Tag Archives: colour sequence

Red Squirrel continuous line and Grey Squirrel photographs

Red Squirrel, continuous line with colour sequence. Mick Burton, Leeds artist.

Red Squirrel, single continuous line drawing with colour sequence. Mick Burton, Leeds continuous line artist.

This continuous line Red Squirrel, completed with colour sequence, is one of my pictures to be hung at the Leeds Art Exhibition and Sale put on for the 15th year by St Gemma’s Hospice.

St Gemma's Leeds Art Exhibition. 29 - 31 October 2015

St Gemma’s Leeds Art Exhibition. 29 – 31 October 2015

This colour sequence squirrel is the last of a series which began with my attempt to produce a continuous line drawing with a shimmering fur effect for the squirrel.

Continuous line squirrel from 1970, with shimmering effect of fur. Mick Burton, Leeds artist.

Single continuous line drawing of squirrel from 1970, with shimmering effect of fur. Mick Burton, Leeds continuous line artist.

I have a treasured memory of seeing a Red Squirrel, when I was four, sitting on a wall next to our cottage at Arncliffe Hall, in the North Riding, where my Dad was Head Gardener to Sir Hugh Bell just after the War.  I thought that completing alternate shading with copper paint would best reflect this colour in this picture from 1970.  My daughter Kate said on the phone today that she remembered this picture being in the hall when she was young.

Red Squirrel with copper alternate shading from 1970. Mick Burton, Leeds artist.

Red Squirrel, single continuous line drawing with copper alternate shading from 1970. Mick Burton, Leeds continuous line artist.

I have many clear memories of living at Ingleby Arncliffe from the age of nearly two, to four and a half when we left.

Falling out of my pram outside the local shop and crawling up the step was the earliest. There was a three legged cat, then at Sunday School one of the stamps I collected was “The Light of the World” by William Holman Hunt (my first taste of the Pre-Raphaelites) and I won the child’s sprint on sports day on the cricket ground.

In the famous terrible winter of 1947, I remember Dad helping to dig a trench in the snow drifts down to the village.  It was amazing to walk along the trench and not be able to see out.

 I once watched a pig being killed in the yard by the cottage and the workman laughed as he squirted me with the pig’s bladder.  This memory came back years later when, as a young police constable, I attended my first post mortem (of a coal miner who had been in an underground tunnel collapse).  My sergeant stood with me and assured me that it would be just like a newly killed pig being cut up, if I had ever seen one.  I said “Yes, I saw one when I was four ! “

I only see grey squirrels now, mainly helping themselves to the bird seed Joan puts out.  With Gledhow Valley Woods at the end of the garden we can have five of them at a time.  Yesterday, a young squirrel was chased by a cat and ended up on the trellis a few feet from our dining room window.  Joan chased the cat away and called to me as the squirrel was too scared to move.

I took some quick photographs whist it was still there, but it became apparent that it was not going to move and was looking at me pleadingly.  So I went out and shepherded it into the bushes.  Here are some photos of a shimmering fur tail.

Young Grey Squirrel from Gledhow Valley Woods. Three feet from my window after being chased by a cat. Mick Burton, Leeds artist.

Young Grey Squirrel from Gledhow Valley Woods. Three feet from my window after being chased by a cat. Mick Burton, Leeds artist.

Young Grey Squirrel not daring to move, even though Joan had chased the cat away. Mick Burton, Leeds artist.

Young Grey Squirrel not daring to move, even though Joan had chased the cat away. Mick Burton, Leeds artist.

Young Grey Squirrel, imploring me to stop taking photos and do something about the cat. So I went out and shepherded it to the bushes. Mick Burton, Leeds artist.

Young Grey Squirrel, imploring me to stop taking photos and do something about the cat. So I went out and shepherded it to the bushes. Mick Burton, Leeds artist.

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.

 

 

 

 

Spherical Continuous Line Abstract with Colour Sequence.

Spherical continuous line with colour sequence.  Flypast Over Rolling Hills. Mick Burton 2015.

Spherical single continuous line drawing with colour sequence. Flypast Over Rolling Hills. Mick Burton, continuous line artist 2015.

