Hyperbolic Crochet and the Pseudosphere

Warning - the author takes no responsibility for any sleep deprivation that may occur as a consequence of trying this at home.

I have a friend on Ravelry to thank for my hyperbolic journey into exponentially expanding surfaces. She posted a link to Gary Hayton's knitted felted Fibonacci Pseudospheres, which just beg you to imagine, wow, however did he make those? The title sent me off to rediscover the Fibonacci numbers and spend time pondering how they might be incorporated into a circular knitting pattern. 

Just as I was developing terminal brain ache, the same good friend explained that all you have to do to create a hyperbolic shape is to make increases at a constant rate. Starting with a magic loop of six double crochet stitches (single crochet in America), I began crocheting two stitches of heavy, inelastic tapestry wool yarn into every stitch, spiralling endlessly outwards.

The initially flat surface develops frills that wrinkle up together in three dimensions, mine formed a pseudosphere after about eight rounds. Watch this video and you'll see what I mean. Because I made two stitches into every one, the stitch count doubled with each round 6 - 12 - 24 - 48 - 96 - 192 - 384 - 768 - 1,526 - 3,072, so deciding to do the final round with crocheted picot edging in a colour change yarn took rather more time and yarn than I had bargained for. Running low toward the end, I finished the last stretch with a plain crochet edge.

Himself was pleased to refer to my new pet as 'The Golden Brain'. A bit more googling about led me through whole coral reefs created with crochet to the brilliant mathematician who made the leap from abstract hyperbolic geometry into tangible yarn constructions. In this lecture, she tells her story so simply, even I felt I understood negative curvature - until I tried to explain it to himself.

Much as I love my pet brain, I had no answer when asked what it was for. Daina made hers to teach students, the crocheted undersea world was intended to raise awareness of coral death due to pollution. Trying to dream up some function to justify my urge to go hyperbolic again, I crocheted a basic hat shape in coloured Romney handspun wool yarn.

Working two stitches into every one for a few rounds in a darker shade of the same wool created a frilly brim. All might have been well had I left it at that, only I carried on, using a wild skein of coreless corespun 'art yarn', only finishing at 2am, when I had used up the last of the wool.

Daina Taimina says in her lecture that Wolfgang Bolyai warned his son of the perils of pursuing non - Euclidean hyperbolic mathematics. 

The same might be said of hyperbolic crochet.

'For God's sake, please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life.' 
Come on in, the water's lovely.

Blending Wool Colours on Hand Carders

"This old fleece is terminally grim, Beaut.  Get over your hoarding issues and chuck the thing out." 
My companion, Elinor Gotland, was staging an intervention rather than supporting my search for inspiration and getting vexed at my disappearances under the spare bed. I called back up from beneath it.
"That's the Welsh Mountain X Dorset Down fleece I used last year for exhausting Japanese Indigo vats. Never was soft and the long soak in alkali has done it no favours.  I knew I kept it somewhere because I was sure these varied blues would be perfect for sky colours. Remember that book, Knit the Sky?"
"I remember telling you this fleece was NOT suitable for knitwear."
"Never mind how harsh the wool is, doesn't matter if you're spinning the sky as art."
Elinor kicked a heap of fleece off the duvet and jumped down, one small sheep and her forceful opinions landing on my prostrate rear end.
"Art?  My cotted rump.  Not another one of your so-called wool works.  Which lucky relative is going to have a sky blue objet de laine foisted upon them?"
I rubbed the offended part.

"Ooo, those hooves could do with a trim. Sharp as your judgements. I know my sister was really pleased to be given the Harp wool work, because it's up on the wall in her hall."
"Be honest, Beaut, it was just too big to stick on the fridge door."
I shoved a long lost pillowcase full of grey fleece in her general direction and felt gratified to hear a muffled bleat.

News of Art Challenge Wales had reinvigorated my flagging artistic morale.  Open to everyone to enter and held last Saturday, just along the coast in Porthcawl, the challenge was to create a piece of art in public on the sea front, between having your canvas stamped at 9am and handing it in to the Grand Pavilion at 5pm. Here are my sister, daughter and niece, enjoying aesthetic sustenance while better breakfasted artists 

sallied past.  My plan was to spin yarn in the colours of the sea and sky.  At 9.46am with the tide full in, I loaded grey and blue locks onto a hand carder.  OK, overloaded, I know I always put too much wool on, which makes heavy work of carding a fat rolag.  Checking the horizon for colours, I dragged away at the carders til I had eight rolags ready to spin longdraw - artistically irregular.

