or human-induced.
3. The ecosystem is able to sustain itself.
4. The river can function as part of a healthy basin.
5. The annual flood pulse "connects" the main channel to its floodplain.
6. Infrequent natural events - floods and droughts - are able to maintain ecological structure and processes within the reach.

A healthy floodplain results in a healthy river. It is also important to understand when developing on a floodplain. Otherwise the result benefits no one.

A quick #ScienceSunday  post and, for the first time, #SignSunday . With all the flooding we've been having in Texas, I wasn't going to miss an opportunity to visit a favorite floodplain not that the trail could actually be walked since it's flooded. Still, the parts I could walk I took pictures to give some sense of a floodplain, and yes, I will be going back this week since the rain hasn't stopped yet!

Sources and Further Reading
Flood Plain | NatGeo (website)
Floodplain River Ecology and the Concept of River Ecological Health (pdf | USGS)
Trail at the +Heard Natural Science Museum & Wildlife Sanctuary.
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I was told I should have saved her for dinner, but alas, I'm not really a big fan of crayfish ;)
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Blue Baby Breakthrough

A story of perseverance and diversity that led to medical history being made. Happy Birthday, Dr. Taussig! 

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Rajini Rao originally shared to Making Sense of Science:
Affairs of the Heart: Dr. Helen Taussig 

❤  On a late November day in 1944, bright sunlight streamed upon the blue-tinged body of 18 month old Eileen Saxon, who was hovering near death. Born with a congenital heart defect that prevented her blood from being oxygenated by her lungs, she now weighed little more than 9 pounds. Across the ocean, World War II raged on, but at the +Johns Hopkins University hospital in Baltimore, another type of history was being made. Under the gaze of 706 doctors gathered around, Dr. Alfred Blalock meticulously rerouted an artery heading to the child's arm, back to the lungs giving the oxygen-starved blood a second chance of rejuvenation. The anesthesiologist cried out in astonishment as Eileen's lips turned from blue to a healthy red. That was the start of a successful procedure that would cure thousands of "blue babies" in the brand new era of heart surgery that followed. Today, we remember Dr. Helen Taussig, whose brilliant idea it was that set the stage.

❤ Born on this day, May 24, in 1898, Helen took medical classes at both Harvard and Boston Universities although neither would award her a degree because of her gender. Worse, she was forbidden to speak to her male colleagues in histology class because of fears that she would "contaminate" them. She completed her MD degree at Johns Hopkins and there, as a pediatric cardiologist did extensive work with anoxemia, or blue baby syndrome. She noticed that blue babies with an additional heart defect (called PDA) fared better, and that a shunt that mimicked PDA could be the solution. She pitched the idea of getting more blood to the lungs much "as a plumber changes pipes around" to surgeon Alfred Blalock and his technician Vivien Thomas. Thomas, a black man whose education did not go beyond high school, practiced the surgery in the animal lab and after modifying instruments for use in humans, coached Dr. Blalock through the first hundred surgeries in infants. In 1976, Hopkins awarded him an honorary doctorate. Sadly, little Eileen became cyanotic again in a few months and did not survive past 2 years even though other babies would go on to live healthy lives. Today, a modified version of the shunt is performed using a synthetic Gore-Tex graft (lower right image). 

¸¸.•*¨*•♫ Happy Birthday, Dr. Taussig!  

Image Note: Helen Taussig became deaf in later years, and actually used her fingers rather than a stethoscope to feel the rhythm of heartbeats.

#ScienceSunday   #STEMWomen  
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Bee-guiling Science

A spectacular photo (can you spot the bee?) combined with some ruminations on circadian clocks, bees and epigenomes makes for a lovely #ScienceSunday  read. Thanks, +Larry Mayer .

The Incredible Bittersweetness of Bee-ing

On a bright spring day in Saguaro National Park (Tucson, Arizona) the giant cacti bloom their laurels,  honey bees assume their circadian tasks, and I ponder my own perceptions and how to express them in images.  The sense of time genetically encoded into many life forms collectively referred to as the circadian clock is somewhat socially plastic in honey bees as some members of the bee social structure, such as nurse bees, may work around the clock. The variability of gene expression under environmental factors which are social rather than physical, has profound implications for all social life forms.  For example,  “disturbing” a bee hive, which we interpret to mean that bees “feel threatened”, causes an aggressive response in bees.  Scientists, discovered the chemical trigger in bees, the "alarm pheromone" isopentyl acetate, induces an instantaneous aggressive response.  But what is more profound is the discovery that the exposure to the alarm pheromone also induces widespread changes at the genetic level which might result in permanent behavioral changes. The ramifications for human social behavior are both complex and profound.  Researchers have already found compelling evidence to suggest that social and emotional processes in humans, once thought to be principally modulated by endogenous oxytocin systems may be controlled instead by epigenetic processes as well.  In the end, I have a color photograph.


