Author Archives: mickburton2

About mickburton2

I am an Artist in Leeds, fascinated by Continuous Line Drawings. I first developed my style and ideas in the 1960's and early 1970's.

Continuous Line Artist view of Haken’s Gordian Knot in “Unknot Hall of Fame”.

Peter Prevos, has included me in his “Unknot Hall of Fame”, within an article on his website about “The Art and Magic of the Trivial Knot”, which also explains many technical aspects of the trivial knot and how magicians have incorporated those ideas. There are designs, in the Hall of Fame, by Goeritz, Thistlewaite, Ochiai and Haken as well as art by Vanuatu and myself and reference to James Sienna. Have a look on – https://horizonofreason.com/science/unknot-gallery/

I had already done my painting when I saw a post on Mathoverflow website “Are there any very hard unknots?” by mathematician Timothy Gowers – https://mathoverflow.net/questions/53471/are-there-any=very-hard-unknots

I responded with posts on my website on in June 2015 and a later update in May 2018.

Noboru Ito, mathematician now at the of University of Tokyo, contacted me in February 2016 about his near completed book “Knot Projections” and my article is referenced in the Preface. “It was very helpful”.

Tomasz Mrowka, mathematician at the Massachusetts Institute of Technology, asked in November 2017 for a copy of my painting, as “it’s really quite striking and would love to hang it in my office”.

David Eppstein, computer scientist and mathematician at university of California, Irvine, featured my painting on his website in November 2018 “Mick Burton, an artist known for drawings that use a single continuous line to create the impression of complex and naturalistic shapes, looks at knot theory, self-overlapping curves, and the visualization of Seifert surfaces.” I had to look in Noboru Ito’s book to check out Seifert surfaces !

In essence my painting of Haken’s Gordian Knot is another example of me finding a well known structure which I can apply my continuous line knowledge and experience to. The way that nature can work in these structures often surprises me.

This is separate to my ongoing art work of producing single continuous lines and colouring based upon interesting subjects – which can be animals, landscapes, portraits, still life and abstracts.

Other examples of looking at structures have been –

Four colour theory maps, where my overdraw method could divide a map up into two streams of alternate colours, hence the four colours. I corresponded with mathematicians Robin Wilson and Fred Holroyd in the mid 1970’s. See my post in August 2015 on Skydiver patterns and my Four Colour Theory.

The artist Escher’s favourite tile at the Alhambra in Spain, which I realised had two continuous lines running through it. I saw that the artist could have made in into a single line with two small alterations. See my posts of April 2015.

Knights moves on a chess board starting and finishing at the same square and landing once on all the other squares. See my 1974 picture in the Gallery 1965-1974.

I am always on the look out for new structures which are suitable.

Red Alert, Continuous Line Detected on Train Tracks Puzzle.

I started doing Train Tracks puzzles in the Daily Mail a few months ago and then moved onto Medium puzzles (dimensions up to 10 x10) on puzzlemadness.co.uk and a month ago tried Large difficulty (dimensions up to 12 x 12).

You start off with a grid which states the number of cells which occur vertically or horizontally and they give you some bits of track initially, including start and end track at the edge.

Train tracks from puzzlemadness.co.uk Large difficulty 12.12.2020. Mick Burton, continuous line artist.

There are many attractive elements to this sort of puzzle, including the possibility of solving them totally without trial and error.  The first thing to do is to add initial offshoots for all these start tracks.  Next look for any rows which already meet the number of cells containing track, such as the right hand vertical which has the required two including the offshoot.  This allows you to allocate spaces to the remaining 10 cells. 

Being an artist, I know the value of space in a picture and it is particularly important here.  Then you have to consider the various types of track and on you go.  Constantly checking and rechecking is the key as you add pieces.  Bear in mind that the aim is to end up with one route from start to finish, avoiding dead ends, and use that to your advantage.  Finding dead ends is also useful as you can allocate spaces.

It is best to start off with smaller easier Train Tracks puzzles to get used to the process.