I have modified my Spherical approach to continuous line from the method I described in my Continuous Line Blog post of 9 July 2014, which did not quite reflect the reality I was seeking.

I have kept the idea that when you draw out of one SIDE of the paper you need to return at the opposite SIDE at the corresponding point, so that the pattern matches vertically and after colour sequence the colours also match if you pull the paper round into a tube shape.  This is similar to the equator on a globe of the world matching.

Previously I had said that when going out of the top of the drawing you also need to return at the corresponding place at the bottom.  I was correct to say that the colours would not match, which would be equivalent to the poles on the globe of the world not meeting, but the treatment of the lines needed to be modified.

I realised that the bunching effect of the top being pulled together totally separately to the bottom being pulled together was fine regarding separate sets of colours but matching the line patterns from top to bottom was the wrong approach.

So, when I go out at the TOP now I need to come BACK IN AT THE TOP at the corresponding distance from the other end of the top.   Similarly if I go out at the bottom I come back in at the bottom.  You could then imagine that folding the picture vertically down the middle would mean that both pattern and colour sequence would now match at the top and bottom respectively (don’t actual fold it and spoil the picture ! ).

I recently drew the following for a demonstration/workshop at Stainbeck Arts Club in Leeds.  I started drawing the line a couple of inches in from the top left side and did a few rolling curves diagonally down from left to right, followed by several exits and returns to the picture – initially out at the lower right side and back in at the lower left side, then down and out at the bottom left and back in at the bottom right.

Spherical continuous line drawing with rolling and jagged lines.  Mick Burton 2015.

Spherical single continuous line drawing with rolling and jagged lines. Mick Burton, continuous line artist 2015.

I later tried some “shark fin” curves and a couple of large jagged sequences.

All the time I tried to draw the line cleanly through existing shapes (avoiding going near previous junctions) and being aware of areas I had not visited much.  Finally I needed to work out how to get back to my start point without spoiling the composition too much (here going out and back in can be handy).

I hope you can check the route of the line through the whole picture fairly easily.  I then applied my Colour Sequence to produce the picture at the top of this post.

The first stage is my usual alternate overdraw of the line (if you are overdrawing a section as you go out of the picture you need to continue to overdraw as you re-enter, or if not overdrawing going out it’s not overdrawing when you re-enter).  See my post of 10 September 2014 for the full ALTERNATE OVERDRAW process and my post of 27 September 2014 for the COLOUR SEQUENCE process.

I have used a series of 6 colours from Pale Yellow through greens to Prussian Blue which I have tried to work out in steps of tone.  This is partly to highlight the overlap effect of continuous lines and the natural depth of the abstract.  As always, there is choice of direction of colours – light to dark or dark to light.  Here it seemed best to have the single lightest area at the top and several darker areas across the lower part of the picture.  The picture also has an Optical Art look about it.

Printing the picture in Monotone is usually a good way of checking the steps of colour and light to dark.  So here it is.

Monotone of Spherical Continuous Line

Monotone of Spherical Single Continuous Line Drawing “Flypast Over Rolling Hills”. Mick Burton 2015.

I also produced another similar abstract for the Demonstration at Stainbeck Arts Club to show the Spherical approach with a different flow of lines and colours.  I had coloured the drawing with a sequence from Yellow through Reds to dark Brown.

Spherical Continuous Line with Colour Sequence.  Forest Fire.  Mick Burton 2015.

Spherical Single Continuous Line Drawing with Colour Sequence. Forest Fire. Mick Burton 2015.

Here is the Monotone of this picture.

Monotone of Spherical Continuous Line

Monotone of Spherical single continuous line drawing “Forest Fire”. Mick Burton 2015.

Twisting, Overlapping, Envelope Elephant. Continuous Line Drawing colouring.

“Fluorescephant”, the original version of “Elephant Grass” which is at the top of this continuous line blog, was my first successful Colour Sequence painting.  The sequence ran from yellow through greens to blues in steps of colour and tones which gave a natural three dimensional effect and dynamism.  Part of this was the overlapping nature of continuous lines which was reflected by the successive darker colouring.

