Tag Archives: crossover continuous lines

Another Stainbeck Artist, single continuous line drawing.

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Another Stainbeck Artist, single continuous line drawing portrait.  Mick Burton continuous line blog, 2018.

For this latest single continuous line drawing, I have used my gap technique to emphasise the crossovers of the lines and thickened certain key crossovers to try and further increase the three dimensional effect.

You can compare the result with the gaps only technique that I used with my blue horse in 2012.

Horse, in Celtic style.

Horse in Celtic style, single continuous Line drawing. Mick Burton, 2012.

You can also compare the portrait (above), based upon a 10 minute sketch of Zina done at Stainbeck Arts Club in late 2017, with my first single continuous line portrait (below) based upon a sketch of Barrie done at Stainbeck in 2012.

Stainbeck Artist, Continuous  Line Drawing.

Stainbeck Artist, a Single Continuous Line Drawing from a 10 minute sketch. Mick Burton, 2012.

I have also used the combined gapping and selected thicker lines on the single continuous line drawing of the Iguana, originally created in 1971.  The colour sequence version of the Iguana being featured on my previous post in July 2018.

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Iguana, single continuous line drawing. I have used gaps and selected thicker lines to enhance 3D effect. Mick Burton, continuous line blog.

“Another Stainbeck Artist” and “Iguana” continuous line drawings will both be on show, along with several other drawings and paintings of mine, at the Stainbeck Arts Club annual exhibition on Saturday 1 September 2018.  See Pamela Cundall’s poster below.

Stainbeck Art Club poster. 20180806_113931(1)

Stainbeck Arts Club annual exhibition, 1 September 2018 in Chapel Allerton Methodist Church, Leeds.  Part of the Chapel Allerton Arts Festival 2018.  Pamela Cundall poster.

Once more the club’s exhibition is part of the The Chapel Allerton Arts Festival.   The festival lasts from 27 August to 2 September 2018.

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Chapel Allerton Arts Festival 2018 – BannerGraphic18.  Mick Burton continuous line artist blog.

 

 

Haken’s Gordian Knot and the Twisting, Overlapping, Envelope Elephant.

I constantly look for Continuous Lines in many fields of art, history, mathematics – anywhere, as I just do not know where they are going to crop up.  Currently I am casting an eye on Islamic Art and Celtic art and am developing ideas on those.

Recently I glanced through a book called “Professor Stewart’s Cabinet of Mathematical Curiosities” and came across Haken’s Gordian Knot, a really complicated looking knot which is really an unknot in disguise – a simple circle of string (ends glued together) making a closed line. Here it is.

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.

When I looked at the Knot, it reminded me of my “Twisting, Overlapping, Envelope Elephant” continuous line in that it has a lot of twists. I realised straight away that a narrow loop on the outside (left lower) seemed to lead into the structure with its two strands twisting as it went, each time in a clockwise direction.  I followed the two twisting lines throughout the drawing until they ended in a loop on the outside (left higher).

I wanted to draw and paint this knot. My first drawing was of the line on its own. The depth of some of the lines reminded me of one of my earliest paintings “Leeds Inner Ring Road Starts Here”, which was based upon a sign board which appeared near Miles Bookshop in 1967 informing us of the route the new road would carve through the City. This was several years before Spagetti Junction was built near Birmingham. My picture had lines swirling all over at various heights in one continuous line.

Leeds Inner Ring Road Starts Here. Use of varying thickness of continuous line, overs and unders.  Pre dates Spagetty Junction near Birmingham. Mick Burton, 1967.

Leeds Inner Ring Road Starts Here. Use of varying thickness of single continuous line drawing, overs and unders. Pre dates Spagetty Junction near Birmingham. Mick Burton, 1967.

My first picture of the Gordian Knot, in black and white, concentrated on the heights of the lines following the overs and unders shown by Haken.

Depth of lines in black and white, in Haken's Gordian Knot.  Mick Burton, continuous line drawing.

Depth of lines in black and white, in Haken’s Gordian Knot. Mick Burton, single continuous line drawing.

