Tag Archives: continuous line artist

Change a four sided continuous structure into a single surface Mobius torus, or Mobioid.

Drawing of Doug Eglen continuous metal sculpture with sides in four colours. Mick Burton, continuous line artist.

In my last post, on 3 June 2025, I said that I would like to draw Doug Eglen’s 3/8″ square forged metal sculpture. 

Continuous Lines in forged metal, by Doug Eglen.

Here it is, but I have used separate colours for each of the four sides.  You can only see Red, Green and Blue because the metal remains flat overall and you cannot see the Black I allocated for the underside.

I have tried to reflect the 3D quality of the sculpture, with its Celtic over and under style, highlights and shadow.

When I first saw the structure, I wanted to understand what would happen if I applied twists to the sculpture.  I thought that there should be one or more types of twist which would turn the culture from being four sided with four surfaces into four sided with one surface.  I knew that the Mobius Strip has two sides before the half twist and one continuous surface afterwards and thought that the single surface should also be possible for Doug’s structure.

Another thing that I wanted do was to try and clarify my idea that his structure reflected the shapes of two Boomerangs.  I wondered what twists I would need to do this.

The poker which I made at the age of 12 at school appeared to have a half twist but it is difficult to visualise how this changed the position of the sides.

Brass handle with half twist on my poker, made at school when I was 12. Mick Burton, continuous line artist.

I had to use a pencil to draw along one surface to confirm that it changed the top side into the bottom side.  This meant that I could use two half twists near the centre of a new drawing of the sculpture to produce two boomerangs which had individual colours.

Using two twists to produce Black and Red Boomerangs on drawing of Doug Eglen’s metal sculpture. Mick Burton, continuous line artist.

Black has now appeared at the top for half the time, so we have four colours on view.  Another outcome is that the two sides, which are Green and Blue, swapped from one side to the other at the twists which has resulted in blue almost disappearing.  This is due to the close photographic angle by Doug showing most of the insides of each boomerang shape and I coloured them almost equally Green and Blue in my first drawing.  Green stayed the same within the Red boomerang here and Blue changed to Green in the new Black one.

I have mentioned the Mobius effect.  The Boomerang drawing has not produced a change in the number of surfaces but just altered their positions. Sides still equal surfaces.  This is because I have used two half twists.  If I had only used one half twist then the number of surfaces overall would become two surfaces, one colour for top and bottom and another for both sides.

It seemed to me that employing one quarter twist would produce a Mobius single surface throughout, as each time a surface comes round again it deflects a quarter and on the fourth approach it is back on top. Maybe a three quarter twist would also achieve this, but I found this more difficult to visualise.  First approach deflects to side 4, Second to side 3, Third to side 2 and fourth to side 1 again.

Anyway, I have drawn simply a single quarter twist as an addition to Doug’s sculpture.

Drawing of Doug Eglen continuous metal sculpture, but with added quarter twist. Mick Burton, continuous line artist.

I have started with black and the result is All Black.  This drawing depicts a 4 sided metal continuous sculpture which has only one surface.  It is a complete Mobius result.  Visually, you can see that it is a quarter twist and our knowledge of the general sculpture helps us to realise that there is in fact one surface.

Yes, a Boomerang drawing and an “All Black” drawing suggest that I have Australian and New Zealand interests.  My mother, maiden name Brenda Mace, was born in a pub in Bedale, North Yorkshire.  Nearly 100 years earlier six brothers were born in the same pub and four of them went to gold fields in both Australia and then New Zealand in the early 1860’s.  They were cricketers as well and Christopher Mace played for Victoria against the first team to visit from England and two years later John and Harry joined with him, in Otago New Zealand, against the first English team to play there.

Back to the drawings.  I looked on the Internet for images of general structures which included a quarter twist and failed to find any.  There were examples of the pure circular twist, including 4 sided, but these are difficult to visualise as there is no obvious start point. 

Mobius Strip Structure of Rectangle Geometric Shape. Issuu website.

This pure circular twist is more understandable than most and the Issuu website shows how they built one which you can walk round in.  I am not sure if this includes walking upside down at one stage!

https://issuu.com/vsvu/docs/prof_is_1000/s/16586493

I feel that a twist anchored into an actual general structure, which has some straight and flat sections, is important.  It is easier to identify the type of twist and how the effect of the twist radiates through the whole structure in a more meaningful way.

