Wednesday, 25 August 2010

Middle Age Spread



Once again, there are stories in the press about the rise of Sexually Transmitted Infections (STIs) in young people (under 24), with half a million new cases in the UK in the last year, a rise of 3% from the 2008 figures. There's an excellent analysis of the data and the media response by Dr Petra Boynton who also deals adeptly with an ill-informed response to the data by a Tory MP.

Although the problem is much more serious with the under 24s, they are not the only group at risk from not using condoms and from poor sex education. As Dr Boynton points out in her blog: 'Sexual health messaging - particularly through education and public health campaigns often overemphasises morality discourses of 'risk' or 'responsibility'... Such an approach also assumes older adults act in different (and more 'appropriate) ways than younger people, which is neither fair nor true'.

The Family Planning Association (FPA) has collected data showing that STIs are also on the increase in the 45-64 age group.

Statistics vary according to different sources. The Royal College of Nursing has noted a 93% increase in gonorrhea between 1999 and 2008 in this age group. A survey done in the West Midlands found that the most commonly diagnosed infection among the over 45s was genital warts – accounting for almost half (45 per cent) of the diagnoses – while herpes was the next most common (19 per cent). Cases of chlamydia, herpes, warts, gonorrhoea and syphilis all rose sharply between 1996 and 2003.

To go back to the actual numbers rather than percentages, according to the HPA's data, Table 4e(ii) shows that chlamydia increased from 1091 cases in 2002 to 2638 cases in 2008. Their data also shows an increase in herpes cases from 1613 to 2903 in the same age group over the same period. These are huge increases in percentage terms but still a small incidence in the population as a whole. So if you see shock headlines about huge increases in grannies with STIs, check the baseline figures.

However, whichever stats you look at, there is an undeniable increase.

One cause is heterosexual couples of that generation splitting up and starting to have casual sex again. For some of them, the thought of dating again is daunting enough, let alone the idea of buying and using condoms. Some people may never have used them. Women who have been through the menopause are mostly of a generation whose main concern was avoiding pregnancy; being on the Pill was considered enough protection and greatly superior to using condoms. The Pill was also seen as empowering women as they didn't have to rely on the man to provide contraception. In addition, the powerful HIV/AIDS adverts of the 80s are now a distant memory and may have come from a time when they thought the campaign didn't relate to them in their steady relationships (which they assumed/hoped were faithful).

A poll by the Royal Pharmaceutical Society of Great Britain found that almost 20% of the 45-54 age group admitted to having unprotected sex in the last five years with someone other than a long-term partner. And a Saga survey of around 8000 people found one in ten not using condoms even though they don't know the sexual history of their partner. Again, a sharp rise from a small number to a slightly larger number is a trend but not a crisis although it is a trend that needs addressing.



While some middle aged people had excellent sex education from schools or parents, many didn't. STIs were often seen as something only the promiscuous got. They may not know, for example, how STIs can be transmitted through non-penetrative sex or that they are at risk at all. And while some people may have plenty of experience, both in having sex and talking about it, not everyone does.

Part of the problem is that sex is often portrayed by the media as something for younger people; the thought of older people having sex or expressing any kind of sexuality can be a bit of a joke or cause (younger) people to wrinkle their noses.

There is a gender bias too, just as there is with younger people where boys are portrayed as predators and girls as victims or 'morally loose'. Older men who are still active are admired (see how many Hollywood stars are still getting the girl in movies well into their sixties) while active older women are a bit distasteful. The alleged Cougar phenomenon in the media is really about women in their forties - maybe early fifties - who look much younger, not grannies. The most explicit portrayal you're likely to see on TV is an advert for a denture product with an older couple kissing (no tongues). None of this helps some older people feel confident in talking about sex openly or seeking advice.

It's encouraging to anyone approaching this age group that the fun doesn't have to stop. But while some are happily embracing their new sexual activity, some older people who grew up in a time when sex was less openly discussed may also find it harder to talk to GPs and health professionals about sex-related matters, especially if they are much younger. They may not even want to admit they are having sex again.

The current government coalition is doing little in the way of public health campaigning for sexual health services for any age group but the Family Planning Association is trying to address the problem for older people with a Sexual Health Week from 13-19 September specifically aimed at people over 50.

So far there has been no media hype or hysteria about older sex as there has been once again with young people, laden with high-handed moral judgements and shock horror headlines. This may change once the campaign launches.