Because the colour changes in the rolags had spun into a single of continuously shifting hues, even Navajo chain plying often mixed shades up within one stretch of yarn. Winding the plied yarn straight from the bobbin round a driftwood stick displayed the broad effect of my colour choices, in a blurred fashion up close, better from a distance.  So, call stick number one Impressionist and try not to panic about the time, 11.15am already.  With the tide turned and the waves much further down the beach, I only made five rolags for the second length of yarn, less focussed on sea greys and more on sky blues.

The frame, which had been stamped for me when we arrived in Porthcawl, was a gnarly piece of driftwood which had already been drilled in the privacy of my own garage.  Six pairs of holes to take copper wire fixings, to be twisted through beach pebbles with holes.  I managed to shatter one stone while curling up the wires, but Pip averted crisis by nipping down to the beach to find shells with holes instead.  

Here are the first two yarns, safely in place by lunchtime.  The sun shone for much of the afternoon in a deeper and deeper blue sky. Keeping to just blue and white wool on the carders gave much crisper colour changes, accentuated even more by the stronger contrast of adding darker blue to the rolags.  The afternoon yarns looked quite different to the morning blends, effects I shall try to bear in mind next time I am carding dyed fleece to make yarn for knitting.  Guided by the falling

tide, only four, three, then two rolags' worth of yarn had to be spun, so all my six sticks were wrapped in yarn shortly after 4pm.  Handing it in at the Pavilion, I realised my thing didn't stand comparison with the proper art on canvas, but I really didn't mind, being most satsfied with my 'Driftwood Tide'.

Elinor Gotland sauntered down the headland to meet us.

"Sky Tide would have been a better name, Beaut.  At least you've got that awful fleece out of your stash - and that blue sky art foolishness out of your system."

"Oh, I'm still blue sky thinking, Elinor.  Might go Yves Klein

abstract with pure indigo next."
My companion looked around at my family, put her head in her hooves and groaned.
"That sister of yours has been encouraging you again.  She's such a bad influence."

Last Dance of the Avant Garde

Penarth Pier Pavilion is holding an art exhibition.  My companion Elinor Gotland and I circled the hall in opposite directions, examining each piece in silence.  Standing in front of what looked like a metal greenhouse workbench, I wondered if the thin grass growing on the tray was real or artificial. Oblong white blocks lay on top.  I read the card beside it.  'Untitled (lard)'.  Blimey.  I peered more closely.  Those blocks really did look like lard.  What would happen if the weather warmed up?  Light coming through high windows left the lower walls in shadow, maybe 'Untitled (lard)' would have been safer over there in the gloom, by my own picture, 'Last Dance'.

Seeing it hung among the other pieces was like meeting an old friend in a strange town.  A small shock, a reappraisal, a what are you doing here?  Elinor joined me, looked at Last Dance for a moment, then moved on without a word.  I busied myself looking through the viewfinder of a plywood version of one of those boxed binoculars you sometimes see at seaside resorts.  No need to feed coins into this one.  Inside, in stop motion animation, birds flapped on the beach, people dumped junk and finally, an oil platform blew up.

"This an art exhibition, is it?  Bloody rubbish, man."  
Three visitors had come in and one had a bell in every tooth.  They were approaching the small TV, where you could watch a film of someone changing her bra without taking her top off.  
"That's porn, that is."  

The South Wales accent does lend itself to expressing a forthright opinion.

Me, I was just bewildered.  

While I have been letting rip just lately blogging about making unlikely wool works, that was not quite as spontaneous an outburst of creativity as it might have seemed.  They were all geared toward The Makers Guild in Wales summer exhibition on the theme 'Weave'.  It was open to anyone to enter and I duly sent in photos of my 'Belles Dames sans Merci'.  All three were refused, which made it even more disorientating to have had Last Dance accepted in Penarth, after a submission made in haste a couple of months ago, on the strength of a chance conversation with a felt artist I was chatting to in the craft shop.  I don't think she anticipated anything like this show either.

"Come on, Beaut, let's go out the back way, through the cafe."  Elinor was at my elbow, steering me towards a pot of tea.  We sat down at a table outside and I piled sugar into my cup while my companion lit up.  The waitress came out and told us smoking wasn't allowed.  Moving to a bench further down the pier, we looked back at the seafront, where not so much as a crisp packet littered the beach, the buildings all looked freshly painted and the only dirty car parked on the esplanade was mine.  I wished I was twenty miles further west, back on the tideline of the Ogmore estuary, enjoying my smoke on a driftwood log amid the comfortable squalor of washed up shoes and plastic bottles.

