Category Archives: Abstract

Alternate Overdraw Applied to Escher Islamic Mosaic Continuous Lines, STAGE 2.

Escher painting 1922 of Islamic Mosaic tile at the Alhambra. WikiArt. Continuous line study by Mick Burton.

Before applying my Alternate Overdraw, which I use to allocate colours to Continuous Lines, I will give you my analysis of the colours in the original Mosaic and what I feel were the artist’s ideas behind the design.

Eric Broug states, in his YouTube demonstration “How Grids and Patterns Work Together” that this is a 16 point star surrounded by 8 point stars. Geometrically you can produce stars with many different numbers of points. Having done many planetary paintings myself, I feel that the original artist has realised that in this case we have a central Sun and 8 planets surrounding it which can represent our solar system (we can ignore Pluto as a planet as it only featured as such for a part of the last century). The colours the artist uses reflect many aspects of this planetary situation –

a. YELLOW is used as the colour for the flaming surfaces of the central Sun and the corner Suns. All other yellow areas have star like shapes and represent distant stars peppering the background.

b. PURPLE is used for the centres of the Suns and the 8 Planets. Purple is also used for the lines of areas along the sides, vertically and horizontally from the centres of the sides and diagonally (the lines of purple areas may simply be decorative).

c. BLACK is used for the “fan blade” shapes emanating from the Suns. In my planetary paintings I often use black for the background outside a drawing and for the gaps through the drawing . The artist here could be using the same idea, so that the blades are in fact deep space seen beyond the Suns.

d. GREEN is used to surround each Planet and I interpret this as representing life on each Planet, not just ours.

The process for completing an Alternate Overdraw is covered in my Post dated 10 September, 2014 (9/10/2014) entitled “Alternate Overdraw on Continuous Line Drawing”.

In the previous post, STAGE 1, I showed that there are two continuous lines in the Mosaic. I apply my Alternate Overdraw to produce a template for me to work with to allocate a colour sequence. I have to bear in mind that there are 2 Overdraw results and 1 colour sequence for a single continuous line and 4 Overdraw results and 2 colour sequences for two continuous lines.

My experience tells me that the Alternate Overdraw, which will produce a Template best representing this Planetary composition, will have –

a. An Overdraw for the Main continuous line commencing by overdrawing (in Red) a side of a fan blade of the central Sun, and

b. An Overdraw for the Minor continuous line commencing by overdrawing (in Blue) a side of a fan blade on a corner Sun.

Main continuous line, Alternate Overdraw, choice 1. Mick Burton, Escher Mosaic study.

Minor Continuous Line, Alternate Overdraw in Blue, Choice 1. Mick Burton Escher Mosaic study.

The aim of the Alternate Overdraw is to create channels within the design where two colours can be allocated alternately within each channel and that adjacent channels have different pairs of colours. An overall sequence of colours then follows across channel boundaries.

My experience told me, at this stage, that my colour sequence was likely to match the original Mosaic in and around the five Suns, but less so elsewhere.

I will show my attempts at allocating corresponding colours in the NEXT POST. I will also explain why I feel that the original artist may have used the Alternate Overdraw or an equivalent method.

Mick Burton Continuous Line Blog.

Continuous Lines in Escher Islamic Mosaic painting, STAGE 1.

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Escher painting 1922 of Islamic Mosaic tile at the Alhambra. WikiArt. Continuous line study by Mick Burton.

I look for continuous lines in all forms of art. I first saw this design in my daughter Kate’s book “Escher, The Complete Graphic Work”, by J.L. Locher. We are both long term admirers of this artist. Escher did this detailed painting in 1922 when in Granada at the Alhambra, and its quality really hit me. It was of an Islamic mural Mosaic tile, which was made up of those geometric lines which are often seen in Islamic art, and I assessed it for continuous lines.

I could see that the overall symmetrical pattern and I saw that Escher had painted the design BORDER, which seemed to indicate what happened to the lines after they hit the sides of the square. I then worked out, from the Border Pattern, that the lines were fed back in the same routes on all four sides of the square. From the point of view of finding a single continuous line, in my experience, such overall symmetry of the structure meant that it was very unlikely that there was only one line.

Here is the basic structure which I arrived at, which shows the “wiring” connections indicated by the border. Let’s see how many continuous lines there are.

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

When I traced over the lines I found that there were in fact two continuous lines making up the whole design. Here are the two results, a Main continuous line (in red) and a Minor one (blue).

Main continuous line, one of two. Escher Islamic tile design. Mick Burton continuous line study.

Minor continuous line, 2nd of two. Escher Islamic tile design. Mick Burton continuous line study.

By experimenting with border changes, a bit like swapping wiring connections, I did come up with a single continuous line, but the borders were no longer symmetrical. It seems likely that the artist realised that two continuous lines was the best he could hope for whilst retaining overall symmetry. In a LATER POST I will show how a border can be “tweaked” by a slight alteration to make one continuous line in the mural mosaic, and how this answer is achieved. I will also show how the artist is likely to have worked out how to achieve two continuous lines by connecting up the correct loose ends.

I now needed to know “How important continuous lines were, within this design, to the artist?” It could be that Continuous Lines were incidental to other aims, or they may have been of prime importance.