The facts are that there is a small but significant upward trend that is indicative of poor education and campaigning. Just as teenagers need to be equipped to have responsible sex in a factual, non-moralising way, so do older people. The week in September is a good start but without a sustained campaign, it could just come and go without making much of an impact. So, there is not a huge new phenomenon, the very fabric of our society is not at risk from feckless pensioners and irresponsible baby boomers but the government is failing both young and old

Wednesday, 11 August 2010

Food Allergies - Fact, Fiction and Fad

There are two common responses when the subject of food allergies comes up. The first, mostly but not entirely from older people, is "Stuff and nonsense. They didn't exist when I was young, we ate whatever was put in front of us. You don't see starving people in the third world with allergies". The second is: "I feel much better and have lost lots of weight since I stopped eating wheat. I know I'm allergic/intolerant because I sent my poo/blood/hair away to be analyzed".

According to one source, 25% of adults think they have a food allergy although studies show that only about 2% really do. Which means that at least nine out of ten are making a big fat fuss about nothing. Recent news said that up to 8% of children now have allergies although a spokesperson from Allergy UK said: "Parents often look for alternative ways to diagnose their children, using tests which aren't scientific at all. Parents tend to think it's an allergy without taking proper medical advice".

It's mostly middle class people with a bit of spare cash who have latched onto food allergies and intolerances (the two are often used interchangeably). Not the life-threatening A&E kind of allergy but the feeling a bit bloaty and tired, self-dramatizing kind which are not allergies at all. Some people will happily say they're 'a bit allergic' to something without any medical evidence whereas they would never say 'I'm a bit diabetic' and not bother going to the doctor. One reason people might well feel better and lose weight by giving up wheat is that by not eating bread, pasta, pastry and pizza they are also cutting back on the high fat, high salt ingredients that go with them - cheese, highly salted meats, mayo, creamy sauces and so on. Or maybe they really are lactose intolerant and have accidentally cut most dairy out of their diet by giving up these foods. That's the trouble with self-diagnosis.

Saying 'I'm allergic to dairy' or 'I'm gluten intolerant' has become a bit of a middle-class mantra, not that different from telling people your star sign in some circles, as if that makes you more interesting and special. People are more than happy to discuss the details of their alleged intolerances in company where they wouldn't dream of mentioning an ingrown toenail or dandruff - two equally unpleasant but minor complaints. I've heard lengthy conversations about how cutting something out of a diet has changed someone's life, usually followed by a discussion of how they found out they had an allergy/intolerance. Inevitably, this does not involve a visit to the doctor. It involves posting some bodily fluid or excresence off for analysis. There are often endless conversations sharing the love and comparing notes on what foods they can't eat and how they got 'diagnosed'. While eating dinner. Of course, the host/ess has been thoughtfully supplied in advance with a list of all the things the guests can't eat.

A food allergy is an adverse immune response to a food protein. The body identifies a protein as something threatening, the immune system thinks it's under attack and triggers an allergic reaction which can range from mildly unpleasant to life-threatening.

In answer to the people who think that allergies are a modern fad - they're not. In the olden days, anyone with a serious allergy wouldn't make it through childhood and in days before the NHS and proper testing, the cause of death mostly went undiagnosed. The same still goes for parts of the third world. These people are often heard saying things like a certain food doesn't agree with them or 'I like it but it doesn't like me' without thinking that this could be a mild allergy. But going on and on about them is a modern fad, part of a more general obsession with food in our over-stocked culture. It's what used to be called being a fussy eater, perhaps followed by a smack on the bottie that quickly put paid to that bit of wilfulness.

An intolerance doesn't involve an immune reaction. It happens when the body is unable to deal with a certain type of food, usually because it doesn't produce enough of the chemical or enzyme needed to digest it. For example, a shortage of the enzyme lactase causes problems breaking down milk sugar (lactose) into simpler forms that can be absorbed into the bloodstream. There's a strong genetic pattern to food intolerances. Lactose intolerance is less common among northern and western Europeans (10 to 15 per cent are affected) than in Asian, African, native American and Mediterranean populations (70 to 90 per cent are affected). Symptoms include nausea, bloating, abdominal pain and diarrhoea, hours or days after. Which are pretty unpleasant. But those nasty squitty, pukey symptoms don't tend to get mentioned in dinner party conversations, which are more likely to involve weight loss and the person's skin improving. If you have regular cramping and throwing up, you'd probably hightail it to the doctor.