 "I'm sorry, Elinor, I had no idea Penarth art exhibition was going to be like this, I've not a clue why they picked my work, I don't know what to make of any of them."

Elinor howled with laughter.

"If they'd wanted people to understand the art, they'd have put little explanations up.  Did you hear that woman saying 'Bloody rubbish!'?  Brilliant, Beaut, bloody brilliant."  

"Well, I don't speak the right language to say what is or isn't rubbish art and I'd have liked a bit of help understanding some of the other things in the exhibition.  I feel such a fraud.  Even the lady on the reception desk had an art degree."

"Better to be a selected artist than a rejected maker.  Drink up your tea and come, my Bohemian chum, we shall not be leaving a tip."  Stubbing out her fag in the saucer, my companion strode back toward the pavilion.  I gathered up the crockery and hurried behind.  Elinor swung round on her hoof for long enough to shout  "You do realise what this means, don't you, Beaut? You're going to have to wear a beret now you've joined the avant-garde!"

  

Making celtic type knots from the different flight patterns of bees when they are searching for or finding nectar seems to me more comprehensible than a recording of their buzzing.  If I tell you Last Dance celebrates the vitality of those who make the most of their season, that the bees still dance at the frayed edge of summer in the face of the autumn wind, does that make you see it differently?

Madder Silk and Wool Work

If there is anyone reading who fancies a go at metalwork jewellery, contact Mike at Tangled Web.  My sister and I went on a day course last year and during the morning, we both learned to make a silver ring .  Mike is a relaxed expert, a thoughtful teacher and a thoroughly nice bloke.  After chatting about my spinning, he twisted up a bit of copper wire into a new orifice hook for me in less than a minute, then helped me spend my afternoon making a copper diz.

We went again this year and while BG and Pip created silver accessories, I spent the day sawing out a circle of copper sheet and hammering it into a gong, while Mike brazed cross struts and fixed driftwood onto a frame of copper piping I just happened to have brought along. He is a total star and the jewellery he makes has a wonderful flow, I've been a customer on and off for years.

Back home, I draped the frame with some silk chiffon contact dyed with geraniums and had a go a spinning silk fibres dyed in a madder root afterbath.  Just as well the effect didn't work out right, because neither did the yarn. Threading up the frame with some common or garden grey wool, handspun from a sheep of unknown breed, might be less of a statement, but in this instance, less proved to be more, as

the whole lot was solely intended as a backdrop to fibres dyed with fresh madder.  A batt of mixed shades got tweaked about and fixed on with a combination of needlefelting, weaving and sewing.  Dissatisfied with any of my other dyed silk fabrics to cover the bottom of the frame, it occurred to me to keep that part simple too, knitting some heavyweight, felted Zwartbles single yarn, using short rows to

shape the piece to fit the space.
After I had hung it on the wall and stood back to consider the effect, my companion, Elinor Gotland, wandered in, .
"Calling that art, are you, Beaut? "
"I'm calling it a Silk and Wool Work.  Knitwear and fairies are not my only fruit.  Actually, Elinor, I think I will call this one 'Rose'."

Elinor peered at it from a safe distance.  She still hasn't quite got over meeting Belle Dame 2.
"You've put a fairy in that fire.  Who's she - Vesta, goddess of the hearth?  Looks like she's burning down the house." 
"Well, that's good, I wasn't aiming for cosy domesticity.  More Ceres without her Proserpine."
Elinor went a step closer.
"Assuming this Rose is another of your 'Belles Dames sans Merci', where's her bell?"
"That round thing.  It's a gong.  And the midwinter spring sun.  The fire and the rose are one, if you catch my drift."
Elinor set her hooves on her hips.
"You need a nice lie down with a wet flannel, Beaut.  T S Eliot's rose is too heavy for a scrap of wool.  Still, All manner of thing shall indeed be well, soon as we've got the kettle on."

Trying to Spin Art Yarn

Clearing the garden borders at the end of last November, the weather had been so mild, there was still a bit of life in the coreopsis stems and even a few flowers.  As the days darkened, I fancied a last go at contact dye printing on a strip of coarse wool fabric.  See the paint brush on that table?  You may have noticed I've been coming over all artistic since I retired.  It is such a luxury to have time to arse about with bits and pieces.