I attempt my puzzles on paper where I draw the grid and enter the numbers and given track pieces.  My fingers are too wide and clumsy to do much prodding on my mobile phone and if I complete the puzzle I then tap in the answer.  Here is my initial drawing of the above puzzle.

Initial attempt at the rail track puzzle (large difficulty) of 12.12.2020. Mick Burton, continuous line artist.

When I loaded this on my phone, I expected that as I tapped in the last piece the completed puzzle would disappear to be replaced by congratulations across the screen, for completing a route from start to finish.  Instead I saw the Red Alert.  It is not normally an offence to produce a continuous line in this blog.

I am good at mending this sort of thing of course and here is the final result – there is a X (space indicator) so that you see the complete shape before the last piece goes in causing the whole thing to disappear.

Correct completion of Train Tracks puzzle, with just the last bit to go in. Mick Burton, continuous line artist.

I am interested in various stand alone structures which have an environmental feel to them, where all the different elements can produce a surprising result.  

As it has been Lockdown etc,  I have completed 94 in about 10 weeks scoring 17,925 points, which put me at position 272 out of 863 listed.  Top is Stirlingkincaid with 2,766,965 !

On the monthly list I am 91st with 7,650 points.  Stirlingkincaid has 228,640 – does this person ever sleep?

Personally, I will probably move on now, looking for more structures which I can unlock with my continuous line knowledge.  Also, I need to finish my current work about Drawing Prime Numbers.

Tawny Owl window impression in Gledhow Valley.

Window impression of Tawny Owl.  Front garden in Gledhow Valley.  Mick Burton, Leeds continuous line artist.

Yesterday morning Joan said that there was a mucky mark on the lounge window and that the Window Cleaner had only just been the other day for the first time since the start of Lockdown.  Maybe a bird had done it. 

The impression was pretty detailed and we thought about pigeon size. We looked outside, as a blackbird had smashed into the window a few years ago and did not survive.  No sign this time so we hope that this bird is ok.

Here is a closer version of the impression, which I have darkened a bit so the grey impression, lit by the sun, shows up more against our evergreen hedge.

Full window impression of Tawny Owl, with good body, head and wing detail.  Mick Burton, Leeds continuous line artist.

I know that we have Tawny Owls in Gledhow Valley, Leeds, but I have only seen one sitting in a tree at dusk and of course heard them.  I looked up Tawny Owl in our RSPB Handbook of British Birds, by Peter Holden and Tim Cleeves.  “37-39cm.  As large as a Woodpigeon.  Has a tubby body, large round head and rounded wings.  Its face is surrounded by a ring of dark feathers….”  I took a closer photo of the body shape to look at this sort of detail.

Close up of the body of the Tawny Owl window impression, showing feathers around the head, beak and tubby body.  Mick Burton, Leeds continuous line artist.

You can see the faint ring of feathers around the head and where the beak has hit the window.  Also the tubby body and chest.  I suppose the impression is made by grease and dust off the feathers.

The impression of the body did not seem to be full size, so this may have been a youngster which first flew at the end of April.

I had been sorting out some of my framed paintings and had left one out on the guest room bed.  It was my single continuous line Barn Owl, which has a virtually identical composition to the window impression, with the sun shining through its wings.  See also my Post of November 2015 about this owl.

Continuous line drawing of Barn Owl onto Wet on Wet watercolour, 2015. Mick Burton.

Double Dominoe to the Rescue in Lockdown

Double domino to the Rescue in Lockdown.  Mick Burton, continuous line artist.

Leeds is in “lockdown” and Joan and I have been playing cards to help fill in the time.  We would have welcomed other games but I took the Monopoly etc up to my daughter Kate in Glasgow last year.   An old tin from the attic was found which was filled with dominoes.

In our second game with the dominoes, Joan started with double six and I responded with six & five.  Joan had a six and played that.  Very symmetrical !

We checked all the dominoes and found that we had one complete set with black backs and a faint fish pattern, plus one dominoe with a black back and a faint greyhound which was also six & five.

M.C. Hitchen & Sons Ltd, Briggate & Kirkgate, Leeds. Tin full of dominos. Mick Burton, continuous line artist, Leeds.