There are plenty of ways to get diagnosed. One involves getting medical advice. The rest don't. Some of these are pretty expensive, often hundreds of pounds. NICE has issued draft guidelines for doctors on diagnosis and treatment of allergies, which contain the advice 'Do not use the following alternative diagnostic tests in the diagnosis of food allergy: vega testing, applied kinesiology, hair analysis'. The guidelines also say that 'it was reported that many people with allergies practice self-care, using alternative sources of support rather than NHS services (for example, complementary services with non-validated tests and treatments)'.

Briefly, kinesiology uses 'energy* fields' in the body to diagnose allergy and intolerance, vega testing involves measuring electromagnetic conductivity in the body using a Wheatstone bridge galvanometer - the same device Scientologists use outside their centres to 'test' passers-by. Hair analysis tests for heavy metals that allegedly cause allergies or involves dowsing - swinging a pendulum over the hair; an allergy is diagnosed if an altered swing is noticed. And then there are the poo samples. Post your poo off to a lab in the UK or US and find out how many different foods you're allergic or intolerant to. As one UK hospital states, samples more than 8 hours old will not be processed as they have degraded too much, so sending poo through the UK postal service to another city, let alone to the States, is hardly going to ensure it arrives in prime condition. And I really don't want to think about what collecting your own poo sample involves. Or what postal workers might make of poorly wrapped packages.

There are some excellent analyses of why all these alternative testing methods are nonsense on stilts on Quackwatch and Holford Watch.

If you really are allergic or seriously intolerant, it can be very unpleasant indeed. If you think you might be or that your child is, see a doctor. Otherwise, kindly shut the fuck up. Or am I being intolerant?

* As soon as you hear 'energy fields', you know you're in quackland.

Friday, 30 July 2010

PSHE update

As the DSCF no longer exists, the Department of Health asked NICE to run a consultation on sex and relationships education. It's pretty much a re-run of the earlier consultation. I wrote this for work.

There is a lot more to say on the subject of PSHE and Dr Petra Boynton has covered all the main issues in her blog.

Sunday, 25 July 2010

Female Genital Mutilation in Britain

Female Genital Mutilation (FGM) is sometimes referred to as female circumcision although it is far more severe than the male version and should always be referred to as what it is - mutilation.

FGM has no health benefits. It involves removing and damaging healthy and normal female genital tissue, and interferes with the natural functions of girls' and women's bodies. It's done to ensure that the girls' future husbands can guarantee their bride is a virgin and to ensure fidelity. The causes are a complex mix of religious, social and cultural factors. Girls who are not cut can face being outcast from their societies and unable to find a husband. In essence, it is a way of controlling women's bodies and sexuality. It's said to reduce their libido, to be a sign of femininity and that women who are unmutilated are 'unclean' amongst other lies.

According to Forward UK, an anti-FGM charity, it's estimated that approximately 100-140 million African women have undergone FGM worldwide and each year, a further 3 million girls are estimated to be at risk in Africa alone. FGM also happens in the Middle East and Asian countries, and increasingly in Europe, Australia, New Zealand, the USA and Canada. Forward estimates that as many as 6,500 girls in the UK are at risk of FGM every year. The summer holidays are when many mutilations happen as they give the victims time to recover before going back to school in the autumn.

There are four types identified by the World Health Organisation, ranging from partial to total removal of the external female genitalia.

1. Clitoridectomy: partial or total removal of the clitoris and, in very rare cases, only the prepuce (the fold of skin surrounding the clitoris).

2. Excision: partial or total removal of the clitoris and the labia minora, with or without excision of the labia majora.

3. Infibulation: narrowing of the vaginal opening through the creation of a covering seal. The seal is formed by cutting and repositioning the inner, or outer, labia, with or without removal of the clitoris.

4. Other: all other harmful procedures to the female genitalia for non-medical purposes, e.g. pricking, piercing, incising, scraping and cauterizing the genital area.

