Tag Archives: Mick Burton

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

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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.  

 

 

Continuous Line Portrait with Colour Sequence.

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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

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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

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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”.

Red Alert, Continuous Line Detected on Train Tracks Puzzle.

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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.

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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.

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.

Sandra Rider, world champ medal. IMG_2245 - Copy

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!

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      .