Tag Archives: single continuous line

Hot Cross Bunny and the psychology of colour

IMG_3425 Hot Cross Bunny

“Hot Cross Bunny”, single continuous line drawing painted in psychological colours. Mick Burton, continuous line artist.

In my posts I have said a lot about colour sequence and, along the way, talked about selecting appropriate ranges of colours for my drawings.  Here are some more colour comments, leading to the one about the bunny above.

I might consider that a yellow, red and brown range would be good for my horse. These have a similarity to its actual colours and give a warm and friendly feel which reflect the horse’s nature and temperament.

Fig 1.  Copy of IMG_5869 Horse complete, furst sequ

Colour Sequence on Single Continuous Line Drawing of horse. Mick Burton, Continuous Line Blog.

A strong harsh colour seemed to be best for my roaring lion and simple black and white achieved this.  In the mid 1960’s when I drew the lion, Bridget Riley had been doing many black and white hard edge pictures, and I did several of my animals in this colouring.  I feel that this worked best for the lion amongst my drawings.

016. 1967-9. Lion. Alternate shading, black.

Lion, single continuous line drawing with alternate shading in black and white. Mick Burton, continuous line Artist.

With my “Flame on the Sun” painting, the sort of anti magnetism represented by complementary red and green hopefully reflect the explosive violence required.

Flame on the Sun. Spherical continuous line. Mick Burton, 1972

Flame on the Sun. Spherical single continuous line drawing, with complementary reds and greens expressing explosive violence.  Mick Burton, continuous line artist.

For a more subtle result – my still life of a radish, apple, mushroom and flower heads – I used water colours to help to show the floppy translucent nature of the radish leaves.

IMG_20180510_Raddish

Radish, apple, mushroom and flower heads still life. Water colour used to show floppy, translucent nature of radish leaves. Mick Burton, continuous line artist.

Sometimes I find that I can use almost actual colours.  Here is a commission drawing, with the continuous line running through both robins and the branch.  I  was asked to do only a hint of pink on the Robins’ chests.  This is fine.  However, I had to have a go at a full colour result for myself.  The perky nature of robins is reflected pretty well, I think, by these “near” natural colours.

IMG_3417 (1) Best. Pair of Robins.

Pair of Robins, single continuous line drawing. Full near natural colour. Mick Burton, continuous line artist.

My yellow, green and blue sequence of colours fits well for “Nibbles”, a friendly rabbit who likes nothing more than eating her greens.

IMG_3498 Nibbles

“Nibbles”, single continuous line drawing.  The rabbit has a suitable range of colours to reflect contentment just eating her greens. Mick Burton, continuous line artist.

However, for a rabbit drawn with exactly the same single continuous line as for Nibbles, but who has a completely different temperament  –  RED, BLACK and WHITE fits the bill.

This is, of course, “Hot Cross Bunny” who lurks at the top of this post.  A real, full on, “Psycho”.

The two Rabbit paintings and the Pair of Robins accompanied several other of my pictures at the Harrogate and Nidderdale Art Club exhibition a week ago at Ripley Town Hall.

At the Preview Evening various prizes are awarded.  One was the annual prize presented at the Spring Exhibition by Sir Thomas Ingleby, the club’s patron, for his own personal choice for the best picture on show.  This was won by Julie Buckley for her “Black Labrador”.  

Sir Thomas also mentioned other pictures which caught his eye.  He said that he liked all the paintings by Mick Burton, but never thought that he would ever consider buying one called “Hot Cross Bunny”.

Here is a bit of background to the Rabbit paintings.  Nibbles and Hot Cross Bunny are based upon my daughter Kate’s rabbits, Harriet and Clover.

Harriet was friendly and cuddly and Clover might have been better named “Cleaver”.  We kept them both in the garage – in separate cages.

When we bought Clover, a lop eared rabbit, the breeder was saying how friendly and harmless the baby rabbit was.  I asked if it was related to an adult lop eared which had just tried to bite my finger off and the answer was “Yes, it’s the granny”.  We still bought Clover!

She was alright at first but later became very aggressive.  Every time we opened her cage for any reason, she would bite viciously.  We also realised that some one else would have to take care of the rabbits when we were on holiday.

Strangely, I found that if I put a hand on Clover’s head as soon as I opened the door she would stay still and relaxed as long as I kept the hand there.  With the other hand I could top up food and water or clean out the cage.  This worked for all of us.  Fortunately, our neighbour was delighted to be able to do this too and things were fine when we were away.