Some other reference sites mention continuous surfaces, with more than the single edge and surface of a Mobius Strip, as Morbioids.  They compare their structure with the Torus (when it has parallel lines drawn around it which can be regarded as equivalent to edges which can produce the Mobius effect).

There are specific explanations of degree of twist, the number of sides, leading to the number of surfaces.  These confirm my assumptions about a quarter (90 degree) twist, or three quarter (270 degree) twist resulting in a single surface for the square structure.  A half (180 degree) twist has two surfaces.  Others explain 5 or 6 sides and there is a formula for n surfaces according to twist and sides.

A useful link that works is headed “Name for a 3 sided Mobius Strip?”  https://reddit.com/r/topology/comments/1bfdu7m/

SamwiseGanges    said that he was going to call them Mobius prisms.  When he referred to square Mobius prisms, he confirmed my assumptions about the effect of their twists.

AceThe Aro   said that Dr. Cye Waldman called them Mobioid’s in 2017 and you can click onto his moving images.  You can also click on Ace’s own slideshow which runs through all the different twist and number of sides possibilities.

I would like to refer to my drawing of Doug Eglen’s structure, with a quarter twist, as an “Anchored mobius torus”, or “Anchored Mobioid”.

Doug may consider loosening the join on his double boomerang ironwork and resetting it with a quarter (90 degree) twist.  That would produce a real single surface anchored Mobioid.  

 

 

Steve Walmsley Surrealist Portrait of Mick Burton, Continuous Line Artist.

Flower Girl With Her Two Small Portraits Of Renowned Yorkshire Artist Mick Burton. By Steve Walmsley, Surrealist Artist.

Steve Walmsley sent me this image, which he created in response to my continuous line Portrait of him which I featured in my Post of December 2023.

My first reaction was that this Lady appears to be looking forward to devouring two pork chops.  Of course I realised that they were really portraits of me.  I think that it is a terrific composition and am pleased to be involved.

As I said in the previous Post, we sketched each other at Harrogate and Nidderdale Art Club and my sketch led of one of my Continuous Line Drawings of him and then a Colour Sequence version.  These are all shown in my previous post.  At that time, I did not include my photograph of Steve’s sketch portrait of me.

Now that he has responded, it is time to produce his sketch of me as a reference.

Portrait sketch of Mick Burton by Steve Walmsley, Surrealist Artist, May 2023.

This sketch does not relate too closely to Steve’s creation, but it does remind me of “front on” sketches done by L.S Lowry.  Here is one that is in the National Portrait Gallery.

Portrait by L. S. Lowry. National Portrait Gallery, NPG 5951.

Steve’s latest Surrealist Art can be seen on his website       

https://steven-walmsley.pixels.com/art/surrealism   . 

Continuous Line Portrait with Colour Sequence.

Continuous Line Portrait “Colourful Musician” by Mick Burton.

This is the second Colour Sequence portrait that I have completed, the first being of “Barry” 10 years ago which had a shorter range of colours.

As usual, I have worked out the natural range of levels running through the drawing and I can choose which end of the range to allocate Red and then Blue at the other end of this 6 colour sequence.  You may ask why the end of the sequence is in an eye coloured Red in some of my pictures of Animals (eg. Hen and Iguana).  The answer is that when I draw continuous line eyes there is a final loop (or even a loop within a loop), which can extend the range of colours if it is already at the end of the existing range (orange in this case).

Normally, only one eye is visible from a side-on view of most of my animals.  I do not then have the situation where the other eye can be at the other end of the colour range.  In the “Colourful Musician” I have ended up with totally different coloured eyes.  Fortunately, the portrait is of a Surrealist painter who is happy with this outcome.

I do not mind either, because continuous line drawing produces its own three dimensional appearance naturally.  Conventional Artists may regard my drawings as very technical, but I can argue that they use perspective and shadows in their art, which I regard as technical, and I get by without using either.  The head in this painting has a natural rounded appearance and the “Blue” eye side implies shadow.

