Category Archives: Famous Artists

Continuous Line Drawing, or single line drawing, by famous artists.

Continuous Line Artist view of Haken’s Gordian Knot.

Depth of lines in black and white on Haken Gordian   Knot.  Mick Burton, continuous line.

Depth of lines in black and white, in Haken’s Gordian Knot. Mick Burton, single continuous line drawing 2015.

Here is an update on posts which I did in May and June 2015 regarding the above Knot and the interest these posts have since generated.

As a Continuous Line Artist I have looked at many angles of what my lines may mean and what they can do.  

One such examination was triggered by Haken’s Gordian Knot, a complicated looking knot which is really an unknot in disguise – a simple circle of string (ends glued together) making a closed line, which I saw in a book called “Professor Stewart’s Cabinet of Mathematical Curiosities”.   The drawing above is my version of Ian Agol’s illustration of the Haken Knot (see it in my post of 31 May 2015).  I used dark and light shades to emphasize the Overs and Unders shown for the line. 

The reason that I was so interested was that it reminded me of my “Twisting, Overlapping, Envelope Elephant” (see below).

Twisting, overlapping, envelope elephant. Continuous line.

This single continuous line drawing is coloured to represent a “Twisting, Overlapping, Envelope Elephant”, which is Blue on one side and Red on the other. Mick Burton, 2013.

How this elephant line works is explained in my post of 31 May 2015.  In essence, you need to imagine that the composition is made up of a flexible plastic sheet which is Blue on the front and Red on the back.  Each time there is a twist, on an outer edge in the drawing, you see the other colour.

In the Gordian Knot, I spotted that there is a narrow loop starting on the outside (lower left on first illustration above)  which seemed to lead into the structure, with its two strands twisting as it went, each time in a clockwise direction.  I followed the two twisting lines throughout the drawing until they ended in a final loop on the outside (left higher).  I counted 36 clockwise twists and one anticlockwise.  My thoughts are explained in full in my post of 2 June 2015.

To aid the explanation I completed a painted version, where I used the same Blue and Red colours, as for the above elephant, to emphasize the twists.

Twisting, overlapping colouring of Haken Gordian Knot.  Mick Burton, continuous line.

Twisting, overlapping colouring of Haken’s Gordian Knot. Mick Burton, single continuous line drawing painting 2015.

Note that the colours in the Elephant define two sides of a surface, but in the Unknot the colours are illustrating the twist of two lines travelling together.  The twin lines go through other loops continually so there are no real surfaces.

After completing the above two posts, I decided that I would try and find out more about the Knot and came across a question posed by mathematician Timothy Gowers, in January 2011, on the MathOverflow website.  He had asked for examples of very hard unknots and after many answers he had arrived at Haken’s “Gordian Knot”.  He described the difficulties he was having.  Timothy said that he would love to put a picture of the process on the website and asked for suggestions.

As I had already done two pictures before I read his post I decided to respond.  The work that I did on this is detailed in my post of 5 June 2015 entitled “How do you construct Haken’s Gordian Knot?”.

My response duly appeared on the MathOverflow website in early 2015, but within a day or two it had been taken down and a notice appeared stating that only mathematicians of a certain status should post on the site.

That’s fine as my only maths qualification is General Certificate of Education at school.  At Harrogate Technical College I was thrown out of Shorthand and, with only three months to go to GCE exams they put me in for Maths and Art.  I owe many thanks to the Shorthand teacher, who thought my only skill was picking locks when someone forgot their locker key.  Also I have never had any discussion face to face with a mathematician about my art or my maths.

Following this setback I decided to set it all down in my Blog, in the three posts up to 5 June 2015.

Although I have not actually talked directly to a mathematician, I did correspond with Robin Wilson and Fred Holroyd at the Open University in the mid 1970’s about my ideas on the Four Colour Map Theorem.  I set out my ideas briefly in my post of 18 August 2015 “Four Colour Theorem continuous line overdraw”.

When Fred Holroyd responded to my write up, he used my own expressions and definitions which was very impressive.  He said that I had proved a connected problem, only proved in the world as recently as 16 years previously.   When I asked Robin Wilson about the announcement from a mathematician who said that he had proved the Four Colour Theorem, Robin said not to worry as he thought that this one was unlikely to be validated.  He said that he would prefer that my theory could be proved as it was elegant and also that they could use it.

The theorem was proven in 1976 by Kenneth Appel and Wolfgang Haken, involving running one of the biggest computers for over 1000 hours.  After this I decided to go onto other things, leaving my art and maths behind for almost 40 years.

Yes, its the very same Wolfgang Haken, who devised the Gordian Knot!

Ok, lets move on.  In February 2016 I received an e-mail from Noboru Ito, a mathematician in Japan, saying that he had read my article of 5 June 2015 “How do you construct Haken’s Gordian Knot?” and it was very helpful.  He would like to add it to the reference of his new book “Knot Projections”.

