Tag Archives: continuous line blog

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.

How do you construct Haken’s Gordian Knot?

After completing my drawings of Haken’s Gordian Knot, which I covered in my previous continuous line blog post, I decided that I needed to find out more about how this unknot was created.  It is one thing me portraying the route of the two strands running through a completed structure, but possible something very different if I to construct it from scratch.

A Google search for Haken’s Gordian Knot took me to a page of MathOverflow website, where a question that appeared “Are there any very hard unknots?” posed by mathematician Timothy Gowers, in January 2011.  In an update after many answers he said that he had arrived at Haken’s “Gordian Knot”.

Haken's Gordian Knot, from Ian Agol.  A simple circle of string (an Unknot) formed into a complicated continuous line.

Haken’s Gordian Knot, from Ian Agol. A simple circle of string (an Unknot) formed into a complicated continuous line.

Timothy said that, after studying the knot for some time, “It is clear that Haken started by taking a loop, pulling it until it formed something close to two parallel strands, twisting those strands several times, and then threading the ends in and out of the resulting twists”. This approach is something like the suggestions I made in my last post on the basis of my Twisting, Overlapping, Envelope painting of the Haken Knot.

Twisting, overlapping colouring of Haken's Gordian Knot.  Mick Burton painting.

Twisting, overlapping colouring of Haken’s Gordian Knot. Mick Burton single continuous line drawing painting.

Timothy then added that “The thing that is slightly mysterious is that both ends are “locked” “.  When I started to build the structure from scratch I began to realise what “locked” may mean.

Constructing Haken's Gordian Knot.  Stages 1 & 2.  Mick Burton.

Constructing Haken’s Gordian Knot. Stages 1 & 2. Mick Burton.

After leaving the looped end at the start, the ongoing route first meets its earlier self at Stage 2.  However instead of the ongoing route going through the earlier one, the initial loop goes back through the later one. This must be what is meant by the first “lock”.

Constructing Haken's Gordian Knot.  Stages 3 to 7.  Mick Burton

Constructing Haken’s Gordian Knot. Stages 3 to 7. Mick Burton

Continuing, things were as expected up to Stage 7.  I now realised that the route could be simplified to one line, as the Twists were not affecting progress but the feed through points were crucial.  I switched to drawing the route by using a simple line and showed Feed Through points as Red Arrows.

Haken's Gordian Knot, Simplified Route showing Feed Points.  Mick Burton.

Haken’s Gordian Knot, Simplified Route showing Feed Points. Mick Burton.

You can see that after point “C”, where the reverse Feed occurs, there are 12 expected Feed Through points until you arrive at point “E”.  Here instead of Feeding through an earlier part of the route, Haken indicates that you are expected to Feed through the End Loop at “E” which is too soon. This must be the other “Lock”.

At this stage, of course, I had no idea what to do.  Timothy did not seem to be using a lot of paper like me, but a “twisted bunch of string” and a small unknot diagram.  So I found some string, but was at a loss to make much sense of anything using that.  Timothy, however, was disappointed that it was so easy with his string initially, but delighted when it became more difficult !

What I did realise about the sections of route lying beyond point “E”, which I have coloured Green, is that they all lie beneath the rest of the structure.

This would allow the Green Area to be constructed separately before you sort of sweep it underneath as a final phase.  When I say “separately” I can only assume that you would need to do all this first, feed the result through the final loop and encapsulate the result.  You would then take this bundle to the start and use it to spearhead the building of the structure, leaving the loop at the other end of the two stranded string back at the start.

Haken's Gordian Knot, Prior action for the Green Route, before starting main structure.  Mick Burton.

Haken’s Gordian Knot, Prior action for the Green Route, before starting main structure. Mick Burton.

Timothy said that he would love to put a picture of the process on the website and asked for suggestions.

Even though I am an artist and not a mathematition, I had already done two pictures of Haken’s knot before I found the MathOverflow website and was fascinated by the production process of the knot and so did some extra diagrams of my own.

I will ask if my drawings match Timothy’s thoughts in any way.

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.

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.

Continuous Line Drawings at “British Wildlife” Exhibition, Martin Mere.

"Mouseman Mouse" based upon Robert Thompson carved mouse.  Association of Animal Artists  "British Wildlife" Exhibition, Martin Mere, February & March 2015.  Mick Burton, Continuous Line Drawings.