Sometimes I have had to alter the lines to ensure that both eyes are the same colour, which I did with Nessie the cockapoo painting.

The “Colourful Musician” painting only came about after we had one of those sketch a fellow member sessions at Harrogate and Nidderdale Art Club, this one being run by Chairman Steve Walmsley who also announced that I would sketch him.

Sketch of Steve at Harrogate and Nidderdale Art Club. Mick Burton, continuous line artist.

Someone asked if I would do more work on my sketch and I said that it may turn into a Continuous Line Drawing.  Steve said “If you do, then I want all your colours”.  So I took a photo of him for added reference.

Steve Walmsley, Chairman of Harrogate and Nidderdale Art Club. Mick Burton, continuous line artist.

I produced a Single Continuous Line portrait using Over and Under lines before I went onto the colour version above.

“Surrealist Artist” Continuous Line Drawing by Mick
Burton.

Steve has his own unique approach to colour in his pictures, which are increasingly Digital Art.  You can view his full range of Surrealism, Abstractions, Landscapes, Portraits and Digital Art on his website www.steven-walmsley.pixels.com.

I particularly like the following pictures he has created.  The first one is acrylic and the rest are all digital art.

“Self Portrait with Sax” by Steve Walmsley, Surrealist Artist.

 

“Desert” by Steve Walmsley, Surrealist Artist.

 

“Neanderthal” by Steve Walmsley, Surrealist Artist.

 

“The Cruel Sea” by Steve Walmsley, Surrealist Artist.

 

“Reflections” by Steve Walmsley, Surrealist Artist.

 

“The Waterwheel” by Steve Walmsley, Surrealist Artist.

Another Artist in the Burton Family

Fathers’ Day card, from my daughter Kate, painted by my grandson Lucas.      Mick Burton, continuous line artist.

This action painting, by my grandson Lucas, reminded me of a fast rushing stream.

My daughter Kate is a professional artist and film maker (see my post of 2 February 2016 – “BB” by Kate Burton, Glasgow film maker, at London Short Film Festival),

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

Three year old Lucas receives plenty of encouragement to make pictures.

Lucas also squeezes paint tubes directly onto a piece of card to create mixes of paint, before Kate provides another piece of card to squash the paint.  There is a sort of ink blot “butterfly” copy effect.

Lucas squeezes paint directly from the tube.        Mick Burton, continuous line artist.

Here are some results, along with “Grandad” type observations.

Lucas watery landscape.         Mick Burton, continuous line artist.

This result made me think of a sort of Chinese or Japanese landscape painting.  Here is a modern version for comparison.

Autumn Mountains at Dawn, by Zhang Daqian.      En.wahooart.com.

The next picture has the appearance of a flying elephant, and I have done a few continuous line elephants in my time.  

Lucas’s flying elephant.    Mick Burton, continuous line artist.

Lucas’s flying elephant.  Naturally, he has a squash copy flying the other way.  See below Dumbo, the most famous flying elephant.

Dumbo the Elephant, from Tim Burton’s remake of Dumbo Takes Flight.

Another Lucas watery image reminded me of a Monet.

Lucas – garden pond squash painting.    Mick Burton, continuous line artist.

Here is one of Monet’s many paintings of water lilies.

Water Lilies Giverny – by Claude Monet.

One day I may tell you about a picture Kate painted when she was four.

Pateley Bridge Art Club Continuous Line Drawings

Pateley Bridge Art Club member’s single continuous line Rhino with internal pattern.

I was at Pateley Bridge Art Club earlier this month with a Demonstration and Workshop for the members.  They have covered the evening in their News Blog with a report by Charles Mellor, which included 16 examples of members’ pictures.  You can find the report at >      https://www.pateleybridgeartclub.org      .

I include here an additional three pictures by members which illustrate how you can devise an internal pattern which represents aspects of the subject.  Members could base their initial attempt at a continuous line, or lines, on a subject of their choosing or one or more of several faint outlines provided by myself.

I demonstrated how the basic ongoing line can involve curves, loops, angles, etc. taking in parts of the outline itself and involving where possible a novel pattern for that subject.  At the same time there is a need to leave spaces for the line to return to the start.  I said that members were free to use rubbers to correct their drawings or have more than one continuous line in their picture to get used to the process.