However, an article in the BMJ questions the usefulness of these classifications, saying that 'The WHO classification fails to relate the defined forms to the severity of the operation'. For example: 'WHO classifies all forms that involve suturing as type III, regardless of whether the labia minora or majora have been cut. Therefore classification as type III does not indicate the extent of the mutilation that has been done. This is important, especially in investigations of FGM and complications'. Another problem is that 'Almost all studies about the prevalence and trends of ... (FGM) have been based on women self reporting their form of FGM. How this reported form corresponds to reality is unknown'. It concludes that 'The WHO should revise its classifications to relate the different forms more to the anatomical extent of the operation.' Far more research needs to be done to get useful statistics and to get rid of the ignorance, secrecy and silence around this subject.

FGM is traditionally done by an older woman with no medical training. Anaesthetics and antiseptic treatment are not generally used and cutting is usually done with basic tools like knives, scissors, scalpels, pieces of glass and razor blades. Often iodine or a mixture of herbs are placed on the wound to tighten the vagina and stop the bleeding. There have been cases of UK doctors willing to carry out the procedure. When caught, they have been struck off.

The most common age is between four and ten, although it appears to be falling. Some of the girls are taken abroad, some are mutilated in the UK. In some cases, there are 'cutting parties' with groups of girls mutilated together to save money.

Immediate risks are death from blood loss and infection, urinary and menstrual problems. Longer-term effects include extensive damage of the external reproductive system, uterus, vaginal and pelvic infections, cysts and neuromas, increased risk of Vesico Vaginal Fistula, complications in pregnancy and child birth, psychological damage, sexual dysfunction, difficulties in menstruation. Period blood can build up and clot, leading to serious, life-threatening infection. There are currently 16 clinics in the UK to deal with the damage.

None of the major world religions demands mutilation. Some religious leaders condemn it while others either turn a blind eye or endorse it. FGM is not limited to Muslims as it is practised in Christian communities too. It is thought to pre-date both religions and to have started in Egypt; type 3 mutilation (according to WHO classification) is also known as pharaonic circumcision. There is nothing in the Koran requiring FGM but there are hadeeths about it. For example: 'Circumcision is a commendable act for men (Sunnah) and is an honorable thing for women (Makromah)' and 'Prophet Muhammad is reported to have passed by a woman performing circumcision on a young girl. He instructed the woman by saying: "Cut off only the foreskin (outer fold of skin over the clitoris; the prepuce) but do not cut off deeply (i.e. the clitoris itself), for this is brighter for the face (of the girl) and more favorable with the husband'. While many Islamic scholars and leaders question these hadeeths, for anyone who wants an excuse, they can provide it.

The UK Prohibition of Female Circumcision Act 1985 makes it an offence to carry out FGM or to aid, abet or procure the service of another person. The Female Genital Mutilation Act 2003, makes it against the law for FGM to be performed anywhere in the world on UK permanent residents of any age and carries a maximum sentence of 14 years imprisonment. To date, no prosecutions have been made.

The UN Convention on the Rights of the Child (1989) requires 'all states to take all appropriate measures with a view to abolishing traditional practices prejudicial to the health of children' and Article 2 of the UN Declaration on the Elimination of Violence Against Women states that 'all violence against women shall be understood to include FGM and other traditional practices harmful to women'.

The UK police have set up Project Azure to combat the crime but have so far taken a soft approach. In 2007, the Met offered a £20,000 reward for information leading to arrest, with no success. Part of the problem is lack of research and the reliance on anecdotal evidence or statistics from doctors treating the after-effects because of the secrecy surrounding the procedure and successive governments' timidity in taking on 'cultural' issues. There have been debates about whether attempts to end the practice are Western cultural imperialism imposing its values on other cultures and whether cultural relativity means that the West has no right to comment on or condemn other people's traditions. Although there needs to be sensitivity in dealing with the subject, especially to avoid stigmatizing the women, this should not be an excuse for doing nothing. This is not some quaint 'ethnic' tradition, it's a non-consensual human rights violation

The West has its own history of fear and loathing of female genitals and sexuality. Freud stated in Sexuality and the Psychology of Love that the 'elimination of clitoral sexuality is a necessary precondition for the development of femininity', for example. In some extreme cases, clitorectomy was practised to prevent women masturbating or as a cure for hysteria and lesbianism.

More recently, women who have been made to feel there is something 'wrong' with their genitals are offered cosmetic surgery, to 'correct' large or assymetrical labia for example. According to one website, 'Many women dislike the large protuberant appearance of their labia. This may cause severe embarrassment with a sexual partner. Surgical labial reduction can greatly improve the aesthetic appearance of the abnormally enlarged labis.' One UK site says that 'It's not unusual for a woman to feel dissatisfied with her labia'.