“Mouseman Mouse” single continuous line drawing based upon Robert Thompson carved mouse. Association of Animal Artists
“British Wildlife” Exhibition, Martin Mere, February & March 2015. Mick Burton, Continuous Line Artist.

This is my second year taking part in the Association of Animal Artists exhibition at Martin Mere Wetlands Centre, Lancashire.  “British Wildlife” runs until 29 March 2015.  My chosen wildlife submissions are “Mouseman Mouse and “Gledhow Foxes Sunbathing”.

My grandad George Burton was born in Kilburn, North Yorkshire, and when I was young my Dad took me to the Church in Kilburn and pointed out the carved mice which appeared on the church furniture.  They were carved by Robert Thompson, who was at school with Grandad, and his family still run the furniture business in Kilburn which is now world famous.

As time went on I found out so many things about Robert “Mouseman” Thompson and his mouse trademark.  It seemed natural that I should do a  mouse in my continuous line drawing style and colour sequence.

Robert "Mouseman" Thompson's trademark carving on the Altar rail in Kilburn Parish Church, North Yorkshire.  Picture by Dave Sumpner at English Wikipedia.

Robert “Mouseman” Thompson’s trademark carving on the Altar rail in Kilburn Parish Church, North Yorkshire. Picture by Dave Sumpner at English Wikipedia.

Dad told me that Grandad and Robert were drinking companions in the late 1890’s and he passed on some stories of those times.

A man went to the pub in Kilburn with his groceries every day before setting off home.  He always went home over the “beck” footbridge, which had vertical rails with strappings through them.  The man habitually stopped half way across, sat on the straps and lit his pipe.  Grandad and others loosened the straps one day and the man later fell into the water.  There was a lot of “fuss” about that.

Another regular at the pub always parked his horse and trap outside and, of course, regardless of how much he had had to drink the horse could find its way home.  One night he came out of the pub and boarded the trap, not realising that the horse had been turned around between the shafts.  He drove off backwards to crash into the church wall.

I attended a talk by one of the Thompson family over 40 years ago in Leeds Central Library and spoke to him later.  He said that each wood carver had his own style of mouse.  Old Robert’s mouse had become very simple, like a wedge of cheese, and they called it “grand prix” mouse.

"Gledhow Foxes Sunbathing".  Association of Animal Artists "British Wildlife" exhibition, February & March 2015.  Mick Burton, Continuous line drawing.

“Gledhow Foxes Sunbathing”. Association of Animal Artists “British Wildlife” exhibition, February & March 2015. Mick Burton, Single Continuous line drawing.

I saw a fox cub at the east end of Gledhow Valley Woods when walking the Airedales over 30 years ago.  Since moving here foxes have regularly been in the garden in the day time.  Last summer they took up sun bathing at the top of the lawn virtually every day for a period.  This usually included a prolonged period of scratching.

When we were completing the patio, with the help of Helen, Janet and Richard, a fox came and sat at the top of the garden and watched.  He had the demeanour of an “overseer” or a General overlooking a battle.  On another day there were two of them sitting up there and they reminded me of the “King and Queen” sculpture by Henry Moore which I saw up on the hill at Yorkshire Sculpture Park in 1987.

Poster for Henry Moore exhibition at Yorkshire Sculpture Park, 1987.

Poster for Henry Moore exhibition at Yorkshire Sculpture Park, 1987.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Continuous line blog by Mick Burton.

Winding Number Theory and Continuous Line Drawing

 

Whirlpool in Space, or Petrol Poluted Puddle. Spherical continuous line with repeat colour sequence with Rainbow colours.  Mick Burton, Continuous Line, 1971.

Whirlpool in Space, or Petrol polluted Puddle. Spherical single continuous line drawing with repeat colour sequence with Rainbow colours. Mick Burton, Continuous Line, 1971.

This painting was one of two pictures hung at the Chelsea Painters Open Exhibition, held at the Chenil Galleries, Chelsea,1971.  I walked along the Kings Road looking for the gallery (I had submitted through and agency) and it was great to see the Whirlpool first in a window by the entrance.

The design was triggered by a browse through mathematics books in the library and coming across Winding Number Theory.  This used a continuous line and every time the line was drawn winding in a counter-clockwise direction a level was added and if you wound back in a clockwise direction a level was taken off.

So far, in my colour sequence numbering based upon Alternate Overdraw, I had not had a sequence of colours greater than about nine.  If I used the Winding Number method and continued to wind around counter-clockwise many times I could have a long colour sequence.  I went a bit mad with the Whirlpool, which was done on a spherical basis (allowing drawing out of one side of the paper and back in at the opposite side), and has a sequence of 20.