Of course I agreed and he later confirmed that he had referenced my work to the preface of his book.

Here is a picture of my copy of his book which was published in December 2016.

Knot Projections

“Knot Projections” by Noboru Ito, published December 2016 by CRC Press, a Chapman & Hall Book.

 

Additionally, in November 2017 I received an e-mail from Tomasz Mrowka, a mathematician at the Massachusetts Institute of Technology.  He said that he was interested in acquiring a copy of my Twisting, Overlapping colouring of Haken’s unknot.  “It’s really quite striking and I would love to hang it in my office”.

I was delighted to send him a photo which he could enlarge and frame.

 

Kaleidoscopic Wild Horses, continuous line drawing with colour sequence.

Wild Horses, June 2017

Kaleidoscopic Wild Horses. Single Continuous Line Drawing with colour sequence in acrylic on canvas.  I happened to have a canvas 36″ x 10″ previously intended for an upright picture idea.  Mick Burton continuous line artist 2017.

This painting originated from a continuous line drawing which I produced for a demonstration at Stainbeck Arts Club, Chapel Allerton in Leeds in May 2017.  

IMG_0883 -Horses line.

Wild Horses,  single continuous line drawing. Demonstration at Stainbeck Arts Club. Mick Burton, continuous line artist 2017.

When I was thinking about a subject for the demonstration I saw an advert on the TV for the Cheltenham Festival which just showed loads of horses running – why there were no riders or jumps I do not know.  This also reminded me of one of my favourite paintings – “Scotland Forever” by Lady Butler in Leeds Art Gallery, painted in 1881.  A bit like “Charge of the Light Brigade” but straight at you, with the horses wild eyed and seeming to leap out of the painting.

See it at   http://www.leedsartgallery.co.uk/gallery/listings/l0081.php

Lady Butler painted a lot of war scenes and of course she had no military experience.  She was, however, married to a General and she persuaded him to let her watch manoeuvres.  In preparation for this picture she asked that the cavalry ride straight towards her so that she could get the feel for facing a charge.

When I had finished the demonstration, which was a result considerably rougher than the above, the members asked about colours.  I had not intended to talk much about colours, as I thought that my approach to drawing the lines would be enough at this session, but we had a solid half hour talking about my method and ideas about colour.  They said that they looked forward to seeing the image in full colour, so here it is.

My original intention was to do a black and white alternate shading version only, and this is shown below.  The tweaking which I did on the horses heads to achieve a better result in black and white was essential both to improve the continuous line and later to enhance the colouring.

IMG_0888 - Horses black & white

Wild Horses, single continuous line drawing with black and white alternate shading.  Mick Burton, continuous line artist 2017

Initially I did my normal approach to colour sequence, where I devised a 6 colour range (white, lemon, golden yellow, orange, vermilion red and crimson alizarin) to fit my alternate overdraw template for this image.  

This resulted in gold and vermilion appearing on all outer areas and I thought that I needed a darker effect in the lower half of the image.  So I substituted cobalt blue for gold along the bottom legs of the horses and finished up also substituting, on an ad hoc basis, some dark blue, violet and green to try and naturally leach colour balance upwards to meet existing vermilion and gold.

A fellow artist who likes my alternate overdraw and colour sequence method has told me that I should always apply it fully to get the natural result.  Generally I would agree, but thought that I needed to break some rules on this occasion.  I try and mirror nature in my art and of course nature evolves by breaking a few rules. 

Joan and I visited my Aunty Ann a couple of weeks ago.  She is 99 years old and still as bright as a bobbin.  She is a good artist and only gave up painting relatively recently, and always wants to see my latest stuff.  i took the Wild Horses along.  It took up the length of the settee and she was delighted with the colours.  I then realised that the painting’s reflection in the shiny metal fire surround made the composition even more abstract.

Aunty Ann’s shiny metal fire surround reflecting Wild Horses. Mick Burton, continuous line artist, 2017.

Two different Reflections of Wild Horses on metal fireplace surround, detail strips. Mick Burton, continuous line artist.

“BB” by Kate Burton, Glasgow filmmaker, at London Short Film Festival.

BB-poster-online

Poster For ‘BB’ Written and Directed by Kate Burton. Poster Design by Jen Davies

My daughter Kate has recently attended the London Short Film Festival where her latest film “BB” is showing.  The film was also selected by the Glasgow Short Film Festival and the Inverness Film Festival, and was nominated for Channel 4 innovation in storytelling award 2015.

The action starts with a bee buzzing around, the synopsis  reads “When Anna discovers an unwelcome intruder in her home she enlists the help of her mild mannered neighbour.  Frank enters into Anna’s strange and chaotic world and finds himself well removed from his comfort zone.  Amusingly awkward social challenges follow and an unlikely relationship is formed.”

The film was shot in Kate’s previous flat in Glasgow, and in the local area.  She was determined to make the film before she left.

Joanne Thomson in the Kate's flat, featured in "BB", short film by Kate Burton, Glasgow, 2015..