After Clover died and I had buried her in the garden, Kate prepared a wooden plaque and nailed it to the fence “Here lies Clover Burton the rabbit”.

An interesting consequence of keeping the rabbits was that straw from the bale became piled on the floor of the garage.  One day the straw was seen to be moving and we feared that we had rats and so I was deputed to check it out.  I found a nest of baby hedgehogs.

 

 

 

 

 

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.

 

“Vortex” by David Kilpatrick. Single Continuous Line and Alternate Overdraw colouring.

Vortex, David Kilpatrick. flat,1000x1000,075,f.u1

“Vortex” by David Kilpatrick, artist from Atherton, Australia.   Single Continuous Line using the Alternate Overdraw method to allocate colours.   March 2017.   Mick Burton blog.

I have been exchanging ideas with David Kilpatrick recently and he has agreed to let me put some of his pictures in my blog.  “Vortex” stands out to me, as I have been a fan of Vorticism for many years.  He has used Alternate Overdraw to allocate colours in sequence and it has worked well.

David’s design gives the impression of a sheet of plastic, coloured green on one side and red on the other, and each twist showing the other side.  With overlaps you get darker greens or darker reds.  Four internal areas let the background shine through.  The whole thing is very natural, including David’s own style of patchy colour radiating outwards.

Next is David’s “Knight’s Tour” which he is still working on.

David Kilpatrick knights tour. image011

“Knights Tour” by David Kilpatrick, artist from Atherton, Australia.   Single Continuous Line based upon moves of a knight and using Alternate Overdraw to allocate colour sequence.   April 2017.  Mick Burton blog.

I did a Single Continuous Line “Knight’s Moves on a Chessboard” in 1973 (see Gallery 1965-74) with the intention of colouring it, but never tackled it properly.  One of the problems was the number of fiddly small areas.  It led to my “Knight’s Tour Fragments” instead (see my previous post on 16.2.2017).

But now we have GIMP!  David said that he used this to move the lines about on his “Knight’s Tour”.  I googled GIMP and it means “GNU Image Manipulation Program”.  Some areas are still fairly small but he has produced a vibrant structure.

David says that these are trial colours (I presume from GIMP) and he intends to work out an improved scale of colours in his own style.

However, the colours shown already demonstrate the natural balance inherent in the Alternate Overdraw colour allocation.  The composition suggests to me an island with yellow “beaches” as well as reds within opposite “volcanic” zones.

There is a choice regarding background, which would naturally be the same colour as the light blue internal areas and result in a surrounding “sea”, or it could be left white as shown above.

I look forward to seeing the final version, which I am sure will be another splendid example of Vorticism.

Another picture that caught my eye was his “The Pram” which is based on a magic rectangle.

“The Pram” by artist David Kilpatrick, from Atherton, Australia.   Based on a Magic Rectangle. 2015.    Mick Burton blog.

This pram picture has lots of line ends in it and makes me want to attempt one myself using a Continuous Line animal.  Such a design would make you want to connect up so many loose ends.  My Spherical pictures already do this to an extent, as I take a line out of the picture at one side and bring it back in at the corresponding opposite side.

I think that David chose the positions of the displaced squares in a sort of random way.  Maybe I would want to be confident that I could move them around, in the way you could on the movable squares game of my childhood, and get back to the actual original picture.

You can see much more of the art of David Kilpatrick on

https://www.redbubble.com/people/fnqkid

Four Colour Theorem continuous line overdraw.

Continuous lines overdrawn on Skydiver formation design, using Four Colour Theory method. Mick Burton

Continuous lines overdrawn on Skydiver formation design, using Four Colour Theory method. Mick Burton

My recent post about the formation design used by the record breaking skydivers included a continuous line overdraw of their design (modified slightly be me to complete links which would have been present with more skydivers).  I said that I would explain how the overdraw (above) was completed.

The structure is made up of circles which have 3 way junctions throughout (3 handed in the case of skydivers ! ).  This can be regarded a map and so I will apply my Four Colour Theorem continuous line overdraw which I devised in the early 1970’s.

