Tag Archives: single continuous line

Colour Sequence Application to Continuous Line Drawings by Mick Burton – demonstration continued.

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Clyde the Elephant, single continuous line with colour sequence by Mick Burton.

This is the continuation post covering my demonstration and workshop at Harrogate and Nidderdale Art Club on 6 December 2018.

Here is a reminder of my marker pen attempt at a continuous line elephant.

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Demonstration of a Single Continuous Line Elephant, initial drawing, at Harrogate and Nidderdale Art Club by Mick Burton, on 6 December 2018.

At home later I followed the line/s around and found that there was more than one line and I needed to do one or two diversions to correct that.  As the pattern at the front of the neck has a sort of square which I needed to get rid of I used that region to also turn the drawing into a single line throughout.  With a bit of general smoothing of arcs all round I arrived at the following revised elephant.

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Revised single continuous line elephant.    Mick Burton, Leeds Artist.

The next stage was to apply my Colour Sequence to the lines, which I completed in the last few days.  The result is shown at the top of this post.

To explain the process I use, and how it works, I will briefly go through the illustrations which I used later on in the Demonstration at Harrogate and Nidderdale Art Club.

We start by drawing a winding line in an anticlockwise direction.

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Stage 1. Single line drawn anticlockwise.   Mick Burton explains colour sequence.

Then, starting on an outside section of line, overdraw in red alternate sections of line.  This results in three different continuous line sections bounded by a red line.

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Stage 2. Overdraw in red missing alternate sections.   Mick Burton explains colour sequence.

We can now number all the areas to indicate where the colours in the sequence go.  Call the outside 0 and number through the sections to 5 in the middle.  You will see that each channel between red lines has alternately numbered areas.

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Stage 3. Number the areas in sequence from the outside (being 0) to the middle (being 5). Mick Burton explains colour sequence.

I have already decided on a sequence of colours to use, running from light tones to darker and from yellow to red.  First apply yellow and gold alternately throughout the outer corridor.

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Stage 4. Paint alternate colours within the outer corridor. Mick Burton explains Colour Sequence.

Paint in the next two colours from the sequence – orange (which looks reddish here) and red – alternately in the inner corridor.  You can see how the colours are lining up in natural sequence of tone and colour.

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Stage 5. Paint second set of alternate colours (orange, which looks reddish here, and red) in the next corridor.   Mick Burton explains colour sequence.

Lastly, for our anticlockwise line we paint the central area (which has its own red line surrounding it).  The result is a simple set of sequences running from the outside to the middle.

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Stage 6. The last colour in the sequence (dark red) is added in the centre. Mick Burton explains colour sequence.

As you will have realised, each loop going over earlier parts of the drawing adds a level, like overlapping shadows or leaves on a tree looking darker as they overlap.  The direction of darker tones of colour in the sequence reflects this.

In more complex drawings, however, the sequences of colours can change direction.  To show this we need to have a different single continuous line.

Start drawing your line with two loops from the lower left in an anticlockwise direction as before.  When you reach the upper left change to doing three loops in a clockwise direction and then go back to the start by a line running underneath.

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Stage 7. Start drawing your line from the lower left in an anticlockwise direction doing loops and when you reach the higher left change to clockwise loops running back to the right. Then finish clockwise running underneath to the start. Mick Burton explains colour sequence.

Here is confirmation of the directions of the line, anticlockwise and clockwise, and how they change and run back over earlier lines.  We now have a more complex drawing for colouring.

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Stage 8. Here is the completed single line with the directions shown – red for anticlockwise and blue for clockwise. Mick Burton explains colour sequence.

By applying alternate overdraw in red we split the drawing into corridors which look a bit more complicated than the simple anticlockwise drawing we did earlier.

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Stage 9. Alternate overdraw in red splits the new drawing up into corridors for colouring. Mick Burton explains colour sequence.

When we number the areas, starting at 0 on the outside as before, we have plus numbers at the top of the drawing but minus numbers appear in the lower corridor.  When we follow the natural sequence of numbers downwards from 2 through 1 and 0 we hit -1 and -2.

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Stage 10. Numbering from 0 on the outside as before we get minus numbers as well as plus. Mick Burton explains colour sequence.

After I had been doing my colour sequence for a few years I found out that mathematicians call this mix of anti and clock directions Winding Number Theory.  When you continue with loops in an anticlockwise direction you are adding levels of overlap and when you change to clockwise you start reducing levels.

We can now apply alternate colours yellow and red to the upper channel.

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Stage 11. First set of alternate colours in the upper channel on the complex drawing. Mick Burton explains colour sequence.

Then we can complete the positive colour direction.

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Stage 12.  Completing the plus direction colours by adding dark red.   Mick Burton, continuous line artist.

Now looking at the lower colours, in the clockwise section of the drawing we add the final two colours alternately.

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Stage 13.  Complete colour sequence on single continuous line drawn in both anticlockwise and clockwise directions. Mick Burton, Leeds artist.

So that is the basis of how I do my colour sequence.  

For my elephant, it is more complicated and I show below my sketch after doing the alternate overdraws to create the corridors of alternate colours and then numbered the colours throughout.