One member drew a Giraffe which incorporated some of the distinctive inner pattern of that animal.

Giraffe by Pateley Bridge Art Club member, showing inner pattern.

My third example is a Zebra where the member has included the famous stripes.

Head of a Zebra, by Pateley Bridge Art Club member.

The Rhinoceros above has a good inner pattern reflecting the armour plating appearance of the animal.  It reminds me of the woodcut by Albrecht Durer, who was amongst the first artists to portray this animal.

Rhinoceros woodcut by Albrecht Durer in 1515.

And that’s not all.  The Pateley Bridge member’s Rhino at the top of this post has a clear single continuous line and includes two specific features I have used in the past which appear in pictures which I displayed on the evening but may, or may not, have have influenced the drawing of this Rhino –

a.  The Rhino’s left eye is depicted by a gap in the outline, similar to my Panther’s right eye below, where I show only the pupil of the right eye.   

Association of Animal Artists Annual Competition Winner !

b.  The Rhino’s armour pattern involves the outside running into the interior of the animal, similar to my Zebra below.

 

 

Continuous line Zebra without crossover lines.

Continuous Line Zebra

I have requested that the Pateley Bridge member, who did the Rhino, copies the line and then applies alternate shading to highlight the “inside outside” effect.  If not I may have to do it myself.

Picasso was certainly aware of this “inside outside” situation.  At my Demonstrations I pass around Picasso’s book “One-liners” which has 50 pictures.  Most have the line starting at one end and then stopping on completion elsewhere, but there are several which are single continuous lines.  The last two pen drawings in the book are as follows.

Picasso “Studies for Mercury”. Picasso’s One Liners. Artisan, 1997.

On the left, the head, arms, body and legs are all inside the single continuous line.  At first glance it is the same on the right, but in fact there is no “inside”.

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.

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

img_5140 - copy

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.

IMG_4950

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.

img_20190108_0002

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.

anticlock 4 first alt colours - copy

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.

anticlock 5 second alt colours - copy

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.

clock 4 number alloc

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.

clock 5 first alt colours

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.

clock 6 last upward colour

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.

clock 7 downward colours

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.

img_20190108_0001

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.    

Christmas Tree Frost Image on Car Roof

IMG_5104 - Copy LEAD PICTURE SHOWING BIT OF CAR

Christmas Tree frost image on car roof, with photograph darkened.   Mick Burton, continuous line artist, 24 December 2018.

I have noticed hard frost images before on our car parked overnight in the drive. The car is on a slope facing upwards towards the south and the frost pattern seems to emanate from the high point of the roof, which is towards the higher front end.

IMG_5081 - Copy Frosted car original

Car with frost image on roof, parked facing south up hill, showing the centre of the pattern at the high point of the roof.   Mick Burton, continuous line artist, photo taken 24 December 2018.

Here is a closer view of the roof.

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View of the frosted over roof of the car, 24 December 2018.   Photo Mick Burton, continuous line artist.

The pattern on the roof of the car reminds me of the view from a plane when flying over the Alps.

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A closer view can be likened to the view when flying over the Alps.   Photo Mick Burton, continuous line artist.

A very close view shows the granules of frost making up the effect.  This is the apex of the car roof and I presume that periodic melting had occurred followed by new freezing.

IMG_5075

Granules of frost making up the image on the car roof.   Photo Mick Burton, continuous line artist.

As the sun hits the roof it highlights the pattern and eventually starts to melt the frost around its edges.   A pattern similar to a fir tree starts to emerge.   The melting starts from the high end establishing the bottom of the trunk of the tree and begins to form the outline of  the rest of the tree.

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As the sun increasingly hits the car roof it highlights the effect and also begins to melt around the edges.  Photo Mick Burton, continuous line artist.  

Making the photograph darker produces the effect shown at the top of this post.

I prefer to leave a bit of the car in the photo myself, but here is a view without the top of the car windows.

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Tree effect without showing any obvious part of the car.   Photo Mick Burton, continuous line artist.

 

I am fascinated by intricate decorative patterns appearing in nature.   Sometimes my Single Continuous Lines include a hint of this naturalness.