The painting was accepted for the International Amateur Artist exhibition, in Warwick Square London, in February 1973 and then a month later in the National Society annual open exhibition in the Mall Galleries.

Fluorescephant.  Continuous line drawing with colour sequence.  National Society Open Exhibition, Mall Gallery, London, 1973.  Mick Burton.

Fluorescephant. Continuous line drawing with colour sequence. National Society Open Exhibition, Mall Gallery, London, 1973. Mick Burton.

I was never totally happy with the colouring.  I thought that there was an extra natural effect, on top of the overlapping, which I was missing.  When I started my art again in 2012, after a gap of nearly 40 years, I once more tried to sort this out.  I realised that I could enhance the twisting of the design and highlight gaps where the outside would show through.

Here is the result, “Twisting, Overlapping, Envelope Elephant”.  Imagine that the continuous lines are describing a sheet of plastic, which is coloured Blue on the front and Red on the back.  Each time a twist occurs, against the outside background, then I colour it Red.  When the overlaps build up, the shades of the blue front go darker blue, and the shades of the twisted areas become darker red.  Where the blue front and the red back occasionally overlap, then I use violet to reflect the mix.

This continuous line drawing is coloured to represent a

This 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.

You can see considerable areas of background colour within the animal showing through. This looks natural within the form of the elephant.

The blue areas, including darker blue overlaps, are the same as the blue areas in the “Fluorescephant”, so it is good to keep a large part of the original colour sequence in this change of style.

Rhinoceros and Ostrich continuous line drawings

Rhinoceros, continuous line drawing with colour sequence.  Based on Mick Burton demonstration.

Rhinoceros, single continuous line drawing with colour sequence. Based on Mick Burton demonstration.

I did a demonstration and workshop at Horsforth Arts Society, in Leeds, in January 2015.  It was a freezing evening and I parked outside in a narrow back street.  This club is an end terrace house, extended into the next house I think, and they have sole use.  No one had arrived, but I was encouraged by a notice in the window “Demonstration of Continuous Line Drawing by Mick Burton at 7.30pm”.  Shirley, who arranged demonstrations, arrived but could not unlock the door.  I managed to open it.

So we were in and I could cart all my kit and pictures up the stairs and decide on my set up.  Joan came with me to help and the room soon filled up with friendly, expectant, members.  Shirley had seen me demonstrate at another club and gave an encouraging introduction.

After showing several pictures of my animals, mentioning a bit about my past and going through the basics of how to do a continuous line animal, it was time to do my first drawing before the members had a go themselves.

Firstly I put my key marks on a sketched Rhinoceros, showed how to join up the marks in the main areas such as the head and legs and asked the members to start on their own subjects whilst I connected up more lines.  I completed a rough and ready version of the Rhino, which a few weeks later I spruced up and added colours as above.  It is in the Harrogate and Nidderdale Art Club spring exhibition this weekend.

The members of the club completed pictures of animals or people with lines, but with a great variety of styles.  I did not insist on complete continuous lines, as the main idea was that their drawings could flow, and many good results emerged.  Several coloured in their creations.

Whilst they continued with their pictures, or started new ones, in the second half I started an Ostrich.  I did the head and neck and put some key marks elsewhere and invited members to come up and have a go at parts of the ostrich with my thick marker pen.  Several did and we arrived at the result below.  It has about three different lines going and a few dead ends.  This is fine at an early stage of my continuous line drawings, before loose ends are then connected up and one continuous line arrived at along with modifications to pattern and smoothing.

Ostrich continuous line, demonstration drawing by Mick Burton, with the assistance of members of Horsforth Arts Society.  January 2015.

Ostrich single continuous line drawing, demonstration by Mick Burton, with the assistance of members of Horsforth Arts Society. January 2015.

I thanked them for their help and in later weeks produced the picture “Ostrich Egg” below.  It has two continuous lines, one of which is the coloured Egg.

Ostrich Egg, continuous lines.  Based on Mick Burton demonstration.

Ostrich Egg, single continuous line drawing. Based on Mick Burton demonstration at Horsforth Arts Society.

A black pen version of the Ostrich is currently in the Association of Animal Artists annual exhibition.