#sciencesunday   #SaguaroNationalPark #epigenetics
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Gaming On Your Mind?

Our teenage kids, and some of us adults too, are going to be happy with this #ScienceSunday  story! 

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SciTech Digest 14 June 2015
Thanks as always, +Mark Bruce 

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SciTech #ScienceSunday Digest - 24/2015.
Permalink here:

Advanced brain interfaces, Seawater lithium mining, Better streaming gaming, Body on chip, Portable lab tests, Synthetic immune organoids, Quantum random numbers, Faster tissue regeneration, Pushing Moore’s Law, Vagus nerve stimulators.

1. Brain Interface via Injectable Nanoparticles & Meshes
Magnetoelectric nanoparticles can be injected into the brains of mice (each receiving 20 billion nanoparticle in the experiment) and when stimulated by an external magnetic field they induce an electric field that interacts with neuronal networks and the electric field they produce, as confirmed via EEG Very interesting platform for interfacing with the brain, especially if it can be shown to work in reverse to pick up discrete brain signals. In related news nanoscale electronic meshes can be injected into the body and brain as intimate sensors and interfaces able to connect to other devices

2. Mining Lithium from Seawater
A new, early prototype system is able to efficiently extract lithium from seawater using a dialysis-like system with a superconducting membrane that only lets lithium ions pass through If it scales it could be timely given the projected demand for lithium batteries against current reserves. Interesting that this was from Japan, which has previously demonstrated a similar uranium-from-seawater system. 

3. Improving Streaming Gaming Bandwidth
A new collaborative rendering process called Kahawai shares rendering between the server and the user’s device to cut down the required network bandwidth by 83%, and is mainly applicable to interactive game-streaming in which a remote server does most of the number-crunching and sends updated video to the user, which enables very “light” user device hardware but suffers with poor bandwidth. 

4. The Latest Body on a Chip
The latest human-on-a-chip or body-on-a-chip device comprises specific spherical micro-tissues loaded into microfluidic compartments that are connected by tiny tubes, allowing circulation of nutrients, drugs, and importantly drug metabolites throughout the system It was tested with (i) liver and tumour tissue, (ii) liver, tumour, heart, nervous tissue, and (iii) developed an eight tissue system for future testing; such devices will transform drug development in future. 

5. Portable Handheld Lab Tests
The latest portable handheld laboratory testing device is the Sceptre from a company called Qloudlab, spun out of the EPFL and currently testing the device at a major hospital The device will use interchangeable connectors to take small patient blood, urine, and saliva samples and will be able to run a battery of tests before sending the data to a mobile phone or cloud service; the first test application will be for certain lipids but if successful will expand to others. Once mature we’d all ideally have one of these devices at home. 

6. Synthetic Functional Immune Organs
A synthetic immune system organoid has been produced out of gelatin-based hydrogels reinforced with silica nanoparticles and seeded with immune cells; mimicking the microenvironment of lymphoid tissue the organoid and demonstrated the ability to proliferate and activate B cells and induce the production of antibodies against invaders Such organoids might be used in future to rescue a patient’s immune system or otherwise employed industrially to optimise production of therapeutic antibodies. 

7. Quantum Random Number Generator
The fastest quantum random number generator has been unveiled, able to generate 68 billion random numbers per second (compared to only 1 million per second with current systems) by creating a highly sensitive interferometer that that converts fluctuations in the phase of emitted photons into intensity changes and so allowing conventional faster photodetectors to be used Immediate applications include quantum cryptography. 

8. Triggering Faster Tissue Regeneration
A new drug shows promise in inducing latent tissue stem cells to repair damaged tissues more quickly and across many different tissues at once and hopes to soon enter human trials Animal models showed massively damaged livers healing twice as fast as normal, while a model of chronic ulcers was healed and further ulcerative symptoms prevented. We could all do with this at various points in our lives, even if just to heal scrapes and strains. 