Joanne Thomson in Kate’s flat, featured in “BB”, short film by Kate Burton, Glasgow filmmaker, 2015. Photograph by Helena Ohman

I asked Kate to give me the background to the film. 

“At the time I wrote the script I was living in a small one bedroom flat in a Victorian townhouse conversion in the west end of Glasgow.  The ceilings were high and there was a split level mezzanine where I worked and completed the script.

There was a huge rose garden opposite the flat and in the summer confused bumble bees would fly inside my flat and roll up into fuzzy balls on my window ledge.  This and many other elements of my surrounding environment fed into the content of the script.”

Kate Burton watches as David Liddell and Helen Ohman McCardle take a close up for "BB", a film by Kate Burton, Glasgow.

Kate Burton director, David Liddell cinematographer and Hannah Kelso assistant camera on the set of  “BB”, a film by Kate Burton, Glasgow. Photograph by Helena Ohman

“I knew the characters very well after a lengthy development time, but the story for the short came relatively fast and after two months writing, in between filmmaking jobs, I was finally ready to let other people read it.

‘BB’ is a character driven story capturing the awkwardness of first attractions.  It takes place mainly in one location.  I wanted the cinematography and style to reflect the simplicity of the story and I decided that I wanted to shoot in black and white to give a heightened feel, emphasising the unique lines of the interior space.  I was interested in long duration takes and capturing physical and theatrical comedy within the frame.  Some of my research references were Woody Allen’s ‘Annie Hall’ and ‘Manhattan’, ‘Breakfast at Tiffany’s’ by Blake Edwards and ‘Francis Ha’ by Noah Baumbach.”

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Kate Burton, writer/director, on set of ‘BB’ 2015.

Ben Clifford and Joanne Thomson in "BB", as short film by Kate Burton, Glasgow, 2015.

Ben Clifford and Joanne Thomson in “BB”, by Kate Burton, Glasgow filmmaker, 2015. Still from film. 

One of Kate’s earlier films was “The Ice Plant”.  I thought that this was a strange title until she told me that it was about ice cubes and that her research led her to  Highland Ice Ltd, a factory in Aberdeen which makes ice cubes, which kindly agreed to let her film there.  She has a good photo of the film crew standing around in woolly hats and scarves.

ice plant still 04

ICE PLANT.022

The Ice Plant 2007.mov.01_02_35_04.Still010

Festivals showing “The Ice Plant” were – Edinburgh International, Glasgow International, Clemont Ferrand International, Seattle International Film Festival, preceding a feature presentation at the GFT Glasgow.

Current television period dramas “War and Peace” and “Dickensian”, featuring Tuppence Middleton, have reminded me of a film Kate made in 2010, “Ever Here I Be”, a 16 minute ‘Digicult’ Film, UK Film Council & Scottish Screen.  Shown at Edinburgh International Film Festival, Nashville International Film Festival, Palm Springs Short Film Festival , Portabello Film Festival London and Inverness Film Festival Scotland. 

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Tuppence Middleton, Ever Here I Be, photograph by Janet Johnstone

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Ever Here I Be Master - cow.mov.10_01_07_15.Still031

Ever Here I Be starred Tuppence Middleton and Christopher Simpson and was nominated for the Underwire ‘Best Female Character’ award 2012.

Kate was a talented artist from a very young age and it was a delight to watch her progress.

She went to Allerton Grange High School in Leeds, where Damien Hirst was a former pupil, and then completed a Foundation course in Fine Art at the Leeds College of Art and Design, where she increasingly studied film.  Kate then moved to Glasgow in 1999 to study Environmental Art at Glasgow School of Art, during which she went on exchange to Massachusetts College of Art and Design, Boston to study filmmaking.

Kate graduated in 2002 and has written and directed a number of shorts, documentary and promotional films.  These include several commissions from Glasgow School of Art to make documentaries and promotional films for them.

Kate has a passion for film education and has taught filmmaking and screenwriting to children and young people for the past 8 years through Into Film, Project Ability Glasgow, Glasgow Film, Edinburgh Filmhouse, Glasgow Media Access Centre and Visible Fictions theatre Company.

Her website is  www.kateburtonfilm.com  which highlights all her main films.  You can watch many, such as “Mrs Pickering’s Music Cabinet”, 2015, where Helen McCook, Artisan Embroidery & Artist, has been requested to reproduce the lost textile screen to go into an original Rennie Mackintosh cabinet.

Kate is currently working on an outline for her first feature film script.

 

Red Squirrel continuous line and Grey Squirrel photographs

Red Squirrel, continuous line with colour sequence. Mick Burton, Leeds artist.

Red Squirrel, single continuous line drawing with colour sequence. Mick Burton, Leeds continuous line artist.

This continuous line Red Squirrel, completed with colour sequence, is one of my pictures to be hung at the Leeds Art Exhibition and Sale put on for the 15th year by St Gemma’s Hospice.