I quite like including eggs in pictures.  “Harriet’s Busy Day”, which now resides in Worcestershire, was a finalist in Britain’s Got Artists in July 2012.

Harriet's Busy day.  Continuous line with colour sequence.  Background based on eggs.  Mick Burton, 2012.

Harriet’s Busy day. Single continuous line drawing with colour sequence. Background based on eggs. Mick Burton, continuous line artist 2012.

 When I showed the Hen picture to my sister Wendy she said  “Why have you stuck all those eggs to the ceiling”.

Escher Islamic Mosaic Continuous Lines, Create and Change Border. STAGE 4.

A key part of the Mural Mosaic tile painting by Escher in 1922, is that he has included the Border in detail. The Border gives an indication of what happens to the lines when they hit the sides and where they feed back into the design. In the quarter section detail of the mural below you can see marks on the Border.

A line leaving the design either joins the border (so that you can follow where it goes) or goes under the border (and you can deduce where it re-emerges).  It is not easy to work all these paths out at first, but there is a logic to it.  If in doubt between two choices, one of them usually has a clear answer leaving only one option for the other.  Another aid to us is that each side of the Border is identical in the same direction around the design, so if the marks are not clear on one side you can check at a corresponding point on another side.

Detail to show Border.  Escher mural mosaic in the Alhambra.  WikiArt.  Mick Burton study.

Detail to show Border. Escher mural mosaic in the Alhambra. WikiArt. Mick Burton study.

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When I first started this research I did a basic hand copy showing all the lines hitting the sides and then showed each one as a loose end outside the square.  I then studied the border on the Mosaic to work out how all the loose ends should be joined up and charted them – this initial chart was in STAGE 1, and I show it again at the end of this post.

That was relatively easy, observing the result of what artist had done.  The hard bit is working out  from scratch which loose ends to tie up to produce continuous lines in a way which would still enable the colours to be allocated by the Alternate Overdraw (or equivalent process used by the artist).

According to Eric Broug in his demonstration video’s, the tile rectangle containing the design would be selected out of a larger pattern area.  In my own art, when I have drawn a large continuous line pattern and completed the Alternate Overdraw (so that I know the colour sequence everywhere) I can pick out a small section to display which of course already has the Alternate Overdraws.  Similarly, the Islamic artist producing the Mosaic would know the full colouring etc for the tile section.

I show below the design with all the loose ends and Alternate Overdraws in Red.  At this stage the artist would not know how many continuous lines would occur in the tile section on its own.  He will have also needed to produce a straight edge on the corners and other parts of the perimeter to block unwanted lines which encroached from the outside pattern.

Section of larger pattern with Alternate Overdraws and loose ends showing whether overdrawn.  Mick Burton study.

Section of larger pattern with Alternate Overdraws and loose ends showing whether overdrawn. Mick Burton study.

You will see from the loose ends that half of them are overdrawn in Red and half not. If you connect up pairs of the overdrawn, and pairs of the not overdrawn, loose ends then there will be continuous lines throughout the design and the Alternate Overdraw Template will be unaffected. If I connect up the not overdrawn pairs around each corner of the design, then working along the sides both overdrawn pairs and not overdrawn pairs work out consecutively. This matches the line direction message in the Border on the Mosaic design.  Here is a chart (previously in STAGE 1) showing all the loose end connections.  We know from STAGE 1 that there are two continuous lines, which makes the case strong regarding the artist using Alternate Overdraw, but it would not have mattered if there were more than two.

Escher Islamic Tile.  Basic line structure, with border connections. Mick Burton continuous line study.

Escher Islamic Tile. Basic line structure, with border connections. Mick Burton continuous line study.

Having looked at Borders in detail, that prepares us for the final STAGE 5 where I show how we can turn this into a Single Continuous Line design.  

I will also give you my opinion on what the original Artist thought about a Single Continuous Line and why I think he is definitely an Artist and not just a craftsman.

Mick Burton Continuous Line Blog.

Colour Sequence Allocation on Escher Islamic Mosaic Continuous Lines, STAGE 3.