I was trying to prove the Four Colour Theorem, which states that no more than four colours are required to colour all the regions of a map.  My basic idea was that drawing a single continuous overdraw throughout a map would split it into two chains of alternate regions, which would demonstrate that only 4 colours were required.  If more than one continuous overdraw resulted then there were still only two types of chains of alternate regions.

As you will probably know, this theorem has many complexities which I will not attempt to cover here.  In the mid 1970’s I corresponded with two mathematicians at the Open University about my approach, Robin Wilson and Fred Holroyd, who were both very helpful and encouraging.  The theorem was proven in 1976 by Kenneth Appel and Wolfgang Haken, running one of the biggest computers for over 1000 hours.  I soon decided that it was time to go onto other things!  However, my journey had been fascinating with numerous amazing findings which have been so useful in my art.

I can keep to relatively simple methods for my pictures.

 Here is the design, used above, with my initial overdraws shown in red.

Assumed formation design used by Skydivers, with initial overdraws. Mick Burton four colour overdraw.

Assumed formation design used by Skydivers, with initial overdraws. Mick Burton four colour overdraw.

On final completion of the overdraws, every junction should have two of its three legs overdrawn and so the start decision (1) above overdraws two legs and this means that the third leg, which I call a “spar”, links to another junction where the other two legs must be overdrawn.

We then carry on making decisions which trigger other overdrawn lines across spars.  Usually there is a “knock on” effect where new overdraws connect with already overdrawn lines which then trigger more overdraws.

If we go wrong and a junction is triggered which has all three legs overdrawn, or none, we have to go back and change earlier decisions in a controlled process.  I usually photocopy the overdraws completed, every two or three stages, so that going back is not too time consuming.

Here is the situation after decision (3).  Decision (2) in blue had only triggered two overdraw sections but decision (3), in green, has triggered ten sections to be overdrawn in green.

Four Colour Overdraw decision 3 triggers 10 further overdraws, in green. Mick Burton, continuous line artist.

Four Colour Overdraw decision 3 triggers 10 further overdraws, in green. Mick Burton, continuous line artist.

Here is the completed overdraw.  It can be seen that some decisions still only trigger one or two overdraws, but decisions 5 and 7 triggered 13 and 12 overdraws respectively.  There are 80 junctions in the design and it took 11 decisions to complete the overdraws.

completed Four Colour Theorem overdraw, on design based upon Skydivers formation design. Mick Burton, continuous line artist.

completed Four Colour Theorem overdraw, on design based upon Skydivers formation design. Mick Burton, continuous line artist.

The completed overdraw has several continuous overdraws.  I tried other variations but had to accept that this design cannot be overdrawn with a Single Continuous overdraw.  This is due to the design having basically only two full rings of circles, which means that some tips of petals cannot be included in a continuous overdraw.

Continuous lines overdrawn on Skydiver formation design, using Four Colour Theory method. Mick Burton

Continuous lines overdrawn on Skydiver formation design, using Four Colour Theory method. Mick Burton

This situation can be overcome by adding links between the tips of the petals to produce that extra ring of areas.  Here is the expanded design and the stages of overdraw.  I managed to complete the Single Continuous overdraw in one sequence without having to go back to change any decisions.

Increased size design with successful Single Line Overdraw using Four Colour Theorem method. Overdraw decisions shown. Mick Burton.

Increased size design with successful Single Line Overdraw using Four Colour Theorem method. Overdraw decisions shown. Mick Burton.

Of course it looks better with one solid colour overdraw and no decision numbers.

Skydiver formation design with links between out petals completed, overdrawn with a Single Continuous Line using Four Colour Theorem method. Mick Burton.

Skydiver formation design with links between out petals completed, overdrawn with a Single Continuous Line using Four Colour Theorem method. Mick Burton.

I have said that the method of overdraw was developed with Four Colours in mind, and so you could use one pair of colours alternately within the above overdraw and another pair of colours on the outside of the overdraw (which can include the background).

I have found another interesting result in that if you use strong colours inside the overdraw, as it is the main image, and neutral colours outside (or even leave the outside blank) then the gaps between the “petals” show good use of space.  Here is the design simply coloured in strong red inside the overdraw, which creates a good contrast as the background seeps in. 

Solid colour within single continuous overdraw, with Four Colour method, showing good use of space. Mick Burton.

Solid colour within single continuous overdraw, with Four Colour method, showing good use of space. Mick Burton.