Neglecting the routine garden jobs in favour of yet more self indulgence, I laid out the coreopsis and some oak leaves, then dobbed on some fermented evernia prunastri, splotches of copper solution, a couple of rusty nails and some Hopi sunflower seeds, rolled the whole thing round a length of plastic drainpipe, tied it up with string and put it to simmer in a dye bath of all the last odds and sods still surviving in the

dye garden.  The pipe was a bit tall for the pot, but what the hell, I left the whole thing to cool, turned the bundle upside down and simmered it again.  By the time the rolled wool had had a week or so to dry out, Christmas was upon me and I had to stop being silly and spoiled and get back to family friendly function.  Got a head of steam up which carried me through a January spent reorganising cupboards and cataloging the incremental growth of my fibre stash, efforts frequently punctuated by escapes to the dunes to walk the dog.  The marram grass had been stretched flat by the onshore winter winds, even the stiffer stalks of dried out flowering plants were permanently stuck on a wonk.

Laying out the contact printed wool fabric, ready for wind inspired needlefelting, all that organising of stash meant I could readily pull out a palette of handspun yarn in natural sheep colours and plant dyes.  What is more, since form here trumped function, it turned out crappy, underplied, lumpy old handspinning would

needlefelt to better effect than my more recent, evenly twisted products. 
"You see, Elinor," I mused during one of our walks, "I was spinning art yarn all along, destiny never intended my wool to become socks."
"Bullshit, Beaut. Proper art yarn is a riot of colour and texture and art is intentional, not  

some random shoddy spinning and dingey plant dyed cock ups."
"Ah, but the old yarn was just for the top half of what I'm making. The whole thing is more about roots, Ygddrasill and Norns.  The important bit will be spinning the earth.  I am going to learn core spinning and make real art yarn."
"Beaut, my inner Norn foretells this yarn will end up a right bouquet of barbed wire."

People on youtube make their skills look everso simple. Much encouraged by this video, I selected locks for colour and texture. No problem for a woman with a card index of her fleece cupboards to find Black Welsh Mountain, unknown Down-type grey fleece, Manx Loaghtan and some Welsh crossbreed.  Using a cone of carpet wool for the core, I had a go at spinning 'funky and cool' yarn from the locks.

It wasn't quite as easy as it looked.   The locks were strangulated by the carpet wool rather than wrapped around it and once threaded through the holes I had drilled in the homemade picture frame, the yarn was much too skinny and far too white to represent earth.
Back to the computer for another youtube search.  More typically, core spinning technique starts with fibre in the form of a batt. The teeth of the Louet Junior Drum Carder disgorged for me a rough batt of the same fleeces with less white and a greater proportion of Black Welsh Mountain. Drafted out, I managed to wrap the carded wool round a thinner core yarn by spinning slowly on the 5:1 ratio on my  Ashford Traveller Wheel.  It was a considerable struggle to pedal BG's Indian Spinner to Navajo three ply the core spun single.  Despite its huge orifice, loose bits of wool kept getting stuck on the flyer hooks and this wheel is really heavy to restart.  My companion pottered into the sitting room, drawn by my grunts of dismay and shrieks of frustration.

"Sounds more like ladies' tennis than spinning in here, Beaut."
"I'm getting the knack, actually, Elinor, but I just realised all the Black Welsh Mountain has made this wool too dark for my picture, since I screwed on that light driftwood."

"Gotta suffer for your art yarn. Get that grey fleece back out and go and mix another batt."

I spun art yarn of a sort, glad I only needed a short length.  Now, the unveiling of my finished object.

"Not being funny, Beaut, but that Norn looks much like another one of your fairies to me. Knitting is she? Always thought Norns and Fates were more into weaving."
"This Norn is a small business Norn, not one of the brand leaders. Like Fafnir the dragon said, 
'Of many births the Norns must be, Nor one in race they were; Some to gods, others to elves are kin'."

"Well, your art yarn spun up sturdy, I'll give it that. What's all this gubbins doing on the Norn's knitting?"
"Don't climb on my art, you Philistine. That 'gubbins' represents small but vital things that get lost.  Coins and keys and rings."
"They're very grubby.  This thimble is all broken."
"Mmmm.  Good, isn't it?  I bought them off a metal detectorist."
"You want your head read, Beaut. So, were these lost things found or stolen by your elf-type Norn?  Will their owners ever get them back?"
"Hard to tell if she's benevolent or malevolent.    Go on, I dare you to ask her."

Turns out even a seasoned ewe of the demi-monde can still look shocked. Afterwards, Elinor tried to explain.
"Doesn't sound so awful when you hear it from me, just the way she said it, totally cool, not dropping a stitch.  'Frankly my dear, I couldn't give a damn.'"