In my NEXT POST I will apply my Alternate Overdraw technique to produce a Template of closed lines, which I use to decide upon the colours to allocate. I will also suggest what the artist’s ideas were for the design and his colour selection. In a FURTHER POST you will see how my colour allocation compares with the original colours and to what extent I feel that my ideas were the same or similar to those used by the artist.

All this has been done without any reference to the construction of the original line structure. I have taken the completed structure as a starting point to apply my ideas. I did not research in any detail on Islamic line construction, until after my whole study was completed.

I have recently found YouTube demonstrations by Eric Broug entitled “How to Draw a Mamluk Quran Page” and “How Grids and Patterns Work Together”, which gave me a good insight into pattern construction and include an explanation of a larger tile containing this Escher Mosaic design as a section. This is a fascinating process used by the Islamic artists over 500 years ago. Otherwise, I have not found any reference to borders, colouring, or specific meaning of this design.

Possibly my ideas will generate a new view on aspects of the creation of this and other Islamic designs.

Mick Burton, Continuous Line Blog. Continue reading →

Winding Number Theory and Continuous Line Drawing

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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.

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.

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 Alternate Overdraw embedded image.

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: 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.

Variable grid single lines

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In 1969 when I was selling prints in the Merrion Centre art exhibition in Leeds, some one asked “Are your drawings done by computer ? ” At the time computers were rubbish regarding any form of drawing, so I eventually made my own “drawing machine”.

In 1973 I built a box with 8 perspex rulers lying in one direction and 8 more perspex rulers lying on top at 90 degrees to the lower ones. Each ruler had alternate inches marked (or not marked) with a thickish black line. Any ruler could be pushed in or out one inch to change the whole pattern of single lines displayed by looking down through the rulers (the box could be lit from underneath).

I could keep altering various rulers until an interesting pattern of lines appeared. I call these “variable grid single lines”. One seemed to represent a church and I applied a colour sequence to the picture. Recently I have modified some of the sky colours and stretched the picture to a rectangle on canvas and here is the result.

Church with Red Sky. Variable grid single line drawing. Mick Burton, 2014

Church with Red Sky. Variable grid single continuous line drawing. Mick Burton, 2014

I did many larger drawings on large square graph paper but found that you can’t vary the lines without a lot of rubbing out. What you can do is look for smaller areas within the grid which provides a good picture in its own right and replicate that. The single lines can go out at the sides of the picture, but it is possible to create a continuous line within the picture and then any lines within that are all closed lines as well.

Both these methods are, of course, stepping off points for putting these sorts of designs onto a modern computer and generating loads of possibilities in the twinkle of an eye. I try not to cross that line and feel that it is important for me to keep in the pre-computer art sphere, so that any of my drawings can be created using the mind and the hand with minimal use of technology. Some latitude is allowed, for as David Hockney has said, “a pencil is technology”.

I am interested in what computers produce, even though I do not want to use their creative expertise myself, and was amused when I read about an artist who programmed his computer to generate hundreds of his pictures overnight, whilst he was asleep, and then in the morning he would wade through the results and pick out a few good ones.

The brick wall, as far as my interest in computer pictures or animation is concerned, is when I cannot tell whether what I am seeing is a photograph or film sequence of the real world or a clever computer animation. That is where art dies.

Why “Continuous Line” ? What is the point of it ?

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You may ask why I am so bothered about the line being “Continuous”. Well here we go –

The Continuous Line gives the drawing an enclosed flexible structure, or environment, which in turn means that all parts are related to some degree. If I modify sections of a drawing there can be ramifications elsewhere, which may be small or extensive. “Skelldale” was one of my earliest continuous line drawings.

When I compose a drawing I have to bear in mind that the line must return to the start point. This is a lot of fun when I do an abstract, but for a figurative drawing it is more difficult as I am aware that the drawing will constantly change. However, I have learned that this difficulty can help to trigger the creative force that often lies within the drawing.

This discipline of having to make choices on the route of the line, or modifying the route, can produce an extra structural effect or dynamic of movement which I may not have foreseen. This creation of a result beyond my intention is similar to what happens in nature, where the practical necessity of combining all the elements needed in an animal or a plant often evolve into a tremendous design.

A further result of the Continuous Line is its creative effect on colours applied. I worked out a method of applying colour sequences which can further enhance the natural structure and dynamic effect. A colour only occurring once can be in a key area, eg. the eye of the Iguana. I used a special repeat pattern for the scale effect.

My “spherical” drawings, where the line goes out of one side of the page and in at the opposite side, also produce a special arrangement of colours which can apply to a sphere. The “Flame on the Sun” has coloured areas which match if the picture has its sides pulled around to meet in a cylinder. However, there is no such match top to bottom, where a “bunching” effect would form the “poles” to complete a sphere.

My knowledge of Continuous Lines also lead to my creating them within natural structures when I researched the Four Colour Map Theorem 40 years ago. This single line along boundaries of the countries of Africa (from my 1950’s school atlas), goes through every boundary junction once only. I could connect up the two loose ends to make it “Continuous” ! You can use two alternate colours for countries inside the line and another two alternate colours for countries (and the sea) outside the line and you have your Four colours. Proving that you only need four colours for any map is a different matter !

So there we are, my fascination with my lines continues. I will cover all these types of line further subsequently.

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