The chains of areas produced by the continuous overdraws can be coloured, not just in two pairs of colours to demonstrate Four Colours, but with a colour sequence or a mixture of sequence, alternate colours or even one colour.  In the last picture I have used colour sequence on main chains of areas related to the central space and, as a contrast,  light grey on the chains connected to the outside of the design.

Star Burst. Four Colour Theorem applied to a map of shell shapes wound round from the centre. Rainbow sequence of colours. Mick Burton, 1971

Star Burst. Four Colour Theorem applied to a map of shell shapes wound round from the centre. Rainbow sequence of colours. Mick Burton, 1971

This is one of the first paintings that I produced after discovering my Four Colour Theorem overdraw in 1971. I called the picture “Star Burst”, one of my first planetary pictures.

 

 

 

 

Skydivers in Ten Petal Flower Formation, link to Four Colour Theory continuous line.

164 Skydivers head down record in Illinois, 31 July 2015.

164 Skydivers head down record in Illinois, 31 July 2015.

Two weeks ago 164 skydivers, flying at 20,000 feet and falling at 240 miles an hour, set the “head-down” world record in Illinois. The international jump team joined hands for a few seconds, in a pre-designed formation resembling a giant flower, before they broke away and deployed their parachutes.

I was intrigued by the design of the formation. I have found many qualities in ten petal (or star) designs and, of course, I look for continuous lines in all sorts of designs that I find and in particular the possibility of a Single Continuous Line.

Here is my sketch of the skydivers formation.  It is made up of many linked circles, starting with a central ring of ten circles which radiate out to ten “petals”.  The plan seemed to involve six skydivers forming each circle by holding hands.  Some extra skydivers started links between petals.  I checked to see if I had included all the skydivers, which made my sketch look like a prickly cactus.

Cactus Count, 164 Skydivers all Present and Correct. Mick Burton, continuous line artist, August 2015

Cactus Count, 164 Skydivers all Present and Correct. Mick Burton, continuous line artist, August 2015

This was such a tremendous achievement by very brave men and women.  My only experience of heights is abseiling 150 feet down a cliff in the Lake District.  I realise that the jump would have been very carefully planned using the latest science and involved a lot of training, etc. but I am particularly interested in the part that the formation design played.

The hexagon appears to be an essential element so that hands can be joined at 3 way junctions.  A core circle of hexagons would naturally be 6, but more would be required for this jump.  The next highest near fit would be 10, which is fine given the variations in human proportions.  This also naturally allows linking between middle circles in the petals to complete a second ring of circles, which was partly done in this jump.

Every participant would need to know exactly where their place would be in the design and yet it is so symmetrical that I struggle to get my sketch the right way up.  Also with the short time involved co-ordination of planned stages would be difficult.  This made me think of a flock (or murmuration) of starlings performing their remarkable patterns in the sky and how they manage to co-ordinate. Apparently each bird relates and reacts to the nearest birds around it.  Absolute simplicity and ruthless efficiency with no critical path.

If the skydivers have adopted a similar approach then the design is ideal. The design is basically 30 circles in sets of 3 in a row making up 10 petals. The process is fluid and adaptable, building outwards from the centre. Think 10 individuals linking hands to start off with, which then recognisably evolves into 10 petals, and think 6 individuals in each of the 30 circles.  Everyone is dropped (there were 7 aircraft I think) in an order which anticipates being able to take up a place a certain distance from the centre of the structure and within a specific circle. As they approach they can recognise the progress and assess whether they can link in as expected or whether a modified position may need to be taken up (and being guided by the people already in place). The last individuals to be dropped will not have  a planned position in any circle but will form the start of the links between the central of the 3 circles in the petals. They need to be prepared to become part of an outer circle which has not been completed.

I have done a sketch of how this may work, with the numbers indicating my thoughts on the expected order of arrival in the building of the formation.

Skydiver formation with possible roles and order of arrival of individuals. Mick Burton, continuous line artist.

Skydiver formation with possible roles and order of arrival of individuals. Mick Burton, continuous line artist.

I hope this was a useful exercise, in trying to work out how the formation worked, and not total tosh (if so my apologies to all concerned).

To help my attempt to apply my continuous lines to the design I have completed the links between middle circles, which was partially done this time and I suppose will be considered for the next larger attempt at the record (say 180 skydivers).  The Continuous Lines are intended to pass through every three handed junction once only (I normally would say three legged ! ).