St Gemma's Leeds Art Exhibition. 29 - 31 October 2015

St Gemma’s Leeds Art Exhibition. 29 – 31 October 2015

This colour sequence squirrel is the last of a series which began with my attempt to produce a continuous line drawing with a shimmering fur effect for the squirrel.

Continuous line squirrel from 1970, with shimmering effect of fur. Mick Burton, Leeds artist.

Single continuous line drawing of squirrel from 1970, with shimmering effect of fur. Mick Burton, Leeds continuous line artist.

I have a treasured memory of seeing a Red Squirrel, when I was four, sitting on a wall next to our cottage at Arncliffe Hall, in the North Riding, where my Dad was Head Gardener to Sir Hugh Bell just after the War.  I thought that completing alternate shading with copper paint would best reflect this colour in this picture from 1970.  My daughter Kate said on the phone today that she remembered this picture being in the hall when she was young.

Red Squirrel with copper alternate shading from 1970. Mick Burton, Leeds artist.

Red Squirrel, single continuous line drawing with copper alternate shading from 1970. Mick Burton, Leeds continuous line artist.

I have many clear memories of living at Ingleby Arncliffe from the age of nearly two, to four and a half when we left.

Falling out of my pram outside the local shop and crawling up the step was the earliest. There was a three legged cat, then at Sunday School one of the stamps I collected was “The Light of the World” by William Holman Hunt (my first taste of the Pre-Raphaelites) and I won the child’s sprint on sports day on the cricket ground.

In the famous terrible winter of 1947, I remember Dad helping to dig a trench in the snow drifts down to the village.  It was amazing to walk along the trench and not be able to see out.

 I once watched a pig being killed in the yard by the cottage and the workman laughed as he squirted me with the pig’s bladder.  This memory came back years later when, as a young police constable, I attended my first post mortem (of a coal miner who had been in an underground tunnel collapse).  My sergeant stood with me and assured me that it would be just like a newly killed pig being cut up, if I had ever seen one.  I said “Yes, I saw one when I was four ! “

I only see grey squirrels now, mainly helping themselves to the bird seed Joan puts out.  With Gledhow Valley Woods at the end of the garden we can have five of them at a time.  Yesterday, a young squirrel was chased by a cat and ended up on the trellis a few feet from our dining room window.  Joan chased the cat away and called to me as the squirrel was too scared to move.

I took some quick photographs whist it was still there, but it became apparent that it was not going to move and was looking at me pleadingly.  So I went out and shepherded it into the bushes.  Here are some photos of a shimmering fur tail.

Young Grey Squirrel from Gledhow Valley Woods. Three feet from my window after being chased by a cat. Mick Burton, Leeds artist.

Young Grey Squirrel from Gledhow Valley Woods. Three feet from my window after being chased by a cat. Mick Burton, Leeds artist.

Young Grey Squirrel not daring to move, even though Joan had chased the cat away. Mick Burton, Leeds artist.

Young Grey Squirrel not daring to move, even though Joan had chased the cat away. Mick Burton, Leeds artist.

Young Grey Squirrel, imploring me to stop taking photos and do something about the cat. So I went out and shepherded it to the bushes. Mick Burton, Leeds artist.

Young Grey Squirrel, imploring me to stop taking photos and do something about the cat. So I went out and shepherded it to the bushes. Mick Burton, Leeds artist.

Haken’s Gordian Knot and the Twisting, Overlapping, Envelope Elephant.

I constantly look for Continuous Lines in many fields of art, history, mathematics – anywhere, as I just do not know where they are going to crop up.  Currently I am casting an eye on Islamic Art and Celtic art and am developing ideas on those.

Recently I glanced through a book called “Professor Stewart’s Cabinet of Mathematical Curiosities” and came across Haken’s Gordian Knot, a really complicated looking knot which is really an unknot in disguise – a simple circle of string (ends glued together) making a closed line. Here it is.

Haken's Gordian Knot, from Ian Agol.  A simple circle of string (an Unknot) formed into a complicated continuous line.

Haken’s Gordian Knot, from Ian Agol. A simple circle of string (an Unknot) formed into a complicated continuous line.

When I looked at the Knot, it reminded me of my “Twisting, Overlapping, Envelope Elephant” continuous line in that it has a lot of twists. I realised straight away that a narrow loop on the outside (left lower) seemed to lead into the structure with its two strands twisting as it went, each time in a clockwise direction.  I followed the two twisting lines throughout the drawing until they ended in a loop on the outside (left higher).

I wanted to draw and paint this knot. My first drawing was of the line on its own. The depth of some of the lines reminded me of one of my earliest paintings “Leeds Inner Ring Road Starts Here”, which was based upon a sign board which appeared near Miles Bookshop in 1967 informing us of the route the new road would carve through the City. This was several years before Spagetti Junction was built near Birmingham. My picture had lines swirling all over at various heights in one continuous line.