I did not simply go from light to dark over the whole 20 (the steps in shade between each colour would have been too small), but oscillated up and down with a smaller range of colours similar to a rainbow.  I had seen the rainbow effect produced by sunlight on petrol spilt on a puddle.

Alternate overdraw with colour sequence numbers.  Continuous Line, Mick Burton.

Alternate overdraw with colour sequence numbers. Continuous Line, Mick Burton.

To illustrate the difference between my Alternate Overdraw and the Winding Number, I start with the Alternate Overdraw in Red on the left.  As shown in earlier posts, each channel of areas between overdraws has two numbers alternately.  You move naturally up to a higher channel or down to a lower channel, through the red line and continue the numbering.

As before, you start with “0” on the outside and 0 can also appear within the drawing.

 

 

When we come to Winding Number allocation, we can use the same basic drawing with little arrows showing the direction it has been drawn.  It can be either direction of course, but I have chosen one which will match the result above.

Winding number allocation.  Continuous Line, Mick Burton.

Winding number allocation. Continuous Line, Mick Burton.

Starting at “0” for the outside, if we cross to another area through a counter-clockwise border for that area, it will be a level higher.  If we cross through a clockwise line we reach a lower area.

Here the + areas are of course higher levels and the (-) areas are lower.

The numbering matches the Alternate Overdraw illustration above.

 

 

Now, just to show the initial thrust of the drawing for the Whirlpool, with many levels, the next illustration shows a line spiralling from the centre outwards and I have shown just 13 winds.

Part of initial Winding Number spiral for Whirlpool  painting.  Mick Burton, continuous line.

Part of initial Winding Number spiral for the Whirlpool in Space painting.    Mick Burton, single continuous line drawing.

Then I have drawn a line from the centre of the spiral directly back to the bottom of the picture as the first phase of breaking up the spiral so that lots more areas start to  appear.  The next such phase is a meandering line near the top of the picture. 

As I have said, this is a shorter version than the one usd for the main Whirlpool in Space picture above.

Next I have decided that the direction of  the line will be counter-clockwise starting from the bottom of the spiral, so that the levels go up towards the centre.  The numbers have then been added.

On the original painting, which is 24″ x 20″, I used alternate overdraw to allocate the colours.  This was because I was used to using that method and I think it is better for an artist anyway.  The Winding Number theory was simply the inspiration for producing a sequence of 20 or more.

Now, to go off at a tangent, I am interested in other artists in the family who keep coming to light.  As part of my research into my mother’s family, the Mace’s from Bedale (from 1825) and much earlier from Cambridge, I have come across a book by Thomas Mace called “Musick’s Monument” published originally in 1676.  It was published again about six years ago.  Amongst his own illustrations within the book is this one of a spiral depicting his idea of God’s world.

 

“Mysterious Centre of All Mysterie…” in Musick’s Monument, by Thomas Mace, 1676. Continuous Line, Mick Burton.

 

Thomas was a famous composer of the 17th century, and craftsman who made lutes and viols, whose main job was a chorister at Trinity College, Cambridge.

To add to this “sort of” co-incidence, my Uncle Harry Mace from Bedale, North Yorkshire, was a joiner and builder.  When he retired he started to make old style instruments, such as viols, and sold them to a music shop in Leeds.  I am sure he did not know about Thomas of Cambridge.

Thomas was not too impressed with a relatively new instrument in his time, the violin.

 

 

 

 

 

 

Continuous line drawing at St Gemma’s Leeds Art Exhibition 2014

St Gemma's Leeds Art Exhibition.  Mick Burton continuous line.

St Gemma’s Leeds Art Exhibition. Mick Burton continuous line.

I have entered seven paintings in St Gemma’s Leeds Art Exhibition, which starts on Thursday 23 October 2014 at Leeds Grammar School.  There are over 800 pictures for sale.  I felt I had to put this in my continuous line blog.

I have entered in the previous 2 years since I started painting again and managed to sell work each time.  Its well worth a visit.  And its in aid of St Gemma’s Hospice.

Here are three of my paintings as a taster.  All are in acrylic on canvas.

 

 

Usain Bolt continuous line drawing.  Several colour sequences.  100 metre Olympic final at night.  Mick Burton, 2013.

Usain Bolt single continuous line drawing. Several colour sequences. 100 metre Olympic final at night. Mick Burton, 2013.