The tin looked medieval, with pictures of Old King Cole, and around the lid “M.C. HITCHEN & SONS LTD, THE SILK HOUSE OF THE NORTH, BRIGGATE & KIRKGATE, LEEDS.”      ( No postcode ! )      “Always at Your Service”.

M.C. Hitchen & Sons Ltd. Back of tin full of dominos. Mick Burton, continuous line artist, Leeds.

On the back was a blackbird pecking off someone’s nose.

I wondered if the company was still around.

M.C. Hitchen & Sons Ltd. dissolved October 2019.  Mick Burton, continuous line artist, Leeds.

No, it was dissolved last year – only just missed it.  In fact M.C. Hitchen & Sons, Limited was a large department store in Briggate, Leeds until it was taken over in 1952 and became Littlewoods which closed in 2004.

Checking whether we had a complete set of dominos was interesting.  Here is the layout. 

Line up of dominoes to check whether complete. We had one extra. Mick Burton, continuous line artists, Leeds.

Active Life, including Table Tennis, at Armley Leisure Centre Leeds

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Active Life at Armley Leisure Centre, Leeds, leaflet.   Featuring Mick Burton, veteran table tennis player.

Active Life is an exercise programme especially designed for the over 50’s that can include more than one activity in each session.

There are a broad range of activities giving a variety every day of the week. Fitness class, gym session, go for a swim or the multi sport sessions which include Table Tennis, Mini Tennis and Badminton.

Joan has been going to the two hour table tennis sessions for about 5 years, starting as a beginner. The standard varies from beginners, people starting again through to improved players now in the local league.  I go along with Joan, when I can, to support table tennis coach, Sandra Rider who runs the Table Tennis and Mini tennis on Tuesdays, Wednesdays and Fridays.

There are 10 table tennis tables with an attendance of about 30 and two mini tennis courts attended by up to 15.

Some people switch between table tennis and mini tennis.

It is a very social group and Sandra also organises separate events such as annual ten pin bowling and the Xmas lunch.

Sandra has vast experience both as player and coach and still plays at League, County and Internationally as a veteran.  She also has medals at Veteran European and World Championships.

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Sandra Rider, on the right, with her Bronze Medal in the over 60’s Ladies Doubles event at the World Veterans Table Tennis Championships, 2018, held in Las Vagas.  Her doubles partner Shirley Gelder is on the left.

I have played in leagues since I was 16, including mostly full seasons in Leeds Division 1 for 50 years for Victoria Table Tennis Club, until 4 years ago when I moved to Leeds Judean Table Tennis Club.

Joan and myself decided to join Sandra at the Veterans World Championships in Alicante in 2016.  I lost all my group games three straight, although the other player who went into the Over 70’s Consolation with me won it.

Joan led a lady from Brazil in the Over 70’s Singles by 2 games to 1 before losing in the 5th.

Joan Frank playing in the over 70’s doubles with her Japanese partner at the 2016 World Veterans Table Tennis Championships in Alicante, Spain.  Photo Mick Burton, continuous line artist.

People just seem to keep on playing table tennis. 

Last week, I was short of two players for my team’s first Summer League match in Leeds Division 1 against Lawnswood YMCA A team.  I thought I may have to re-arrange the match but was given two lower division players.  Step forward Malcolm Shedlow, age 86, and Dennis Fisher, age 80, who both started playing for Leeds Judean Table Tennis Club in the 1950’s and spent many years in Division 1.  I am only 75 so brought the average age of my team down to 80.

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Leeds Judean table tennis C team in the Leeds Summer League against Lawnswood YMCA A team at the YMCA on 4 June 2019. Dennis Fisher, aged 80, Mick Burton, age 75 and Malcolm Shedlow, age 86.   Photo by Mark Bleakley of Lawnswood YMCA. 

Our opponents were Mark Bleakley, Ankush Vidyarth and Kiran Babra with average age early 40’s.  The result reflected our respective ages!

Tour of Britain, Continuous Line, new version by Mick Burton. Inspired by Tour de Yorkshire 2019.