Feeling bad about the dare, I poured a good slug of sloe gin into Elinor's teacup.  Really, I suppose I should have pointed out the sign showing the knitting Norn was another kind of Belle Dame sans Merci. 

I think I shall call this work 'Gone'.

Dyeing Wool with Dried Double Maroon Hollyhocks

The colours that come out of a sequence of afterbaths when dyeing with fresh double maroon hollyhock flowers remind me of the sea.  Previously, trying to preserve spare flowers by freezing them seemed to kill off the blues, leaving only greens and greys.  After dyeing the skeins in this photo with fresh flowers, while my plants carried on blossoming last summer, I laid the spent petals on a tea towel to let them

dessicate before being put in a paper bag.  In January, with a design in mind to weave a wave, I put my last couple of hundred grams of scoured Speckled Face Beulah fleece in the bath to mordant with alum for 24 hours, while my stock of 50 shrivelled hollyhocks soaked in plain water. Next day, the fluid had turned deep maroon, much like the original colour of the flowers.

The flowers had half an hour at a very gentle simmer, as boiling destroys the blue pigments, just like freezing.  For such fragile molecules, once you have them fixed onto wool, I have found the colours surprisingly light and wash fast. Sieving petals out and slopping them into a net bag to stay in the dye bath, I added about 50g of wet, alum mordanted fleece for an hour's simmer and an overnight soak.  The wool turned a familiar blue, though not as deep a colour as fresh flowers have offered.

Repeating the process with four more portions of 50g fleece showed that drying the double maroon hollyhocks had preserved a muted version of their original colourway, better than frozen ones did.  Combing condensed the shades - this is flash photography, not quite true to the real appearance, but you can see how the blue tones change, rather than just getting paler.  

Spun worsted and Navajo plied, hopefully, you can just about see colour changes in each strand of yarn on the niddy noddy.  Making mixtures of fleece shades on the hand carders and spinning rolags into chunky two ply gave the adjacent, irregular, puffier yarn a more uniform colour .  I have been building another driftwood triloom.  Since reading a comment made about the last one, ideas have been washing around my mind about harps and harpies, wondering, did those lethal sirens sing intending to lure ships onto the rocks or was their song an end in itself? Winding my yarns around the pegs, the colour changes were too subtle to give the sea weave any unwanted tartan effect and the heavier, loftier yarn seemed a better base to needlefelt into.  So, the final yarn 

construction went three rolags of each shade in turn, spun longdraw and Navajo plied.  

To add emphasis where the sea weave wrapped round the nails on the plank symbolising shipwreck, I dissolved soda ash to make an alkaline solution and painted it onto the wool.  Bit of a potch to get the dry fibres to soak it up from the brush, still, the resulting green colour shift exploited this dye's pH sensitivity.

My harpist or harpy was constructed same way as the small fairies, except using a whole batt of drumcarded fleece for a long full skirt.  A florists's wire running down from the head meant it could be held in a Fibonacci curve; carded, Down-type Beulah fleece did needlefelt onto the woven yarn with all the volume and texture that merino tops lack, yet my efforts dyeing blues from maroon hollyhocks lacked the weight of the sea I had imagined.  Standing back to see the final effect, I had to acknowledge these soft colours from dried flowers do lack the definition I had from dyeing with fresh material.

"Perhaps the pale green you chose to decorate this sitting room has sapped their strength. Didn't like to say at the time, but this green never was a cheery choice."
Sod it.  I got out the roller and painted the back wall white.  It took three coats.  
Once I had hung the loom up again, my companion, Elinor Gotland, eyed it critically.

"Fair play, the room is less gloomy, bit of a shame your harpist still looks like a triangle of mist."
I scraped flakes of white emulsion off my nails.
"Mist might be dangerous enough at sea, but nebulous risk is not my idea of what harpies are about.  How can I give her the inexorable power of a big breaker?"

Asking a Gotland sheep for advice got me a predictable answer. Grey Gotland locks dyed with woad did add lustre, body and depth of blue.  Hooray for a considerable stash of past experimentally dyed fleece and even more hooray that I have got organised enough to find stuff.  
"Loving the fish, Beaut."  
I knew my companion would appreciate a little drama.

"Now she's a 'Belle Dame sans Merci', isn't she, Elinor?"
"Aye, doing her own thing without consideration for others.  Don't you go getting ideas, Beaut, that's no way for a middle aged woman to live."
"Ha, you're just worried you might have to start making your own cups of tea.  This could be the end of your days as Belle de Laine Sans Souci."