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Single continuous line elephant showing alternate overdrawn lines in red and colour numbering. The key to the colour sequence and numbering is shown. Mick Burton, continuous line artist.

I have shown the key to the colour sequence and numbering in the top right corner.  The colours can be employed in the opposite direction, of course, but with all my drawings the choice of which direction of sequence to adopt is not too difficult.  The darker colours fall lower down or on the main body of the animal and the more delicate red, orange and yellow mostly on the face. 

I only use red once, and that is on the eye.  This really reflects the greater detail on a face which extends the colour range.  Several of my colour sequence animals have the eye coloured by an end of range colour only used once in the drawing, eg. Iguana, Harriet the Hen and Olympic Lion.

The completed elephant, at the top of the post, has a story behind it.  I did the initial drawing in my demonstration to Harrogate and Nidderdale Art Club on 6 December 2018, which is the day my first grandson, Lucas, was born in Glasgow, son of Kate and Mark. 

I have decided to call the elephant Clyde after the famous Glasgow river.  Lucas can have a picture on his wall which is exactly as old as he is.    

Demonstration and Workshop at Harrogate and Nidderdale Art Club by Mick Burton, Continuous Line Artist

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Mick Burton explains how alternate shading can be used to colour a completed single continuous line.  This is Dottie, a lurcher pointer cross.   Harrogate and Nidderdale Art Club, December 2018.  Photo by Chris Noble.

As a member of Harrogate and Nidderdale Art Club I was delighted to run a workshop in December 2018 to demonstrate how I do my Single Continuous Lines and here I explain (above) how black and white alternate shading was applied to Dottie at the request of her owners.

Here is a photo of Dottie (below) checking out her portrait.

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This is Dottie checking out her portrait, done in Single Continuous Line with alternate shading by Mick Burton.  Photo by Stuart Firth.

I explained what my approach was to drawing Single Continuous Lines.  People often assume that I start at one point and draw the line, depicting my subject, all in one go and finish where I started.  I have done this from time to time, and my cat drawing is an example, but I now complete all my drawings in sections and then gradually connect up all the loose ends.

One of the more enjoyable parts of doing continuous lines is the freedom to incorporate all sorts of patterns involving curves, loops, sharp corners, etc.  In my case doodling these patterns was first triggered when I saw examples of Art Nouveau when I was about 9 years old.   I now drew some examples for the members and asked them to have a practice.

I then explained my approach to drawing an animal.  After doing a very basic sketch of my subject, I put in key marks throughout and then start on one section, such as the head.  Next I will initiate other parts such as legs and other distinctive features before connecting up all the lines.  I do not worry at this stage if there is more than one continuous line throughout, or that the lines may appear to be crudely drawn.

I said that I would demonstrate this approach by drawing an elephant, a subject which I have not attempted for about 50 years.

The result is shown below.  At home I usually start by using pencil on A4 size paper so that I can change the line as I go on.  The result can be scanned into my computer so that I can scale up to any size using Excel.  For Dottie, above, scaling up resulted in printing off 10 A4 sheets to stick together so that I could then trace through onto a big canvas.

For demonstrations I use a thick marker pen, usually on to A2 size paper but as there is a large screen at this club I used A3 size paper.  Poor quality paper is alright as the marker moves more smoothly, but of course a slightly shaking hand is magnified on the big screen.

It is important to keep an eye on loose ends.  I realised that I had three at one stage and was struggling to see the fourth, but a member spotted it on the big screen.  It was not too far away and I could link it back in without making the lines look too congested.

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Demonstration of a Single Continuous Line Elephant, initial drawing, at Harrogate and Nidderdale Art Club by Mick Burton, December 2018.

I said that this was fine as an example and the members could now have a go at any subject they wanted.  Also not to worry too much about loose ends or not being able to keep the lines clean.  Part of my aim was to introduce elements that could be incorporated into their own work and to encourage people to develop patterns or techniques of their own.

Regarding my elephant, I said that I would smarten it up later at home, by making sure that there was only one continuous line, smooth out the curves, etc and show them the result at a later meeting.  Also, I would produce a coloured version at home to link in with my intention to explain my colours later in the current session.

I was pleased with the drawings the members produced and enjoyed going round discussing their progress.  Here are a few examples of their lines, continuous or otherwise, including some colouring (which I did not start to cover until after these drawings).

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Kingfisher continuous line by member of Harrogate and Nidderdale Art Club, December 2018. Photo Mick Burton.

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Dolphin continuous line by member of Harrogate and Nidderdale Art Club, December 2018. Photo Mick Burton.

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Butterfly continuous line by member of Harroagate and Nidderdale Art Club. Photo Mick Burton

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Runners continuous lines by member of Harrogate and Nidderdale Art Club. Photo Mick Burton.

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Rhino continuous line by member of Harrogate and Nidderdale Art Club. Photo Mick Burton

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Horse continuous line by member of Harrogate and Nidderdale Art Club. Photo Mick Burton.

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Pig continuous line by member of Harrogate and Nidderdale Art Club. Photo Mick Burton

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Dog continuous line by a member of Harrogate and Nidderdale Art Club. Photo Mick Burton.