9. Pushing Moore’s Law with Better Semiconductors
New work from IBM has successfully fabricated single crystal nanostructures and 3D stacked nanowires with III-V materials (indium, gallium, & arsenide alloys) and for the first time integrated these with silicon in an economically viable process compatible with standard chip fabrication technology Such materials are considered important for enabling further Moore’s Law style performance gains from conventional silicon chips. 

10. Vagus Nerve Stimulator for Brain Health
A company called Microtransponder has developed an implanted vagus-nerve stimulator to induce targeted relearning in the brain, for example, to treat tinnitus and stroke by retraining the brain to route around damage that causes these diseases Future targets will include post-traumatic stress disorder and obsessive-compulsive disorder, while others are pursuing epilepsy and migraine. 

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Sitting Down With Science

We always appreciate a combination of art and science. Thanks for finding this one, +Justin Chung!

#ScienceSunday #SciSunCB
#ScienceSunday + #SundayPunday = Periodic Table!

This visual pun is pure awesome! "Periodic Table of Elements" made by Nazila Alimohammadi and Anna Clark in 2003 at Wake Forest University. Actinide and lanthanide series are the bench. (Photo: Larry WFU)

If you like science news, check out my "Science" collection:

#chemistry #periodictable #elements #geek #humor #pundaysunday #pundayeveryday #punday #visualpun #pun #science #sciencepunday #scienceeveryday
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SciTech Roundup

It's #ScienceSunday! This means it is time to catch up on the latest and greatest news on Science and Technology from +Mark Bruce .

SciTech #ScienceSunday Digest - 23/2015.
Permalink here: 

Immune system discoveries, DNA click-chemistry, Human reference genome, Metal plating prints, CRISPR vs viruses, Bioengineered limbs, Carbon nanotube RAM, WiFi powers sensors, Amazing robots, Crunching regulatory networks. 

1. Immune System Discoveries & Innovations
Decades of anatomy have been overturned with the discovery that the brain has subtle but direct lymphatic connections to the immune system, throwing up new questions and opportunities for the role this plays in diseases of the brain and therapies that might be developed Meanwhile a new blood test costing $25 called VirScan can determine every single virus the person has ever been exposed to Finally, a new immunotherapy retrains the immune system to not attack specific proteins in the body that lead to rheumatoid arthritis and shows promise as a platform for treatment against autoimmune diseases

2. Nanostructures from DNA Click-Chemistry
Continuing the strong DNA origami theme in recent weeks we have a modification of DNA building blocks that (i) form interlinked catenane chainmail ring structures and (ii) exploit functionalised oligonucleotides that undergo click-chemistry reactions to lock and stabilise the structure against high temperatures and further chemical / enzymatic modification; this comprises a structural platform for nanostructures with the possibility for non-enzymatic gene synthesis

3. A More Sophisticated Human Reference Genome
The human reference genome is getting a significant and overdue boost with the help of graph theory that will combine many thousands of human genomes into a single, annotated reference source able to draw far more accurate and meaningful comparisons to the differences that individual genomes possess

4. Metal Plating for 3D Prints
The Orbit1 is a tabletop electroplating device for 3D printed objects in which (i) the object is spray-coated with conductive paint, (ii) placed on a rack in the Orbit1, (iii) the device electroplates the object and applies a metallic (copper, nickel, palladium, or gold) coating 0.1mm - 0.2mm thick Make your own utensils, circuit boards, glasses frames, etc. 

5. CRISPR Suppresses Hepatitis B Virus
A construct comprising a number of distinct CRISPR gene therapy vectors against conserved regions across HepB viral genotypes has proven effective in enabling robust suppression of viral expression and replication in mice CRISPR is ideal for this purpose and I’ve been waiting to hear someone do this - I also expect this method to deliver effective cures for not only Hepatitis but HSV, HPV, and other genome-integrating viruses. 