But my main aim now was to use blue and red to show the twisting nature of the pair of lines running between the starting loop and the end loop.  This was intended to allow the viewer to more easily follow the loop and the twists throughout the structure.

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

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

Just like viewing my “Twisting, Overlapping, Envelope Elephant”, from my previous post, imagine that you have a strip of plastic which is blue on the front and when you twist it over it is painted red on the back.  Where blues cross each other you have darker blues, and correspondingly with reds.  Where blue crosses red you have violet.  I show the strips feeding through each other, like ghosts through a wall.  There are some darks and lights in there as well.  Most usefully, the background shines through to help make the strips stand out.

You can now get more of a feel for what is going on.  I counted 36 clockwise twists and one anti-clockwise (number 26).  Continued twists in the same direction tie in the ongoing loop, when it feeds through the two strands of its earlier route at least 12 times.  Twist  number 26 probably cancels out the effect of number 25.

This is a preparatory painting, in acrylic but on two sheets of copy paper sellotaped together.  When I exhibit these pictures they will be hung as portrait, rather than the landscape shown here for comparison with Haken (as you will note from where my signature is).  I think they look a bit like the head of the Queen in portrait mode !

Having got this far, I realised that I should find out more about the Haken knot (or unknot), beyond Professor Stewart’s brief introduction.  How did Haken construct the knot and why?

Please see my next post, on this continuous line blog, to see how I got on.

Continuous Line Drawing Alternate Overdraw embedded image.

 

Abstract before Alternate Overdraw  embedded Dog appears.  Mick Burton, Continuous Line.
Abstract before Alternate Overdraw embedded Dog appears. Mick Burton, Single Continuous Line Drawing.

 

 

Here is an abstract Continuous Line Drawing which conceals an image of a dog.  Possibly you can see some clues as to where the outline of the dog is.  The idea is to carry out an Alternate Overdraw along the line throughout the picture which will produce the image of the dog.  Start the overdraw with the arc marked with chevrons.

After I developed Alternate Overdraw in 1970, which enabled me to allocate my colour sequence to continuous line drawings, other possibilities started to occur to me.  The first was that you could hide an image of an animal within what looked like a totally abstract continuous line drawing.

See below how the dog finally appears.  In fact it looks a bit like Ben, who we have been looking after this week.

Alternate Overdraw embedded dog appears.  Mick Burton, Continuous Line Drawing.

Alternate Overdraw embedded dog appears. Mick Burton, Single Continuous Line Drawing.

The start of the process was to sketch a simple dog outline and then , knowing that the outline had to include many crossing lines, I broke the outline down into short lines or arcs which were at an angle to each other.

Next, I needed to run lines through the dog, from various directions, which used these arcs.  For it to work, there had to be an odd number of arcs in each line which went across the dog, between each two outer arcs.  This was so that, after completion, when you drew an alternate overdraw across the dog, both arcs on the outline were overdrawn.  This would result in all the arcs around the outline being overdrawn, thus forming one loop of overdraw. 

Within the body of the dog, several overdraw loops were also formed.  Similarly in the background a number of overdrawn loops and inner loops resulted. 

Of course, trial and error is involved in connecting up all the loose ends (of the lines running through the dog) to achieve a single continuous line through the whole drawing.

Finally, having completed a continuous line, I needed to check that there were no obvious sections which would indicate that an animal was in there. 

I did one more embedded image in 1970 before moving on to other things.  This time, instead of making the abstract continuous line from flowing curves with no straight lines, I decided to use mostly straight lines and right angles.

Abstract before Alternate Overdraw embedded steam engine appears.  Mick Burton, Continuous Line Drawing.

Abstract before Alternate Overdraw embedded steam engine appears. Mick Burton, Single Continuous Line Drawing.

 

 

 

 

 

 

 

 

 

 

 

This time I  was concealing a steam engine and the Alternate Overdraw result is shown below.

Alternate Overdraw embedded steam engine appears.  Mick Burton, Continuous Line Drawing.