Tour of Britain, new continuous line drawing by Mick Burton. Inspired by Tour de Yorkshire 2019.

The Tour de Yorkshire annual cycle race has become a fixture in the Yorkshire calendar, but can be disruptive to other events or day trips we may plan.

Harrogate and Nidderdale Art Club’s exhibition, intended to take place on Early May Bank holiday, was moved this year to Spring Bank Holiday weekend 25-27 May 2019 due to the Tour de Yorkshire coming through Ripley, where we hold the exhibition, on Friday 3 May.

Harrogate and Nidderdale Art Club Spring Art Show and Sale of Work, Ripley Town Hall, 25-27 May 2019.

My Tour of Britain drawing has a continuous line starting and ending in Yorkshire as well, but would take slightly longer than the 4 days of the Tour de Yorkshire and require some trips over water.

The Tour de Yorkshire passed Ripley Town Hall, where the Exhibition will be held this weekend, and the Television coverage did a feature on Ripley including aerial views of Ripley Castle and the family of Sir Thomas Ingilby our art club’s patron.

Ripley Town Hall.   Photo from Harrogate and Nidderdale Art Club website   www.handnart.co.uk

That day’s stage, from Doncaster to Bedale, passed some other places which have a close connection to myself.  As well as passing Scholes Village Hall, near Leeds (where Joan and myself play table tennis on a Sunday morning), Harrogate (where I went to school and served as a Police Cadet) and Ripley (as above), into Ripon passing two road ends where I grew up in the 1950’s and it ended in Bedale where my mother’s family (Mace) were based from the early 1800’s.

Last year’s Tour de Yorkshire went through Bedale and the reception was so impressive that the organisers decided to finish a stage in the town this year.  Here is a photo from the 2018 race where the riders went over the railway level crossing from Bedale into Aiskew and on the left is Park House, the Mace family house from the 1920’s.

Tour de Yorkshire 2018 at level crossing from Bedale into Aiskew passing the Mace family Park House on the left.  Photo Northern Echo 2018.

Joan and myself had intended to visit my Aunty Vi Doyle, 98 years old and who’s first husband was my mother Brenda’s youngest brother Harry Mace, on Friday 3 May.  When I realised that the Tour was finishing in Bedale that day I knew that we would not be able to get any where near her house and so we went a few days earlier.  Vi’s health had been deteriorating for some months and she was distinctly weaker this time and did not eat much of her fish from Fishy Hall’s for the first time ever.

We found out about the exact route of the race which included going past Vi’s bungalow in South End at the start of the finishing straight and we told her she would hear the cheering.

Joan and myself watched the end of that stage on the television and after passing Vi’s the riders went up the main street passing the top of Emgate, in sight of the Oddfellows Arms (now The Three Coopers) where my mother was born, and finished next to the house in North End where my parents had their first home.

The cheers of the crowd would be one of the last memories of Aunty Vi who sadly died peacefully this morning in her own home.

 

The Sunbathing Foxes are back in Gledhow Valley.

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Two foxes sunbathing in my garden in Gledhow Valley on 15 February 2019.  Photo by Mick Burton, continuous line artist, Leeds, Yorkshire.

This burst of warm spring weather is bringing out the foxes just about every day. These two spent about 30 minutes wandering around, sitting and just relaxing.

Not too different to the painting which I did of a couple doing similar things a couple of years ago.

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My single continuous line painting of two foxes sunbathing a couple of years ago.   Mick Burton, continuous line artist, Leeds, Yorkshire.

The first time I saw foxes in Gledhow Valley was in the late 1970’s, when I lived near the middle of the valley and brought the dog to this end of the woods, above the Well House, and spotted a pair of cubs playing.

To see more animals go to the Friends of Gledhow Valley Woods website    http://www.fgvw.co.uk      .

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.

anticlock 1 line

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.

anticlock 2 alt overdraw

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.

anticlock 3 number alloc

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.

anticlock 6 full colours

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.

clock 1 line

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.

clock 2 directions of line

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.

clock 3 alt overdraw

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.