Now that we have applied my Alternate Overdraw to the Continuous Lines in the Escher Islamic design, I can show how I allocate colours.  We can then compare the result with the colours on the original Islamic design painted by Escher in 1922.

My basic method of allocating colours is covered in my Post on 27 September 2014 entitled “Colour Sequence on Continuous Line Drawing”.

I will start with that same basic process where colour “0” is the outside of the drawing and this is alternated with “1” in its channel or channels.  When we cross through an overdraw from a “1” area we allocate “2” to this adjacent area on the other side and then alternate this with “3” (if there are any) in that channel.  In the negative direction, if we go from a “0” area through an overdraw we will allocate “(-)1” and alternate with “(-)2” in that channel.

Five colour number allocation on continuous lines for Escher Mosaic.  Mick Burton study.

Five colour number allocation on continuous lines for Escher Mosaic. Mick Burton study.

There are no areas coloured “3” and so we have 5 colours allocated, compared to only 4 colours used in the original Mosaic.

At this stage things did not look promising.  Trying to equate the 4 original colours in the Mosaic to my 5 numbers produced a best set of matches of 156 out of 313 (I won’t go into much detail here) which is just under 50%.

One thing that I did observe was that YELLOW matched “1” on 76 occasions and “(-)1” on 88 occasions.  This reminded me that I occasionally allocate colours positively by ignoring (-) signs.  When switched to simply using “0”, “1” and “2” I had 3 numbers to compare with the 4 original colours on the mosaic.  This now produced a best match of 241 colours out of 313 which gives 77% and was much more respectable.  Here is the 3 colour allocation.

Colour sequence allocation of 3 colours to continuous lines on Escher Mosaic.  Mick Burton study.

Colour sequence allocation of 3 colours to continuous lines on Escher Mosaic. Mick Burton study.

Of course the fourth colour GREEN used in the mosaic does not appear at all in mine.

As with a lot of art, including craft, there may be processes (or even rules) which get you a long way in a design but you have to know when, and how, to break away from them.  I may be a bit rigid with my Continuous Lines but my studies of Picasso and Dali doing them demonstrates that nothing is certain.

This Islamic artist, who I regard as very special, probably used a method equivalent to mine to allocate most of his colours but probably made the following over riding decisions to finish the colouring off –

a.   GREEN was allocated to the 8 areas surrounding each of the 8 planets, and nowhere else.

b.  Each of the 8 planets was coloured PURPLE, instead of black, to mirror its use for the centres of the Suns.

c.  Each Purple junction block at the middle of each side has three directional areas surrounding it which are coloured PURPLE instead of black.  I originally considered these to be decorative.

Allocation of all green colours and changes of black to purple on Escher Mosaic.  Mick Burton study.

Allocation of all green colours and changes of black to purple on Escher Mosaic. Mick Burton study.

If the above decisions were made first, then the remaining allocations would be made totally on my 3 colour allocation.  That is 229 areas remaining where my allocation matches 100% with the original Escher Mosaic colours.

229 colour sequence areas matching original Escher Mosaic colouring.  Mick Burton study.

229 colour sequence areas matching original Escher Mosaic colouring. Mick Burton study.

So there we are. I hope you have found my attempt to explain how this Escher Islamic Mosaic contains two continuous lines, which I believe was deliberate by the artist, and how most colours matched a colour sequence directly linked to the continuous lines.

The basic elements in the design largely match the template produced by my Alternate Overdraw method and, after specific allocation decisions were made by the artist, there was a total match of all other colours allocated by my method using the template.  Whether of not the artist used a similar method to myself, there is a direct link between the colour sequence and the two continuous lines.

In my searches through other forms of art, on the look out for continuous lines, I have not found any other example of art which contained both continuous lines and a related colour sequence, or signs of possible use of Alternate Overdraw with its Template.

There is a modern mathematical theory called “The Winding Number Theory” which could allocate colours in an equivalent way to my initial 5 colours, but it is not as much fun.

I will do a FURTHER POST (STAGE 4) on how the artist could have used Alternate Overdraw to help him to connect up the loose ends on the borders when actually constructing his continuous lines.

Mick Burton Continuous Line Blog.