Leeds Inner Ring Road Starts Here. Use of varying thickness of continuous line, overs and unders.  Pre dates Spagetty Junction near Birmingham. Mick Burton, 1967.

Leeds Inner Ring Road Starts Here. Use of varying thickness of single continuous line drawing, overs and unders. Pre dates Spagetty Junction near Birmingham. Mick Burton, 1967.

My first picture of the Gordian Knot, in black and white, concentrated on the heights of the lines following the overs and unders shown by Haken.

Depth of lines in black and white, in Haken's Gordian Knot.  Mick Burton, continuous line drawing.

Depth of lines in black and white, in Haken’s Gordian Knot. Mick Burton, single continuous line drawing.

But my main aim now was to use blue and red to show the twisting nature of the pair of lines running between the starting loop and the end loop.  This was intended to allow the viewer to more easily follow the loop and the twists throughout the structure.

Twisting, overlapping colouring of Haken's Gordian Knot.  Mick Burton continuous line.

Twisting, overlapping colouring of Haken’s Gordian Knot. Mick Burton single continuous line drawing.

Just like viewing my “Twisting, Overlapping, Envelope Elephant”, from my previous post, imagine that you have a strip of plastic which is blue on the front and when you twist it over it is painted red on the back.  Where blues cross each other you have darker blues, and correspondingly with reds.  Where blue crosses red you have violet.  I show the strips feeding through each other, like ghosts through a wall.  There are some darks and lights in there as well.  Most usefully, the background shines through to help make the strips stand out.

You can now get more of a feel for what is going on.  I counted 36 clockwise twists and one anti-clockwise (number 26).  Continued twists in the same direction tie in the ongoing loop, when it feeds through the two strands of its earlier route at least 12 times.  Twist  number 26 probably cancels out the effect of number 25.

This is a preparatory painting, in acrylic but on two sheets of copy paper sellotaped together.  When I exhibit these pictures they will be hung as portrait, rather than the landscape shown here for comparison with Haken (as you will note from where my signature is).  I think they look a bit like the head of the Queen in portrait mode !

Having got this far, I realised that I should find out more about the Haken knot (or unknot), beyond Professor Stewart’s brief introduction.  How did Haken construct the knot and why?

Please see my next post, on this continuous line blog, to see how I got on.

One Line Drawing cover for Theatre Arts, October 1947, by Doug Anderson

The New Season on Broadway, a one line drawing cover for Theatre Arts magazine, October 1947, by Doug Anderson.

The New Season on Broadway, a one line drawing cover for Theatre Arts magazine, October 1947, by Doug Anderson.

Here is a terrific example of one line drawing by Doug Anderson, on the cover of Theatre Arts magazine in October 1947, which he entitles “The New Season on Broadway”.

Doug illustrates six plays on Broadway and includes the title in each whilst connecting them all up with his one line.  I know I go on about a Continuous Line Drawing starting and finishing at the same point and that it is only one line if it does not, but he starts under the last “e” in Theatre and ends on the left side towards the top, so he could easily have connected them up.

I like his use of small loops throughout, which helps the simplification of most male figures, the snake and the tramcar.  Lady’s dresses have lines stroked back and forth and their hats and hair have more detailed wiggling.  I love the progressive pattern of the window and heads in the tramcar.

Here are some detailed sections.

Street Car Named Desire, detail of The New Season on Broadway, cover for Theatre Arts, October 1947, by Doug Anderson.  One Line Drawing.

Street Car Named Desire, detail of The New Season on Broadway, cover for Theatre Arts, October 1947, by Doug Anderson. One Line Drawing.

High Button Shoes, detail of The New Season on Broadway cover for Theatre Arts, October 1947, by Doug Anderson.  One Line Drawing.

High Button Shoes, detail of The New Season on Broadway cover for Theatre Arts, October 1947, by Doug Anderson. One Line Drawing.

Man and Superman, detail of The New Season on Broadway, cover for Theatre Arts, October 1947 by Doug Anderson.  One Line Drawing.

Man and Superman, detail of The New Season on Broadway, cover for Theatre Arts, October 1947 by Doug Anderson. One Line Drawing.

Antony and Cleopatra, detail of The New Season on Broadway, cover for Theatre Arts, October 1947,  by Doug Anderson.  One Line Drawing.

Antony and Cleopatra, detail of The New Season on Broadway, cover for Theatre Arts, October 1947, by Doug Anderson. One Line Drawing.

How about the cat at the bottom !

Another difference compared to my approach to this style is that I usually think of the possibility of applying colours later. If you look at the lower foot of Antony, the outside space flows in through the foot which would confuse thoughts of colour. Similarly, the lady marked “Medea” to the left of Antony, has the outside flowing in through the bottom left of her dress.

It is interesting that this one line drawing dates from late 1947 and the pen and ink sketch that I have, in the style of Salvador Dali (covered in my post in August 2014), dates from 1948 when Dali was doing similar drawings.  So here it is again, “Guitar Player on a Horse”.