6. Transplantable Bioengineered Limbs
The first transplanted bioartificial replacement limb has been demonstrated in a process that took a limb from a rat, decellularised it, incubated the matrix in a bioreactor, added vasculature & muscle progenitor cells, electrically stimulated muscle development, confirmed the development of limb vasculature and muscles, added a skin graft, and then transplanted the limb onto another rat in which blood flow was restored Next step is to include bone and nerves. 3D printed hydrogel structures are also getting better and more sophisticated for tissue engineering applications

7. Nantero’s Carbon Nanotube RAM Chips
Nantero claims to have installed its carbon nanotube memory NRAM process in multiple production fabs and promises to be 100s of times faster than NAND, very low power, low cost, scalable down below 5nm and hinting at a range of future device possibilities Although apparently there are already microSD cards with 512GB of storage

8. Camera Powered by Ambient WiFi
New chip design, signal-processing software, and updates to existing routers result in a system in which low-power sensors and devices can be powered remotely via WiFi To prove the concept they wirelessly powered a small surveillance camera that captured images, and also wirelessly recharged a fitness tracker, however all devices currently have to be less than seven or so meters away from the router. 

9. The World’s Best Robots
As you all should know and should already be following, the DARPA Robotics Challenge is on this weekend where we get to see the most advanced robots in the world make their way through a tough obstacle and task course; CMU’s CHIMP robot performed well early on but the final winner and best performer overall was the Korean Hubo team Also this week, robots are learning to push and pull heavy objects with their bodies, and Amazon has just run its Warehouse Challenge competition for robots

10. Regeneration Model Discovered by Smart Software
The regeneration mechanism of a type of small worm has been reverse engineered by a software system based on evolutionary algorithms Fed a dataset of 16 key regeneration experiments the algorithm discovered and returned the regulatory network that correctly predicted all 16 experiments and is the most comprehensive model of regeneration in this worm to date. I’m thinking systems like these could be a boon to unravelling the complex regulatory networks at play in many human diseases and phenotypes. 

I couldn’t pass this one up: Bolt Threads emerges from stealth with a lot of cash to scale production of bacterial synthesised spider silk threads for a range of purposes

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Amino Acid Pun

Q: What's a pirate's favorite amino acid?
A: Arrrrrrrrginine.

That one was easy. Now try this...
(Psst...try not to give the answer away, pretty please?) 
Bonus points if you find the error in the structure! 

H/T +Pam Adger

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Day of the Dog

New DNA evidence suggests that arctic breeds of dogs had another, ancient origin. Thanks +Chad Haney for shedding some light on man's best friend!

Taimyr wolf and the origins of dog
There's an ongoing debate about where and when dogs originated. The when part might be closer to an answer now. Genetic drift is used by evolutionary biologist to try to recreate the lineage of species. The discovery of a 35,000-year-old wolf rib bone in the Taimyr peninsula in northern Siberia was the key to this story. The DNA from that bone suggests that it diverged from a common ancestor of present-day wolves and dogs near the beginning of the domestic dog lineage. Their technique uses genetic drift of 'regular' DNA and mitochondrial DNA.

► Genetic Drift
There are non-lethal random mutations in DNA that survive to the next generation due to natural selection and sometimes due to 'luck'. Surviving by natural selection makes sense, a mutation affords an advantage so that offspring should excel and survive. Genetic drift is when a mutation doesn't necessarily result in an advantage but is nevertheless passed on 'by chance'. Tracing these mutations help create a lineage for evolutionary biologists.

► Mitochondrial DNA vs. Nuclear DNA
Mitochondria are the energy power plants inside cells. They have a few genes necessary for oxidative phosphorylation, which is a fancy term for making energy. The nucleus of the cell is where the chromosomes are. Nuclear DNA is the DNA that you hear about in the news, for example in forensic science. In the figure below, you can see that mitochondrial DNA is passed on only by the mother while nuclear DNA is passed along by both parents. Genetic drift in mitochondrial DNA is much slower and helps refine the lineage of a species. It is slower because it is only inherited by half of the genetic source, i.e., the mother.

You can read a summary of the article in layman's terms here:
Arctic find confirms ancient origin of dogs

Full article and source of the very cool graphical abstract:
Ancient Wolf Genome Reveals an Early Divergence of Domestic Dog Ancestors and Admixture into High-Latitude Breeds
Skoglund et al
Current Biology May 2015

Source for the mitochondria DNA figures:
University of California Museum of Paleontology's Understanding Evolution (http://evolution.berkeley.edu

A bit more reading:
How the wolf became the dog (full article behind paywall)

Late for #FidoFriday  but always on time for #ScienceEveryday  
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Color Us Fractally

A colorful way to start your +ScienceSunday with a tutorial on fractals from our resident mathematician +Richard Green . Thanks, Richard, for another stunning post. 