I have been a big fan of Usain Bolt and wanted to use my style to try to capture the dynamic speed and flowing movement of this great athlete.

As the race took place under floodlights, I have used a shimmering effect against the dark background.

 

 

 

 

 

 

 

Skelldale is totally drawn with one continuous line and various colour sequences have been used. Mick Burton, 2013.

Skelldale is totally drawn with one continuous line and various colour sequences have been used. Mick Burton, single continuous line artist 2013.

I was brought up in Ripon, a North Yorkshire small market town.  There are three rivers which virtually surround the place – the Laver, the Skell and the Ure  in order of increasing size.

I lived near to the Skell, and we sometimes would walk along it upstream to Fountains Abbey.  One of the local myths was that there was an ancient  tunnel from Ripon Cathedral to Fountains Abbey and we would discuss where the route might be.

Red Kites at Harewood, continuous line and colour sequence. Mick Burton, 2013.

Red Kites at Harewood, single continuous line drawing and colour sequence. Mick Burton, 2013.

Yesterday, on the bus back from Harrogate to Leeds, we approached Harewood Bank and saw the herd of deer in the park and above there were six red kites circling.  I have never seen that many at once. 

Since they were re-introduced near Harewood they have spread many miles and sometimes float above our house in Gledhow Valley in Leeds.

I had to try to capture this amazing bird with my continuous line and colour sequence.

 

 

 

Colour Sequence on Continuous Line Drawing

Fig 1.  Completed Colour Sequence on Continuous Line Drawing of horse.  Mick Burton, Continuous Line Blog.

Fig 1. Completed Colour Sequence on Single Continuous Line Drawing of horse. Mick Burton, Continuous Line Blog.

How do I apply Colour Sequence to my Continuous Line Drawings, which I first developed in the late 1960,s ?  In my last blog post, about Alternate Overdraw of My Continuous Lines, I pointed out that Colour Sequence was the next stage and so here we go.  I will now show the stages involved in completing the colouring of this Horse.

Other Alternate Overdraw on Continuous Line of horse.

Fig 2. Alternate Overdraw on Single Continuous Line Drawing of the Horse, as the first stage of Colour Sequence. Mick Burton, Continuous Line Blog.

From the two Alternate Overdraw examples in the previous post, I have chosen Fig 2 commencing at point “X” for this example (either “A” or “X” would result in the same colour sequence).

We are going to number all areas of the drawing, commencing with the background which will be numbered “0”.  In this example the background will remain uncoloured but “0” will also occur within the drawing and have a colour. 

Fig 3.  Initial numbering (0 and 1) of channels between Alternate Overdraws on the Continuous Line Horse.

Fig 3. Initial numbering (0 and 1) of channels between Alternate Overdraws on the Continuous Line Horse.

You will notice that between all the closed lines, formed by the Alternate Overdraws, there are channels of areas.  These can be completely numbered alternately by only two numbers, which in this case are 0 and 1.  So, starting with 0 on the background, work through all these linked channels, see Fig 3.  This also sets the direction of the number sequence throughout the drawing.

 

Fig 4.  Colour Sequence numbers 2 and 3 on the Continuous Line Horse.

Fig 4. Colour Sequence numbers 2 and 3 on the Continuous Line Horse.

 

 

The numbering progresses both upwards through positive numbers and downwards through negative numbers.  We will start with the positive direction and allocate the next pair of numbers, 2 and 3.  By moving from an 0 area into a 1 area, and on through its Alternate Overdraw border, we will enter an un-allocated area we can mark 2.  Now deal with all the other areas in this new channel, marking alternate areas 3 and 2, to complete this allocation.  After this we need to check for any further Alternate Overdraw channel, or channels, at this level adjacent to 1 areas and then allocate 2 and 3 to them also, see Fig 4.

We then need to check for any further Alternate Overdraw channels enclosed within any of the 2 and 3 channels.  If we found one we would allocate 4 and 5 to the new channel or channels.  In this case there is no higher level channel. 

Fig 5.  Colour Sequence numbers (-)1 and (-)2 on the Continuous Line Horse.   Mick Burton, Continuous Line Blog.

Fig 5. Colour Sequence numbers (-)1 and (-)2 on the Single Continuous Line Horse. Mick Burton, Continuous Line Blog.