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Pigs continuous lines by a member of Harrogate and Nidderdale Art Club. Photo Mick Burton.

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Teddy continuous line, done on a laptop, by a member of Harrogate and Nidderdale Art Club. Photo Mick Burton.

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Hen continuous line by a member of Harrogate and Nidderdale Art Club. Photo Mick Burton.

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Lady continuous line by a member of Harrogate and Nidderdale Art club. Photo Mick Burton.

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Cat continuous line, with colour, by member of Harrogate and Nidderdale Art Club. Photo Mick Burton.

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Abstract continuous line, with some colour, by member of Harrogate and Nidderdale Art Club. Photo Mick Burton.

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Abstract continuous line, with overs and unders, by a member of Harrogate and Nidderdale Art Club. Photo Mick Burton.

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Abstract continuous line, with red alternate shading, by member of Harrogate and Nidderdale Art Club. Photo Mick Burton.

Whilst members were continuing with their continuous line drawings I talked about the backgrounds that I had gradually introduced into my pictures to add to the overall composition including my continuous lines.

Rather than simply have a plain background I have added to many paintings a simple coloured pattern effect which I feel complements the individual composition.  One example is a layered graduation of colours for my Single Continuous Line of a pig with my colour sequence.  I call the picture “Pig with Rasher Sky”.

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Mick Burton explaining his layered background to his painting “Pig with Rasher Sky” at his demonstration and workshop at Harrogate and Nidderdale Art Club. Photo by Chris Noble.

Another background is in my “Stained Glass Window Horse” which appears below.  Having spent considerable time in Ripon Cathedral when young I was always impressed by stained glass windows.  I also read a lot of Dandy comics where Desperate Dan sometimes jumped through a brick wall, “into the middle of next week”.  Consequently the horse has a gap in the wall similar to its outline and I have not included any cement and so that the sun shines through the gaps in the stones as well as the glass.  I chose a canvas where the sun can shine through as well.

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Mick Burton explains the stone wall effect as background to his painting “Stained Glass Horse” during workshop at Harrogate and Nidderdale Art Club, December 2018. Photo Chris Noble.

Later in the session I explained how my colours are devised and applied and I will cover this in a further post soon, which will also include the finished version of my new elephant and how my colour sequence naturally applies to it (hopefully).      

 

 

The Secret Art Project in St Gemma’s 2018 Art Festival

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“Loch Knares Monster” submitted to St Gemma’s 2018 Secret Art Project by Mick Burton, Continuous Line Artist.

As the open session for bidding on e-bay for the A5 size card paintings and drawings submitted to the St Gemma’s Secret Art Project has now closed, I am free to say which two pictures were submitted by me.  Of course, they are not single continuous lines.

The first one, above, is called “Loch Knares Monster”.  I used coloured pencils to produce delicate shades in the water and sky in contrast to the acrylic pen outline on the Serpent.

I have always been interested in the Loch Ness Monster, so what is wrong with turning the famous railway bridge in Knaresborough into a giant serpent.  My first attempt at the monster, years ago, was to add one to a mural of Venice which had been painted all over the bathroom wall of a house I shared with several others in Leeds in the late 1960’s.

Also an artist friend of mine, Bryn Glover, constructed a sculpture of “Nessie” from a motor cycle chain in 1969.  He worked at Leeds General Infirmary and once used a huge pair of forceps in a sculpture of a pelican.

There had to be a train in it, particularly a steam train, but I did not feel that my favourite engine “Mallard” would be appropriate.  See photograph below of Mallard crossing the Knaresborough bridge.

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“Mallard on Knaresborough Viaduct” in 1987. Photograph by Jo Turner (https://www.geograph.org.uk/profile/14389).

One day in the mid 1950’s, when I was on holiday staying with relatives, my cousin John Simmister and myself wandered into the railway sidings in Peterborough.  We saw Mallard, all be itself and so dirty that you could hardly tell that it was green. We climbed into the cab and talked about what it would be like to travel at 126 miles an hour and break the world steam record.

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“Mange 2 – Rail Root North” submitted to St Gemma’s 2018 Secret Art Project by Mick Burton, Continuous Line Artist.

“Mange 2 – Rail Root North” was coloured in acrylic and in a style which I hoped would be very different to my Knaresborough picture.

The HS2 railway project from London to Leeds and Manchester has been dragging on for years and I thought that I would compare that train to a streamlined pea pod.  My wife Joan comes from Wakefield, which is Rhubarb Triangle country, and as she is a vegetarian I thought she may appreciate the “jokes”.

Here is a clipping from this month’s Yorkshire Reporter, showing that HS2 is still big news.

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Yorkshire Reporter, November 2018, showing plans for Leeds Railway Station as part of the HS2 project.

Therasa May is one of the celebrities (including John Bishop and Kaiser Chiefs) who have agreed to submit a picture to the Secret Art Project, but there is probably no danger that people will think that she painted Mange 2.

 

Hot Cross Bunny and the psychology of colour

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“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.

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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.

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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.

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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.

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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.

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“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.

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“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.

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“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.