Notes on Fibonacci, spirals, the Chinese concept of Li, and examples of geometric patterns Fibonacci and Spirals2
A mythical people known as akephaloi (Greek “headless ones”) or Blemmyes had no head or neck and their eyes, nose and mouth were placed in their chest. They lived by the Nile, in Ethiopia, and in parts of India. Often naked, fierce and combat loving they were eight feet tall, their skin could turn to a golden colour and their beards could grow down to their knees. It was said their lacking of a heard was due to the sins of their ancestors
I always see Thursday as green. I’m told this is a type of synesthesia. This picture I made from recycled Mills&Boon romance novels. It is loosely about lost love on a Thursday evening. I had a private view of my work that night, my boyfriend at the time came along as it ended and brought me a bunch of white roses. They looked unwell. I think we both knew it was over. The green of the leaves didn’t look quite right to me, and was much more noticeable than the flowers themselves. It was a messy London Thursday goodbye, an oldness pretending to be young.
On the visible spectrum green is the colour between blue and yellow. In painting it is considered a secondary colour because it can be mixed from the primary colours of blue and yellow. Green is middle of our colour range. It contains no red, no ultra-violet or infer red, it is just green.
Looking at the colour green has been found to help with cancer. The people of the rainforest are said to have very many words for green. If you walk into a wood in the summer and look up you can understand why. In nature there are so many different greens, it is of course the colour of photosynthesis, that magical spell that converts sunlight into chemical energy and gives us our oxygen. Interesting though I recently learnt that green is the only colour that is actually not used in the process of photosynthesis, which is why it is the one that is reflected out. A simple experiment that shows this is when tomatoe plants (or cress, I don’t think it makes much difference) are grown under different colours of light. They will be fine growing under only red light, only yellow or only blue, but under just green light they are not able to carry out photosynthesis, so die.
This explains that chlorophyll are green because they don’t use green light energy so green is reflected out. This is because chlorophyll arose in organisms in the ocean where halobacteria was already converting light energy to chemical energy using green wavelengths but not so much of red and blue wavelenghs, so chlorophyll was entrepreneurial and made use of the red and blue, reflecting out the green. Imagine if that had been the other way round, the world would look very different. Purple trees!
The modern English word for green comes from the same root as the Germanic words for grass and grow.
I am currently burning a green candle because green is the colour for Venus, the goddess of love and I could do with some care free love in my life right now.
In Europe and the U.S. green is the colour most associated with nature and growth, however is does have the negative symbolism of envy and illness. In America it is the colour of money, and it is the national colour of Ireland.
In Japan green is associated with eternal life, in China it is the symbol for health and happiness. Though in old Japanese, Chinese, Thai and Viennese green isn’t a separate colour but a shade of blue.
In North Africa it is the colour of corruption
In Islam it is the sacred colour representing respect and the prophet Mohammed, it was the colour of the banner of Mohammed and represents the lush green of paradise.
In Indonesia it is a forbidden colour.
For anyone who get curious about the colour green, mixing it is the ultimate way to get to know it. When painting greens for plants, ready made greens brought from a shop are rarely accurate to portray a green in nature. A ready made green can often look garish and false when applied directly to the paper. Even if one ready mixed one in the palette looks close I will try it with maybe a little alizarian, it’s complementary colour, to bring it down a touch and try this next to the subject. It amazes me what a difference just a spec of red can make.
Exercise mixing greens
Start by putting some lemon yellow in your palate. Using a soft flat brush put a sample of it in the top corner of a sheet of paper.
Clean your brush in water and take a very small amount of cobalt blue and add it to the lemon yellow. Put a sample of this next to the original yellow on your paper.
Repeat the last stage again adding a little bit more cobalt blue to the lemon yellow and add another sample alongside the previous two.
Continue this along the page with the greens getting increasingly bluish until the sample you have is almost completely blue. Label the sample Lemon yellow and cobalt blue
From yellow gradually adding more blue
Repeat this exercise all over again but instead of using cobalt blue use French Ultramarine. Remember to label the names of the colours next to the samples so you can use it for reference later. Do another sample strip u using Prussian blue. Now your sheet of paper should start to show the huge variety of greens it is possible to mix. Carry on the exercise doing a sample strip using all the different blues in your palate. Once you have done that choose one of those blues to keep the same and instead try all the different yellows you have, try cadmium yellow, yellow ochre, Indian yellow.