Dali continuous line drawing in pen and ink, guitar player on horse, dated 1948.

Dali continuous line drawing in pen and ink, guitar player on horse, dated 1948.

Escher Islamic Mosaic Change to One Continuous Line. STAGE 5.

Escher painting 1922 of Islamic Mosaic tile at the Alhambra.  WikiArt.  Continuous line study by Mick Burton.

Escher painting 1922 of Islamic Mosaic tile at the Alhambra. WikiArt. Continuous line study by Mick Burton.

In my post of 4 April 2015, Continuous Lines in Escher Islamic Mosaic painting, STAGE 1, I mentioned that the original Islamic artist had deliberately created two Continuous Lines, when he could have just as easily created one, because he wanted to retain overall symmetry of design and border connections.

I stated that I had examined the design and worked out how to make a change to the border connections of lines to create one continuous line throughout the design, and this is how it’s done.

Here is the chart from STAGE 2 again, which shows the Main Continuous Line in Red and the Minor Continuous Line in Blue and the colours are also shown as the connections loop outside the Border.  The change has to be done without changing the Alternate Overdraw in the main design and this is done by linking a Red Overdraw with a Blue Overdraw at the same time as linking two not overdrawn lines.

Minor Continuous Line, Alternate Overdraws in Red and Blue.  Mick Burton Escher Mosaic study.

Minor Continuous Line, Alternate Overdraws in Red and Blue. Mick Burton Escher Mosaic study.

We need a crossover on the Border involving a Red loop and a Blue loop.  If we part them at that junction and re-join the Red with the Blue, and then join both not overdrawn ends as well, we have united the Main and Minor continuous lines.  See Below.

Joining of Main Red Continuous Line to Minor Blue, leaving both non Alternate Overdraw lines joined at the former junction.  Mick Burton Escher Mosaic study.

Joining of Main Red Continuous Line to Minor Blue, leaving both non Alternate Overdraw lines joined at the former junction. Mick Burton Escher Mosaic study.

To show how this change is reflected in the Border, here is a before and after “Spot the difference” comparison which I have drawn.

Change of Border on Escher Mosaic to enable one continuous line. Mick Burton study.

Change of Border on Escher Mosaic to enable one continuous line. Mick Burton study.

As you can see, the difference between having two continuous lines and one is just a couple of flicks of a pen. Obviously, the artist would have known there was a one continuous line option and that he could have done it without losing any design or colouring options.

Presumably, the artists were required to retain overall symmetry above all else, including in the Border.  Eric Broug has also informed me that continuous line drawing is very rare in Islamic geometric design. 

I think that the Artist chose two continuous lines in the Mural Mosaic to demonstrate that he was only one step from having one line, and he made sure that the Border was drawn so that this change opportunity (which occurs on each of the four sides)  was as simple as possible.  He is saying “I could easily have drawn One Continuous Line ! “

After completing my research into the Escher painting, and explaining the one continuous line alternative, I realised that I needed to draw the single continuous line myself.  Here it is.

One Continuous Line Drawing, including Border signals, based on Escher Islamic Mosaic.  Mick Burton, March 2015.

One Continuous Line Drawing, including Border signals, based on Escher Islamic Mosaic. Mick Burton, March 2015.

 
This completes my five STAGES of explaining my thoughts on Escher’s terrific painting, in 1922, of the Islamic Mural Mosaic in the Alhambra.  I hope you found this abstract continuous line it to be interesting and stimulating.

Finally, I would like to thank Margaret Graves, Assistant Professor of Islamic Art and Architecture at Indiana University, for her encouragement and guidance after I completed my research.

Escher Islamic Mosaic Continuous Lines, Create and Change Border. STAGE 4.

A key part of the Mural Mosaic tile painting by Escher in 1922, is that he has included the Border in detail. The Border gives an indication of what happens to the lines when they hit the sides and where they feed back into the design. In the quarter section detail of the mural below you can see marks on the Border.

A line leaving the design either joins the border (so that you can follow where it goes) or goes under the border (and you can deduce where it re-emerges).  It is not easy to work all these paths out at first, but there is a logic to it.  If in doubt between two choices, one of them usually has a clear answer leaving only one option for the other.  Another aid to us is that each side of the Border is identical in the same direction around the design, so if the marks are not clear on one side you can check at a corresponding point on another side.

Detail to show Border.  Escher mural mosaic in the Alhambra.  WikiArt.  Mick Burton study.

Detail to show Border. Escher mural mosaic in the Alhambra. WikiArt. Mick Burton study.

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When I first started this research I did a basic hand copy showing all the lines hitting the sides and then showed each one as a loose end outside the square.  I then studied the border on the Mosaic to work out how all the loose ends should be joined up and charted them – this initial chart was in STAGE 1, and I show it again at the end of this post.

That was relatively easy, observing the result of what artist had done.  The hard bit is working out  from scratch which loose ends to tie up to produce continuous lines in a way which would still enable the colours to be allocated by the Alternate Overdraw (or equivalent process used by the artist).