Surgery is touted because it is a woman's 'right' to have beautiful genitalia - but also her duty if she wants to avoid shame and embarrassment. Although this in no way compares with the forced mutilation of girls and young women, it is an indicator that no society is immune from the pressure on women to conform to artificial norms of what are acceptable genitalia, creating yet another dissatisfaction with their bodies.

Saturday, 24 July 2010

Noah's Ark Zoo wins an award



Noah's Ark Zoo in Wraxall, North Somerset has won a Learning Outside the Classroom Quality badge for its schools programme.

This is surprising for two reasons.

Firstly, an investigation by the Captive Animals Protection Society (CAPS) and the BBC Programme Inside Out found that the zoo was breeding tigers for a controversial circus owner and that staff were under strict orders not to tell anyone.

One of the tigers died 10 days after giving birth to four cubs, one of which also died. The zoo claimed that she died from Feline Infectious Peritonitis but there was no proper post-mortem. The tiger's head, paws and skin were cut off and the body was buried in breach of animal disposal legislation.

A woman working undercover for CAPS found the head in a freezer. According to CAPS, the zoo's education officer, also a qualified vet, admitted to her that the burial was illegal, that she turned a blind eye and that no proper examination was done, even to check if the tiger had died of something infectious. The education officer told the undercover worker that the tiger's owner (the circus) wanted the head and paws.

As a result of the CAPS investigation, the zoo lost its membership of the trade body BIAZA - the British and Irish Association of Zoos and Aquariums. Nevertheless, North Somerset Council has recently approved plans for an elephant house.

Secondly, it's a creationist zoo. The website says:

'Undoubtedly, Darwin helped science to see that nature is continually changing, but along with this great progress there began a subsequent movement to remove any notion of God from our understanding of life. This is unjustified and we look to put the case for the Creator across to those who wish to investigate'

and

'Is it right for Darwin's evolutionary theory to be portrayed as "fact" in today's scientific media and the idea of God generally abandoned?'

and

'Important scientific theories have been proposed and much research done on the subject, but these, while widely accepted, have serious problems with them. After looking at the current explanations for origins and evolution; it is our view that the evidence available points to widespread evolution after an initial Creation by God'.

And much more.

According to the LOTC website, the award is judged on 'six high level generic quality indicators'. They are:

1. The provider has a process in place to assist users to plan the learning experience effectively;
2. The provider provides accurate information about its offer;
3. The provider provides activities or experiences which meet learner needs;
4. The provider reviews the experience and acts upon feedback;
5. The provider meets the needs of users; and
6. The provider has safety management processes in place to manage risk effectively.

As long as your learner needs don't include animal welfare, science or the meaning of the words 'fact', 'evidence' and 'theory', then you're fine. Are teachers keen for pupils to learn that God made everything or do they ignore that part as long as the kiddies can look at the nice animals?

The Bristol Animal Rights Collective has a petition against the zoo and holds regular protests outside. There's a big demo on August 30th.

Incidentally, according to Genesis 7:2-3, the animals didn't all go in two by two. The clean went in seven by seven and the unclean two by two. The seventh of each clean species was sacrificed once they reached dry land (v20). Which must have taken quite a long time.

UPDATE 18 August 2010
My comments to a Welsh newspaper on the zoo.

Thursday, 15 July 2010

Vatican Causes Cancer?

The Vatican has been accused of giving children cancer. Highly amusing as it is to think of a radioactive Pope spreading Vaticancer, he's too busy with all the child abuse cover-ups and conning the UK taxpayer into spending up to £100 million on his visit to waste energy emitting Papal Death Rays. He is getting on a bit, after all.

Professor Andrea Micheli has written a 300 page report focussing on 19 deaths from leukemia or lymphoma between 1980 and 2003 in the Cesano area north of Rome. Vatican Radio has 60 masts nearby in Santa Maria di Galeria. Micheli's investigation was ordered by a Roman court five years ago after concerns were raised about an increased incidence of cancer in the area. It's not clear exactly who was concerned.

He claims that children under 14 living within a 7.5km radius of the masts have a raised cancer risk. As a result of his research, six Vatican Radio officials are under investigation for manslaughter.

The charges mean that this is not just yet another lame conspiracy theorist attempt to link masts or electromagnetic waves and cancer or the usual Daily Mail cancer scare.