Alternate Overdraw embedded steam engine appears. Mick Burton, Single Continuous Line Drawing.

 

 

 

 

As always with my various styles, I wonder who else may be using them  and whether they were in use long ago.

Alternate Overdraw on Continuous Line Drawing

After my early attempts at continuous line drawing, and then alternate shading, I tried Alternate Overdraw on top of my continuous line drawings.  This produced some fascinating results which led to developments throughout my art.

Alternative Overdraw on Continuous Line of the Horse, start A to B.

Draw from A to B to start Alternate Overdraw on Single Continuous Line Drawing of the Horse.

Lets use the Horse as an example.  Here is a lightly drawn Continuous Line (sorry if you have to tilt your lap top to see it all).  Start at point A and use a thicker pen or marker and draw over the first section of line, in the direction of the arrow, between the two crossovers.  Then miss a section before overdrawing the next section of line.  Keep going overdrawing alternate sections to point B.  You will see that already some overdraw sections are forming closed lines.

 

Alternate Overdraw of continuous line of horse.

Complete Alternate Overdraw of Continuous Line Drawing of horse from point A.

 

 

The next illustration shows the complete Alternate Overdraw and all these new darker lines form closed lines.

 

 

 

Naturally, if we start the Alternate Overdraw in a section which was not overdrawn in the above example (eg at X below), then this produces a result where a completely different set of closed lines appear.

 

Other Alternate Overdraw on Continuous Line of horse.

Other Alternate Overdraw on Single Continuous Line Drawing of horse, starting at X.

 

 

 

 

 

 

 

 

 

 

From the above findings I first developed my Colour Sequence ideas, which I will expand upon in the next post.

Later I used the closed lines to help in the construction of large models of my continuous line drawings as well as to devise hidden drawings within continuous lines.  More later on those.

The Alternate Overdraw method also led to a way to find a path through Four Colour Theory maps as part of my attempt to prove that theory nearly 40 years ago.

So, watch this space !!

Continuous Line Zebra

I visited Yorkshire Wildlife Park in June 2014, along with fellow members of the Association of Animal Artists.  It was an introduction viewing of the animals to be followed up by an Exhibition of our paintings which took place at the Park on Saturday 26 July.  Tigers, Lions, a Leopard and the Zebras were particularly impressive in their large enclosures. 

I have aways been keen to draw a Zebra in my style but the stripes are such a strong feature that I could not work out a way of doing the animal justice with my crossover continuous lines.  Of course I had seen prints of Victor Vasarely intertwined Zebras, done before the war, which helped kick start Optical Art.

Zeus, 5 year old stallion Zebra at Yorkshire Wildlife Park

Zeus, 5 year old stallion Zebra at Yorkshire Wildlife Park

Here is my photo of Zeus, a 5 year old stallion Zebra (with a brown nose). 

 

 

 

 

 

I decided that I could use a continuous line, without any crossovers, to follow the pattern of the stripes as far as possible.  As the background of my picture is white, the gaps in the lines around black stripes allow the white to flow through and become white stripes.

 

 

Zeus, Zebra at Yorkshire Wildlife Park

Zeus, single continuous line drawing of Zebra at Yorkshire Wildlife Park

 

Of course I like to have a separate picture of the continuous line drawing without any shading  or colour and I considered calling this version “Albino Zebra”.  However, on searching this phrase on Google it turns out that there is only one albino Zebra in captivity in the world and that is in Hawaii (and this is not really an albino but a White Golden Zebra with a lack of pigment in its stripes).  In the wild the stripes are pretty essential for camouflage and “albinos” do not survive for long.  The Hawaii Zebra is a female called Zoe and so is smaller (and a bit scruffier) than Zeus.  I therefore had to do a specific continuous line drawing of Zoe with a faint slate colouring.

Zoe, albino Zebra, Three Ring Ranch, Hawaii

Zoe, albino Zebra, Three Ring Ranch, Hawaii.  Mick Burton single continuous line drawing.