According to Eric Broug in his demonstration video’s, the tile rectangle containing the design would be selected out of a larger pattern area.  In my own art, when I have drawn a large continuous line pattern and completed the Alternate Overdraw (so that I know the colour sequence everywhere) I can pick out a small section to display which of course already has the Alternate Overdraws.  Similarly, the Islamic artist producing the Mosaic would know the full colouring etc for the tile section.

I show below the design with all the loose ends and Alternate Overdraws in Red.  At this stage the artist would not know how many continuous lines would occur in the tile section on its own.  He will have also needed to produce a straight edge on the corners and other parts of the perimeter to block unwanted lines which encroached from the outside pattern.

Section of larger pattern with Alternate Overdraws and loose ends showing whether overdrawn.  Mick Burton study.

Section of larger pattern with Alternate Overdraws and loose ends showing whether overdrawn. Mick Burton study.

You will see from the loose ends that half of them are overdrawn in Red and half not. If you connect up pairs of the overdrawn, and pairs of the not overdrawn, loose ends then there will be continuous lines throughout the design and the Alternate Overdraw Template will be unaffected. If I connect up the not overdrawn pairs around each corner of the design, then working along the sides both overdrawn pairs and not overdrawn pairs work out consecutively. This matches the line direction message in the Border on the Mosaic design.  Here is a chart (previously in STAGE 1) showing all the loose end connections.  We know from STAGE 1 that there are two continuous lines, which makes the case strong regarding the artist using Alternate Overdraw, but it would not have mattered if there were more than two.

Escher Islamic Tile.  Basic line structure, with border connections. Mick Burton continuous line study.

Escher Islamic Tile. Basic line structure, with border connections. Mick Burton continuous line study.

Having looked at Borders in detail, that prepares us for the final STAGE 5 where I show how we can turn this into a Single Continuous Line design.  

I will also give you my opinion on what the original Artist thought about a Single Continuous Line and why I think he is definitely an Artist and not just a craftsman.

Mick Burton Continuous Line Blog.

Colour Sequence Allocation on Escher Islamic Mosaic Continuous Lines, STAGE 3.

Now that we have applied my Alternate Overdraw to the Continuous Lines in the Escher Islamic design, I can show how I allocate colours.  We can then compare the result with the colours on the original Islamic design painted by Escher in 1922.

My basic method of allocating colours is covered in my Post on 27 September 2014 entitled “Colour Sequence on Continuous Line Drawing”.

I will start with that same basic process where colour “0” is the outside of the drawing and this is alternated with “1” in its channel or channels.  When we cross through an overdraw from a “1” area we allocate “2” to this adjacent area on the other side and then alternate this with “3” (if there are any) in that channel.  In the negative direction, if we go from a “0” area through an overdraw we will allocate “(-)1” and alternate with “(-)2” in that channel.

Five colour number allocation on continuous lines for Escher Mosaic.  Mick Burton study.

Five colour number allocation on continuous lines for Escher Mosaic. Mick Burton study.

There are no areas coloured “3” and so we have 5 colours allocated, compared to only 4 colours used in the original Mosaic.

At this stage things did not look promising.  Trying to equate the 4 original colours in the Mosaic to my 5 numbers produced a best set of matches of 156 out of 313 (I won’t go into much detail here) which is just under 50%.

One thing that I did observe was that YELLOW matched “1” on 76 occasions and “(-)1” on 88 occasions.  This reminded me that I occasionally allocate colours positively by ignoring (-) signs.  When switched to simply using “0”, “1” and “2” I had 3 numbers to compare with the 4 original colours on the mosaic.  This now produced a best match of 241 colours out of 313 which gives 77% and was much more respectable.  Here is the 3 colour allocation.

Colour sequence allocation of 3 colours to continuous lines on Escher Mosaic.  Mick Burton study.

Colour sequence allocation of 3 colours to continuous lines on Escher Mosaic. Mick Burton study.

Of course the fourth colour GREEN used in the mosaic does not appear at all in mine.

As with a lot of art, including craft, there may be processes (or even rules) which get you a long way in a design but you have to know when, and how, to break away from them.  I may be a bit rigid with my Continuous Lines but my studies of Picasso and Dali doing them demonstrates that nothing is certain.

This Islamic artist, who I regard as very special, probably used a method equivalent to mine to allocate most of his colours but probably made the following over riding decisions to finish the colouring off –

a.   GREEN was allocated to the 8 areas surrounding each of the 8 planets, and nowhere else.

b.  Each of the 8 planets was coloured PURPLE, instead of black, to mirror its use for the centres of the Suns.

c.  Each Purple junction block at the middle of each side has three directional areas surrounding it which are coloured PURPLE instead of black.  I originally considered these to be decorative.

Allocation of all green colours and changes of black to purple on Escher Mosaic.  Mick Burton study.

Allocation of all green colours and changes of black to purple on Escher Mosaic. Mick Burton study.