Richard Green originally shared to Mathematics:
The Gamma Function and Fractal Factorials!

This fractal image by Thomas Oléron Evans was created by using iterations of the Gamma function, which is a continuous version of the factorial function.

If n is a positive integer, the factorial of n, n!, is defined to be the product of all the integers from 1 up to n; for example, 4!=1x2x3x4=24. It is clear from the definition that (n+1)! is the product of n+1 and n!, but it is not immediately clear what the “right” way is to extend the factorial function to non-integer values.

If t is a complex number with a positive real part, the Gamma function Γ(t) is defined by integrating the function x^{t–1}e^{–x} from x=0 to infinity. It is a straightforward exercise using integration by parts and mathematical induction to prove that if n is a positive integer, then Γ(n) is equal to (n–1)!, the factorial of (n–1). Since Γ(1)=1, this gives a justification (there are many others) that the factorial of zero is 1.

Using a technique called analytic continuation, the Gamma function can then be extended to all complex numbers except negative integers and zero. The resulting function, Γ(t), is infinitely differentiable, except at the nonpositive integers, where it has simple poles; the latter are the same kind of singularity that the function f(x)=1/x has at x=0. A particularly nice property of the Gamma function is that it satisfies Γ(t+1)=tΓ(t), which extends the recursive property n!=n(n–1)! satisfied by factorials. It is therefore natural to define the factorial of a complex number z by z!=Γ(z+1).

At first, it may not seem very likely that iterating the complex factorial could produce interesting fractals. If n is an integer that is at least 3, then taking repeated factorials of n will produce a sequence that tends to infinity very quickly. However, if one starts with certain complex numbers, such as 1–i, repeated applications of the complex factorial behave very differently. It turns out that (1–i)! is approximately 0.653–0.343i, and taking factorials five times, we find that (1–i)!!!!! is approximately 0.991–0.003i. This suggests that iterated factorials of 1–i  may produce a sequence that converges to 1.

It turns out that if one takes repeated factorials of almost any complex number, we either obtain a sequence that converges to 1 (as in the case of 1–i) or a sequence that diverges to infinity (as in the case of 3). However, it is not possible to take factorials of negative integers, and there are some rare numbers, like z=2, that are solutions of z!=z and do not exhibit either type of behaviour.

By plotting the points that diverge to infinity in one colour, and the points that converge to 1 in a different colour, fractal patterns emerge. The image shown here uses an ad hoc method of colouring points to indicate the rate of convergence or divergence. The points that converge to 1 are coloured from red (fast convergence) to yellow (slow convergence), and the points that diverge to infinity are coloured from green (slow divergence) to blue (fast divergence)

Relevant links

Thomas Oléron Evans discusses these fractals in detail in a blog post ( which contains this image and many others. He (and I) would be interested in knowing if these fractals have been studied before.

The applications of the Gamma function in mathematics are extensive. Wikipedia has much more information about the function here:

This post appears in my Mathematics collection at

#mathematics #sciencesunday  

Various recent posts by me
Camellia flower:
Horse chestnut tree:
A Curious Property of 82000:
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Official page of #ScienceSunday and #ScienceEveryday (brought to you by Robby Bowles, Allison Sekuler, Rajini Rao, Chad Haney, Buddhini Samarasinghe, Aubrey Francisco, and Carissa Braun)
You have found the official page for #ScienceSunday (co-curated by Robby Bowles, Allison Sekuler, Rajini Rao, Chad HaneyBuddhini SamarasingheAubrey Francisco, and +Carissa Braun)! Post anything related to science and tag it with #ScienceSunday, +ScienceSunday, and each curator to ensure we see your post. If you are a photographer, post a science related image and explain why it relates to science to you - doesn't need to be too specific (science is all around us!). If you are not a photographer, simply post anything related to science - drawings, movies, songs, and text are all welcome. Regardless of the type of post, feel free to add your 2 cents into a discussion in the comments. We always have some great posts with amazing images, great science information, and a lot of interesting conversations, and we're looking forward to even more in the weeks to come. If you miss the "Sunday" in #ScienceSunday, feel free to tag with #ScienceEveryday - we try to monitor those posts as well.