The method I use to complete the overdraw was developed in the early 1970’s when I was working on trying to prove the Four Colour Theorem.   A single continuous overdraw throughout a map would split it into two chains of alternate colours which would demonstrate that only four colours were needed.  I will explain how this is done in a future post.

Continuous lines overdrawn on Skydiver formation design, using Four Colour Theory method. Mick Burton

Continuous lines overdrawn on Skydiver formation design, using Four Colour Theory method. Mick Burton

This overdraw has resulted in several continuous lines and no alternative would produce a Single Continuous Line. This is due to the lack of width going around the structure.

Consequently, I have extended the design further by adding linking lines between all outer petals and succeeded in drawing a Single Continuous Line on that. A future Skydiver jump completely assembling this design would require about 220 participants (I am not suggesting that this be attempted) !

Skydiver formation design with links between out petals completed, overdrawn with a Single Continuous Line using Four Colour Theorem method. Mick Burton.

Skydiver formation design with links between out petals completed, overdrawn with a Single Continuous Line using Four Colour Theorem method. Mick Burton.

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.

Continuous Lines in Escher Islamic Mosaic painting, STAGE 1.

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.

I look for continuous lines in all forms of art.  I first saw this design in my daughter Kate’s book “Escher, The Complete Graphic Work”, by J.L. Locher.   We are both long term admirers of this artist.  Escher did this detailed painting  in 1922 when in Granada at the Alhambra, and its quality really hit me.  It was of an Islamic mural Mosaic tile,  which was made up of those geometric lines which are often seen in Islamic art, and I assessed it for continuous lines.  

I could see that the overall symmetrical  pattern and I saw that Escher had painted the design BORDER, which seemed to indicate what happened to the lines after they hit the sides of the square.  I then worked out, from the Border Pattern, that the lines were fed back in the same routes on all four sides of the square.  From the point of view of finding a single continuous line, in my experience, such overall symmetry of the structure meant that it was very unlikely that there was only one line. 

Here is the basic structure which I arrived at, which shows the “wiring” connections indicated by the border.  Let’s see how many continuous lines there are.

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.

When I traced over the lines I found that there were in fact two continuous lines making up the whole design.  Here are the two results, a Main continuous line (in red) and a Minor one (blue).

Main continuous line, one of two.  Escher Islamic tile design.  Mick Burton continuous line study.

Main continuous line, one of two. Escher Islamic tile design. Mick Burton continuous line study.

Minor continuous line, 2nd of two.  Escher Islamic tile design.  Mick Burton continuous line study.
Minor continuous line, 2nd of two. Escher Islamic tile design. Mick Burton continuous line study.

 

By experimenting with border changes, a bit like swapping wiring connections, I did come up with a single continuous line, but the borders were no longer symmetrical.  It seems likely that the artist realised that two continuous lines was the best he could hope for whilst retaining overall symmetry.   In a LATER POST I will show how a border can be “tweaked” by a slight alteration to make one continuous line in the mural mosaic, and how this answer is achieved.  I will also show how the artist is likely to have worked out how to achieve two continuous lines by connecting up the correct loose ends.

I now needed to know  “How important continuous lines were, within this design, to the artist?”   It could be that Continuous Lines were incidental to other aims, or they may have been of prime importance.

In my NEXT POST I will apply my Alternate Overdraw technique to produce a Template of closed lines, which I use to decide upon the colours to allocate.   I will also suggest what the artist’s ideas were for the design and his colour selection.  In a FURTHER POST you will see how my colour allocation compares with the original colours and to what extent I feel that my ideas were the same or similar to those used by the artist.

All this has been done without any reference to the construction of the original line structure.  I have taken the completed structure as a starting point to apply my ideas.  I did not research in any detail on Islamic line construction, until after my whole study was completed.

I have recently found YouTube demonstrations by Eric Broug entitled “How to Draw a Mamluk Quran Page” and “How Grids and Patterns Work Together”, which gave me a good insight into pattern construction and include an explanation of a larger tile containing this Escher Mosaic design as a section.  This is a fascinating process used by the Islamic artists over 500 years ago.  Otherwise, I have not found any reference to borders, colouring, or specific meaning of this design.

Possibly my ideas will generate a new view on aspects of the creation of this and other Islamic designs. 

Mick Burton, Continuous Line Blog. Continue reading