Make sure your water is clean and if not change it, you will get muddy unintended colours if using dirty water.
If painting natural objects you may find the greens you mix are a bit too bright. Improve this by adding the very tiniest drop of red to bring it down a touch, try Alizarin Crimson or Rose Madder. Be gentle though, you will be surprised at how the smallest amount can change the colour. Red is the complimentary colour to green, on the other side of the colour wheel, add too much to the mix and you’ll end up with a brown or grey. Though these can be used to good effect in shadows.
Even if you never intend to paint a picture, sitting and mixing greens is a very calming exercise. I recommend it on messy Thursdays.
I have a horrible cough right now which just doesn’t seem to go away. I read on the internet that finely powdered hazelnuts mixed with water and honey can get rid of a stubborn cough. So I give it a go, hand grinding the hazelnuts in my pestle and mortar. I’m not sure if I’ve ground them fine enough but it does make quite a nice drink. We’ll see what it does for the cough.
Hazel was the name of my best friend at primary school, she was very clever. She got to the posh grammar school for intelligent girls, I got sent to the units for special needs children in the roughest school in the area. I was a very slow developer and could barely read at the time. I didn’t want to be Hazel’s friend after that, I ignored her calls and avoided her in town. Pride eh? Very foolish of me!
The Hazel was the tree of wisdom, according to Irish mythology. In the otherworldly realm there is a well from which the rivers of Ireland flow. In this well there swims a salmon and around it are nine sacred Hazel trees. The hazelnuts from these trees fall into the pool and are eaten by the salmon everyday so they themselves become wise. These wise salmon swim from the pool to the sea and back. If you manage to catch and eat the salmon you too will become wise and able to tell the future. Fionn mac Cumhailfrom, the hero of many an Irish legend, was cooking this salmon for his Druid mentor, who had been seeking the fish for a long time. He accidentally burnt his finger and sucked it to make it better, but juices of the salmon are on his finger so sucking it means that he gets the wisdom. His poor mentor gives up then, seeing at once that Fionn now has The Knowledge. This links into the practice of Imbas Forosnai, a type of inspired, fortune-telling poetry once practiced in Ireland. I’ll write more about this in another blog.
Hazel comes under the planet Mercury, the colour orange, the element air, and of course the god Hermes/Mercury. Hermes has the caduceus, a winged staff with two snakes twirling round it, and this was made of hazel wood.
The tree has been regarded as playful, wise, and enchanting. It was frequently used for divination and to find water or buried treasure. When my parents first moved to Pembrokshire and needed to find a well on their land, the locals didn’t hesitate to recommend the local diviner who, I believe, used a forked hazel branch, and it worked. Hazel is also excellent for making magic wands and walking sticks. In Irish legend it is sacred to the god of love and eloquence Oengus mac Og.
To enlist help of faerie folk thread several hazelnuts together on a string and hang in your home. Hazelnut twigs on a windowsill are said to protect against storms. Hazelnut necklaces are thought to bring good luck into the home. Three hazelnuts clumped together are lucky. If you are looking for poetic inspiration and magical insight chew on a hazelnut to induce this.
Hazel is a deciduous tree, often growing underneath oak and birch. In managed woodland it is frequently coppiced which extends its life from 80years to several hundred. Both male and female flowers grow on the same tree, but hazel flowers must be pollinated by pollen from other hazel trees. It is mainly wind pollinated, bees find it difficult to carry hazel pollen as it is sticky and the grains repell each other. The male flower is a yellow catkin that comes out in February before the leaves. The female flower is small and bud like with red styles. Once pollinated the female flowers develop into round fruits that hang in groups. They mature into nuts with a woody shell surrounded by a leafy husk. Hazel leaves are hairy and soft to the touch, oval in shape they are toothed and pointed at the tip. Hazel leaves turn yellow before falling in winter. Many caterpillars live off the hazel, this is particularly good for The Hazel Dormouse for they can eat the caterpillars in the summer months and save hazelnuts for hibernation in the winter.