If the above decisions were made first, then the remaining allocations would be made totally on my 3 colour allocation.  That is 229 areas remaining where my allocation matches 100% with the original Escher Mosaic colours.

229 colour sequence areas matching original Escher Mosaic colouring.  Mick Burton study.

229 colour sequence areas matching original Escher Mosaic colouring. Mick Burton study.

So there we are. I hope you have found my attempt to explain how this Escher Islamic Mosaic contains two continuous lines, which I believe was deliberate by the artist, and how most colours matched a colour sequence directly linked to the continuous lines.

The basic elements in the design largely match the template produced by my Alternate Overdraw method and, after specific allocation decisions were made by the artist, there was a total match of all other colours allocated by my method using the template.  Whether of not the artist used a similar method to myself, there is a direct link between the colour sequence and the two continuous lines.

In my searches through other forms of art, on the look out for continuous lines, I have not found any other example of art which contained both continuous lines and a related colour sequence, or signs of possible use of Alternate Overdraw with its Template.

There is a modern mathematical theory called “The Winding Number Theory” which could allocate colours in an equivalent way to my initial 5 colours, but it is not as much fun.

I will do a FURTHER POST (STAGE 4) on how the artist could have used Alternate Overdraw to help him to connect up the loose ends on the borders when actually constructing his continuous lines.

Mick Burton Continuous Line Blog.

Alternate Overdraw Applied to Escher Islamic Mosaic Continuous Lines, STAGE 2.

Escher painting 1922 of Islamic Mosaic tile at the Alhambra.  WikiArt.  Continuous line study by Mick Burton.

Escher painting 1922 of Islamic Mosaic tile at the Alhambra. WikiArt. Continuous line study by Mick Burton.

Before applying my Alternate Overdraw, which I use to allocate colours to Continuous Lines, I will give you my analysis of the colours in the original Mosaic and what I feel were the artist’s ideas behind the design.

Eric Broug states, in his YouTube demonstration “How Grids and Patterns Work Together” that this is a 16 point star surrounded by 8 point stars.  Geometrically you can produce stars with many different numbers of points.  Having done many planetary paintings myself, I feel that the original artist has realised that in this case we have a central Sun and 8 planets surrounding it which can represent our solar system (we can ignore Pluto as a planet as it only featured as such for a part of the last century).  The colours the artist uses reflect many aspects of this planetary situation –

a.  YELLOW is used as the colour for the flaming surfaces of the central Sun and the corner Suns.  All other yellow areas have star like shapes and represent distant stars peppering the background.

b.  PURPLE is used for the centres of the Suns and the 8 Planets.  Purple is also used for the lines of areas along the sides, vertically and horizontally from the centres of the sides and diagonally (the lines of purple areas may simply be decorative).

c.  BLACK is used for the “fan blade” shapes emanating from the Suns.  In my planetary paintings I often use black for the background outside a drawing and for the gaps through the  drawing .  The artist here could be using the same idea, so that the blades are in fact deep space seen beyond the Suns.

d.  GREEN is used to surround each Planet and I interpret this as representing life on each Planet, not just ours.

The process for completing an Alternate Overdraw is covered in my Post dated 10 September, 2014  (9/10/2014)  entitled “Alternate Overdraw on Continuous Line Drawing”.

In the previous post, STAGE 1, I showed that there are two continuous lines in the Mosaic.  I apply my Alternate Overdraw to produce a template for me to work with to allocate a colour sequence.  I have to bear in mind that there are 2 Overdraw results and 1 colour sequence for a single continuous line and 4 Overdraw results and 2 colour sequences for two continuous lines.

My experience tells me that the Alternate Overdraw, which will produce a Template best representing this Planetary composition, will have –

a.  An Overdraw for the Main continuous line commencing by overdrawing (in Red) a side of a fan blade of the central Sun, and

b.  An Overdraw for the Minor continuous line commencing by overdrawing (in Blue) a side of a fan blade on a corner Sun.

Main continuous line, Alternate Overdraw, choice 1.  Mick Burton, Escher Mosaic study.

Main continuous line, Alternate Overdraw, choice 1. Mick Burton, Escher Mosaic study.

Minor Continuous Line, Alternate Overdraw in Blue, Choice 1.  Mick Burton Escher Mosaic study.

Minor Continuous Line, Alternate Overdraw in Blue, Choice 1. Mick Burton Escher Mosaic study.

The aim  of the Alternate Overdraw is to create channels within the design where two colours can be allocated alternately within each channel and that adjacent channels have different pairs of colours.  An overall sequence of colours then follows across channel boundaries.

My experience told me, at this stage, that my colour sequence was likely to match the original Mosaic in and around the five Suns, but less so elsewhere.

I will show my attempts at allocating corresponding colours in the NEXT POST.  I will also explain why I feel that the original artist may have used the Alternate Overdraw or an equivalent method.

Mick Burton Continuous Line Blog.