Having  completed the numbering of areas in the positive direction, we now go into the negative in Fig 5.  By looking at an area 1 and moving through a 0 area with an Alternate Overdraw border we can cross through that into a (-)1 and (-)2 channel.  Mark the initial one (-)1 and then allocate alternately through the channel with (-)2 and (-)1.  After completing that channel, look for other un-allocated channels adjacent to 0 areas and allocate (-)1 and (-)2 to them.  Now look for further channels in the negative direction enclosed within a (-)1 and (-)2 channel.  There is one such, a single area (enclosed by its own Overdraw) in the front leg of the horse, which I have left blank in Fig 5 , which will be (-)3.

Fig 6.  Colour Sequence colour chart for Continuous Line Horse.  Mick Burton, Continuous Line Blog.
Fig 6. Colour Sequence colour chart for Continuous Line Horse. Mick Burton, Continuous Line Blog.

I was inspired by Rainbows in deciding on the sort of Colour Sequences I wanted to use for my Continuous Lines.  For shorter sequences, I settled for “partial rainbows” involving two prime colours only with a progression of colour mix and tones from light to dark.  For the Elephant I used yellows, greens and blues and for the Horse it was yellows, orange, red and browns in Fig 6.

I have carefully selected colours which have a stepped progression, both in colour and tone, and where possible I apply them from the tube (poster colour in the late 1960’s or acrylic now) to achieve an even and solid result.  I avoid mixing if I can, to retain the pure consistency of colour application across the painting, but sometimes it is necessary.

 

Fig 7.  Black and white photocopy of Colour Chart for Continuous Line Horse.
Fig 7. Black and white photocopy of Colour Chart for Continuous Line Horse.

 

To assess the accuracy of the progression steps of my Colour Sequence chart, I do a black and white (or grayscale) photocopy of my chart to check that the steps still work in monochrome, see Fig 7.

Having produced the Colour Sequence chart, we need to decide the direction of the colours matched to the numbers, ie. Light to dark in an upward or a downward direction.  Generally I see whether a scale would mostly coincide with where a natural highlight would be, or have more darks towards the lower parts in a drawing to infer shadow.  Usually it is fairly obvious, but you can always start again with the other direction of colours.  Note that my style may take advantage of natural hints of highlight or shadow on a subject, but generally these aspects (along with perspective) are absent.

I remember that when doing equations at school, which produced two answers (+ or (-) ), was a puzzle to me which no one could explain.  I understand the concept of a practical outcome from having two answers a bit better now.

Fig 8.  Initial Colour Sequence pair of colours on Continuous Line Horse.   Mick Burton, Continuous Line Blog.

Fig 8. Initial Colour Sequence pair of colours on Continuous Line Horse. Mick Burton, Continuous Line Blog.

Once we have decided on the colour match with the numbers, the initial two colours can be painted in, ie.  Vermillion = 0 and Orange = 1, see Fig 8.

 

 

 

 

Fig 9.  Second Colour Sequence pair of colours on Continuous Line Horse.
Fig 9. Second Colour Sequence pair of colours on Continuous Line Horse.

 

We can then match numbers 2 and 3 in areas to the colours required in the next channels up, or simply apply Golden Yellow to areas across the overdraw from Orange and then its alternate colour Permanent Yellow, in Fig 9.

 

 

 

 

Fig 10.  Third Colour Sequence pair of colours, in the negative direction, on the Continuous Line Horse.   Mick Burton, Continuous Line Blog.

Fig 10. Third Colour Sequence pair of colours, in the negative direction, on the Single Continuous Line  Drawing of Horse. Mick Burton, Continuous Line Blog.

Now we can match numbers (-)1 and (-)2 in the negative direction, or simply apply Light Brown to areas across the Overdraws from Vermillion.  When these Light Brown and Burnt Sienna channels have been completed the last channel colour is (-)3 which is Burnt Umber.  In Fig 10 I have left this final area blank  (on the front left leg of the Horse).

So you have seen my Colour Sequence method, using Alternate Overdraw, for Continuous Line Drawings.  Sorry if it has been a long explanation (particularly if you grasped it quickly or had already come across parts of it), but I have tried to pitch it as helpfully as I can, based on my demonstration sessions.    

A couple a years after I started Colour Sequence I came across the Winding Number Theory.  There is a connection and I did pick up one or two ideas from it.  I will talk about this in a later post, but as always I am not a trained mathematician and so I will keep talking in pictures. 

 I hope that you will give it a try and I am sure you will enjoy the ride, as I have for so long.

If you display or publish your results, it would be great if you could specifically acknowledge me and my ideas.