In the spring hazel branches are particularly bendy. Semi permanent structures can be made by bent hazel poles tied into dome shapes and stuck into the earth and covered with hides or waterproof tarpaulin.
My cough seems a little better now than it was this morning. I also read that hazelnuts taste particularly good with Salmon, I decide to give this a go. Delicious! And maybe it might make me a little wiser.
Mushrooms are amazing, I love to eat them, to look at them, to draw them, and when I investigate them they are quite mind boggling. No, before you ask, I haven’t tried magic mushrooms, one day maybe.
Opposite where I live in Newington Green there is a magnificent greengrocers which sells all sorts of vegetables and fruit, from the everyday parsnip to the weird and wonderful where I can only guess at name and purpose. Among this there are mushrooms of many types. Although recently it has been decided that mushrooms aren’t actually vegetables, but closer to animals, I and the greengrocers aren’t worrying about that right now. Yesterday I brought a selection of the more visually enticing mushrooms to paint. A friend popped round and on seeing the mushrooms said “Are those colours real? They’re not edible are they? They look poisonous”. I paint them in watercolour laid out in a line. It is difficult though, they wither very quickly and darken in colour.
Autumn is the time for wild mushrooms, that smell of autumn woodlands is created by fungi working their way up through the soil. The mushroom itself is of course the flowering body of the fungi, the part that disperses the spores. Fungi themselves are everywhere, often microscopic they are on every surface, in the air we breath, and everywhere we put our foot. Underneath, in the soil, is an intricate web of fungi threads, called the mycelium, which can exist in the tiny body of a dead fly or span across an entire forest. In the Oregon’s Blue Mountains in the United States there is a mycelium that occupies 2384 acres and is thought to be between 2000 and 8000 years old!
A friend and I once created a mycelium installation at the ICA. It was good fun, black inside with threads criss crossing through it. Members of the public enjoyed going and just sitting inside. They said they found it comforting. Recently I feel like I need to dig a hole in the ground and bury myself inside, amongst the roots and threads, I haven’t done so yet, it is probably from me reading too much Brian Catling and his book of abandoned angels.
As mentioned before trees have symbiotic relationships with fungi. Apparently 90 per cent of all land plants have mutually beneficial relationships with fungi so it is nothing unusual. The tree obtains sugars through photosynthesis for the fungi and the fungi obtains nutrients such as phosphorus and nitrogen from the soil for the tree. Plants also communicate with each other through fungi. Mycelia link up plants that are wide apart. In the media this is often described as being like the world wide web, but so much is described as being like the internet these days the phrase makes me cringe. But trees can transfer carbon, phosphorous and nitrogen between themselves through the mycelia. A large tree can help a small young tree in this way. It has also been found that old trees that can no longer photosynthesis are sometimes kept alive by trees they are connected to through the mycelium. No one knows why.
Amazing thought that, plants are communicating with each other and using the fungal networks to do so. Trees can also use mycelium to transfer chemical signals warning other plants of oncoming signals. This was initially discovered on tomato plants. The tomato plants are grown in pairs. Some of them are allowed to form fungal networks and some aren’t. The leaves of one plant in each pair was sprayed with blight disease. Air-tight plastic bags were used to stop any above ground signalling between plants. After 65 hours the scientists tried to infect the second plant in each pair. They found that if the plant pair had been allowed to develop mycelia the second in the pair was much less likely to get the blight and if they did they had significantly lower levels of damage.
I suppose I cant really mention this relationship without mentioning the other side of it. Some trees have been found to pass poisons across through the mycelium. Some trees don’t like other trees growing too near them, they like some space to themselves, so they send out poison via their roots and the mycelium to poison potential newcomers. Bit like me in my flat.
Fungi also feed on dead organic matter, and what a vital role that is for without this the world would pile up with dead leaves, dead wood, dead animals and other matter. The dead matter is broken down and returned as nutrients in the soil for plants again. There is even rumours that mushrooms can affect the weather!