Quackwatch has very thoroughly shown why there is no conclusive link.

Moreover, the Italian Navy also operates masts in the area but Micheli insists that it's the Vatican masts that are to blame. Perhaps there is some added toxic ingredient being emitted because of what they are broadcasting. As Quackwatch says:'what they emit is not understood by the public. Nor can they be felt, tasted, seen or touched. This makes them mysterious, easily portrayable as threatening'. Temptation to draw a parallel with certain aspects of religion will be resisted.

There are other problems with Micheli's findings. Firstly, the research was submitted to a court, not for peer review. The contents were leaked.

A research paper that is available without leakage in the American Journal of Epidemiology called Adult and Childhood Leukemia near a high-powered radio station in Rome, Italy finds that rates were higher than expected but that 'The study has limitations because of the small number of cases and the lack of exposure data.' It adds that 'no causal implication can be drawn'.

And the Lancet finds that: 'In the European population, about 1% of all malignant neoplasms arise in patients younger than 20 years. This low frequency represents a major difficulty for studies of putative risk factors'.

An article in The Hematology Journal called Expected number of childhood cancers in Italy from 2001 to 2015 states: 'The total number of children with incident cancer in Italy has never been specifically estimated. Specialized population-based Childhood Cancer Registries have only been operating in Piedmont (CCRP) and in the Marche region, while general population cancer registries cover about 20% of the Italian population'.

This means that there is insufficient data to tell if cancer rates have gone up above the expected rate compared with other mast-free parts of Italy. It's hard to gauge what's higher than expected when there is no accurate definition of 'expected'.

Leukemia and lymphoma are the commonest childhood cancers. Italy has nearly the highest rate of them in the whole world.

In Europe, the overall incidence increased by 1% a year from 1970-99 in children and by 1.5% in adolescents. The average incidence in Europe is 140 per million for children up to 14. That's 1.4 children per ten thousand. According to the American Journal of Epidemiology research, nearly 50,000 people live in a 10km area around the station.

[edited 22/3/11: In the Perugia region, about 150km north of Rome, for example, around 1.3 children in ten thousand get leukemia or lymphoma every year.

Nineteen children got leukemia or lymphoma in a twenty three year period in the Cesano area. In the Perugia region in the same period, you would expect just under 30 children to get them.]

While the data from these various sources are not directly comparable, it looks very much like nineteen deaths is not a suspicious figure.

This is probably the one and only time I will ever defend the Vatican.

Thursday, 8 July 2010

Hyperbolic Crochet

In 1997 a mathematician at Cornell figured out how to make a model of hyperbolic space that her students could handle so they could understand the concept better. Dr Daina Taimina got the idea from William Thurston but his paper models were too fragile to be of practical use. Crochet to the rescue.

With hyperbolic space, as you move away from a point, the space around it expands exponentially. While all spheres have the same form, hyperbolic surfaces can differ substantially. This quality is characterized by the radius of the plane; the more crenellated the surface, the smaller its radius and the flatter the surface, the greater its radius. A regular Euclidean plane can be thought of as a hyperbolic plane of infinite radius.

To show you what this means in practice, here are my own attempts. This is what one looks like after just two rows of crochet:

And after four rows:

And six:


And eight (at which point, I ran out of yarn):


The width is 9cm and the edge measures over 2.5m. Dr Tamina's biggest one had a width of 4 inches, a perimeter length of 369 inches and weighed nearly a pound.

The photos are not great quality, but you get the idea. There are some better quality ones here. For mathematicians, an increase is made every Nth stitch so the number of stitches from one row to the next is in the constant ratio N to N+1. For crocheters, I used a 3.5mm needle, double acrylic yarn and started with a ring of 6 stitches then increased in every stitch, working in double (or, if you're American, single).

There are examples of hyperbolic geometry in nature, like lettuce, kelp, sea slugs, flatworms and nudibranches. Margaret and Christine Wertheim of the Institute for Figuring have made a crocheted coral reef with kelps, anemones, sea slugs and corals by using variations and permutations of the basic algorithm. Crocheters all over the world have contributed and there are now many sub-reefs, like the Bleached Reef:



After which, my own little sea creature looks a bit lonely:



It's really really easy to do. Who says maths can't be fun?

Next time, the science of kittens and pink things.


Thanks to my crochet guru for this one.