Today the mushrooms on my table have become shrivelled shadows of what they were. I finish the painting and am still determined to eat them. I slice them and fry them with a lot of garlic. Delicious! Much more tasty than your regular mushroom. And I’m not dead yet…
A class on drawing and painting mushrooms will take place at 3pm this Sunday (18th June 17) at The Greenhouse, 49 Green Lanes N16 9BU. thegreenhouselondon.com
I’m in Cornwall again, staying in the woods as before. It is raining ferociously which makes my plans of sleeping under the trees redundant, but it is still amazing. I like the rain, I don’t know why but I always have, perhaps it was because at school it used to mean games would be cancelled and I hated games. I remember once in a physics lesson leading a rain dance ritual to the horror of the physics teacher, because games was scheduled that afternoon. A few drops of rain landed on my nose that afternoon, but not enough for games to be cancelled.
I think it is the smell and the bright colours that rain brings which are now why I love it. Lou, whose wood this is, has just given me an article on the smell of rain. Apparently it is from bacterium released by the soil when it rains which humans are particularly sensitive to.
There is a big Alder tree by the river, I got a little wet trying to sketch it from the other side of the river yesterday. A curious tree, it has been cut back many times and regrown, I wonder how old it is, alders only live to about 60. I spend all afternoon studying it and the moss that crawls up its sides. There is a summer house nearby so I don’t get soaked, but do feel somewhat heroic being out in the cold and rain.
The Alder tree was once seen to symbolise the balance between male and female as both male and female catkins appear on the same branch. It has also been associated with courage, strength and resurrection. In Austria it was once thought that Alder trees could raise the dead.
For me there is something friendly and strong about the Alder, I can’t say what, but it makes me feel comfortable. Though in the past some have thought of it as unlucky or hostile, perhaps because when cut the Alder turns an orange colour due to the sap which can look like blood.
It is a pioneer tree, fertilising the ground for future species, growing to around 20 m tall, it grows in wetland, swamps and by the side of rivers. Alder roots are visible above ground and often provide homes for otters, or fish. The flowers are in the form of catkins, the male catkin are long pendulous and yellow, the female are small, rounded and green, with 3 to 8 on a stalk. They flower between February and April and are mainly wind pollinated, though occasionally visited by bees.
The Alder lives in a symbiotic relationship with the bacterium Frankia alni. The bacterium lives in the root nodules of the Alder tree, these can grow to the size of a human fist, where it absorbs nitrogen from the air and makes it available to the tree. The Alder in return provides the bacterium with sugar through its photosynthesis. This relationship is very beneficial to the soil, fertilising it and providing nitrogen for the plants and trees that follow.
The roots of the Alder are particularly tough in water and can become like stone. They are very resistant to rot when in water and were often used to shore up river banks. Due to this resilience under water the piles on which Venice stands are made of Alder. However when out of water in the open air it does rot, so is not so good for building outdoors. It is good for making whistles and flutes. Fender guitars are made from Alder because of the smoothness of the wood.
Red dye can be made from the outer bark and yellow dye from the inner bark, green dye can be made from the flowers and is apparently what Robin Hood and faerie folk dyed their clothes in.
Alders by rivers and swamp can create a mysterious atmosphere indeed. They were thought to be closely connected to the faerie folk. In Irish mythology the first human is thought to be made from an Alder Tree, the first woman from a Rowan.
The giant and king, Bran the blessed, is connected to the Alder. Bran (meaning crow or raven) in Welsh mythology is said to make the bridge between Wales and Ireland for the Welsh to walk across in the battle to rescue his sister Branwen, similar to how the Alder has been used to build bridges. Bran was killed in the battle, but the welsh won. Bran’s still talking head remained talking after it was chopped off, and even managed to entertain the troops. It was eventually taken and buried where the Tower of London now stands.
Medically Alder has many uses that benefited the celts and native Americans alike. Put Alder leaves in your shoes before a long walk to keep your feet cool and prevent swelling. Alder contains salicin which is an anti-inflammatory. It has been used to treat skin irritations, insect bites, lymphatic disorders and tuberculosis. It is also thought to be of benefit in the treatment of some tumours.
Back to my Alder by the river. In the evening the rain ceases and there is a calm mist over the whole wood. We have a fire in the summer house. I listen to the water rippling and the birds in the tree, now the bats start to swoop through its branches. I drink my kings ginger nightcap and Mike, Lou’s partner, talks of his time in Cambridge studying philosophy, he recommends David Hume. On the way back to the house we come across lots of toads on the path. Fat beautiful creatures with warty skin in interesting patterns. The perfect way to end the night.
When I get back to London I will paint another toad picture on handmade paper, this paper seems to suit toads flesh. Maybe I will attempt to make dye from the Alder bark to paint it in.
Sketch of the Alder tree whilst in the rain.
I really enjoyed drawing this part of the poplar tree. I’d never looked that closely at a poplar before and didn’t realise how sticky the balsam is or how sweetly it smells. I highly recommend drawing it.
The other day I went into the garden to plant poplar tree sticks. They are sticks left over at the end of a botany class. I took loads of different sticks and put them in water in a tall glass jar. Their buds sprouted into leaves which I’ve been drawing, and amazingly the poplar sticks have started to grow roots. It gives off lots of very sticky sweet smelling treacle like substance, the balsam. I dug three holes in the garden, two near the fence where an old tree used to be, and one over the other side in the shade. I’ve no idea if they will grow, but it seems a shame not to give them a go now they have started rooting.
The treacle substance can be turned into a balm. It used to be very poplar with the witches for its flying properties. Poplar balsam was used in flying potions. I read that if I smear it all over my naked body and get on my broomstick I will be able to fly far and wide through the night sky. Smeared on certain parts of the body prior to ritual or meditation it can help with astral projection.
The wild poplar is very rare in Britain now, though it used to be native. There are many cultivated varieties though which can often be seen in parks. There is a phantom tree planter who has spent the last 30 years going round Britain planting Black Poplar trees where ever he sees a bit of space. He doesn’t bother getting permission, well then he wouldn’t be a phantom would he.
Black Poplars can grow to 30 metres tall and live 200 years. They grow very quickly and are best suited to damp marshy landscapes. The bark is a dark brown often appearing black. The leaves are triangular shaped and tremple and quiver in the wind, often sounding like they are singing, it was said that this is the tree praying.
Male and female catkins of the Poplar grow on different trees (dioecious), the female catkins are yellowish green, the male catkins are red and it used to be said that these red catkins, once fallen, were Devil’s fingers and bring bad luck if picked up.
Once fertilised the female catkins turn into fluffy seeds which fall in late summer, very attractive but difficult to draw.
Poplar wood was used to make shields by the Celts, and seen as very protective. The black poplar is sacred to Hecate, the death goddess. There was once a tradition of burying lamb’s tails under newly planted poplar trees at lamb docking time, as a sacrifice to the goddess of death.
It is the sticky balsam that most interests me at the moment. Its origins are explained in the Greek legend where Phaethon asks his father Helios, god of the sun, if he can drive his chariot of the sun across the heavens one day. He was not very successful at this, he did not have the strength to control the horses and the chariot was taken off course, taking the sun so close to the earth it nearly burnt. Zeus was very cross with this and killed Phaethon with a bolt of lightning. Phaethon’s sisters, who had helped convince their father to let Phaethon drive the chariot, saw his death and weeped so bitterly that the gods decided to turn them in to Poplar trees and their tears to amber tears formed by the oozing balsam.
The balm made from these tears has been used for many medical purposes such as rheumatism, gout, coughs and colds, but I’m going to use it for flying! One warm night this summer I’ll be venturing out to find a suitable black poplar, lying under it’s singing branches, covered in sticky balm I will go into a trance and I shall astral project myself to who knows where. Unfortunately I probably won’t be sky clad, as crowded London doesn’t lend itself to such freedom.
So I’ve agreed with some friends to help them out with their garden. I decide I’m going to do little pencil sketches of plants in the garden (see above) and write a blog about each.
The first thing I do is clear away some weeds. The place is covered in thick stinging nettles that go up to my knee. I dig them up, but it seems a shame to just throw them out so I make nettle soup. It’s nice once I get the hang of it, a little “textured” but I imagine that wouldn’t be the case if I had a food blender. The second day it tastes even better. I also make nettle tea in a lovely china teapot a friend gave me. It tastes of nettles, I would be pleased only I’m getting a bit nettled out now, my hands and arms are stinging permanently despite having worn gloves. I decide to lookup what benefit all these nettles might be doing me:
Nettle is very high in vitamins and iron. They stop bleeding and used to be ground into a fine powder and used as a snuff to stop nose bleeds, or used in an infusion. They are also good for treating colds. The leaves are said to improve ones complexion and circulation and can be used to clear the chest of phlegm.
As for magic, the nettle apparently has powers of exorcism, protection and lust. It is seen as masculine, comes under the planet Mars and the element of fire. It belongs to Thor, the Norse god of thunder. To remove a curse and send it back carry a sachet of nettle around with you. Sprinkle nettle around the house to keep evil out. Throw it into the fire to avert danger or wear it as an amulet to keep ghosts and negativity away.
It has been used as a lust inducing herb, used in purification baths and the irritant within the hairs has been used as an aphrodisiac to stimulate the sexual organs.
I’m just sticking to the soup.
Salt and pepper
Cut and wash nettles tips (whilst wearring gloves)
Boil in a saucepan of water for a couple of minutes. This removes most of the sting
Slice them into small pieces and remove tough stems
Fry some onions and garlic in a pan with butter till the onions go soft and golden (I love butter but I suppose you can use oil if you choose)
Add the nettles
Add some rice
Add a good amount of hot water with vegetable stock mixed in
Bring to the boil and simmer for 15 to 20 minutes, or until the rice is done
Add salt and pepper to taste (I add loads of salt, but then I’m addicted to the stuff and my blood pressure isn’t high)
And there you have it, very simple , tasty and good for you, just be careful not to get stung to pieces like I did.
This picture is of a Dor beetle. The Dor beetle is a type of dung beetle under the family of Scarab. It looks very much like the ancient Egyptian symbol for the god Khepri. He was thought to roll the sun across the sky everyday in much the same way as a dung beetle rolls dung. For this reason the dung beetle represented recycling and reincarnation, the sun going each evening and coming back each morning.
I think the dung beetle is a good symbol for recycling and reincarnation anyway, for its use of dung helps return the nutrients (for there are plenty in dung!) back to the soil for the plants to grow. The Dor beetle is known as an “earth-boring dung beetle”. They usually work in pairs, a male and a female will dig a passage in the earth under a pile of dung. They then dig side passages off of this and into each one a piece of dung is placed. An egg is laid into the dung and the passage is then closed off with more dung. The larvae hatch from the eggs and feed on the dung for a year until they pupate and adult beetles emerge.
I came across this beetle on the body of a recently deceased stag. It is not unusual to find dung beetles on carcasses, the “Beetles that eat bodies” webpage lists them as one of the beetles entomologists look for on cadavers to help determine the time of death. The one I watched was determined to get on the top of the stags shoulder, it kept trying then falling off, then trying again. Whenever it fell off it rolled over onto its body and then I could see its metallic blue and purple underbelly and legs. It really was a very beautiful creature. Unfortunately I did not take a photo so these drawings are done from memory and what I could find on google. The beetle’s determination paid off and eventually he climbed onto the shoulder and, seemingly proud of his accomplishment, strutted across the body.
The Dor Beetle is is also known as the Lousy Watchman because if often has small mites living on its belly. I couldn’t see any mites on the one I saw, this may have spoiled my vision of it as a lucky omen.
“The ancient Chinese, Indians, Egyptians, Babylonians, and Native Americans were all herbalists. The oldest known list of medicinal herbs is Shen Nung’s Pen Ts’ao or Shennong Ben Cao Jing (c. 3000 B.C.), a Chinese herbal that is probably a compilation of an even older oral tradition.”
University of Virginia