# 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.

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.

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.

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.

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.

# Salvador Dali continuous line drawing

Dali continuous line drawing in pen and ink, guitar player on horse, dated 1948.

This is an original pen and ink drawing on paper and is dated 1948 and signed Dali.  I have referred to One Line drawings by Picasso in a previous post, but this drawing is virtually a continuous line drawing.

When I say virtually, I mean that the artist has used a series of lines throughout the drawing which could be connected up.  I presume that using a dip pen meant that as ink ran out he took the pen off the paper to dip the nib and then continued from a point nearby.

In effect, he has drawn all the key areas in single lines, which is the initial stage in my drawings, but presumably with no intention of connecting them up or reviewing them further.  I have little doubt that the whole drawing would have been completed relatively quickly in one session.

I bought the drawing “in the manner of Salvador Dali”, as there was no provenance with it, but my first glance convinced me that I had to have it if possible.  It was the continuous line drawing effect, with an added bonus when I saw the signature.  Whoever did the drawing greatly impressed me and my researches into Dali pictures of around that time confirmed that he was producing drawings similar to this, with several elements the same.

Many of these elements appear in “50 Secrets of Magic Craftsmanship” by Salvador Dali published in 1948.  In fact he seems to have done a quick drawing inside the front cover of  some of the original edition copies.

# Definition of “Continuous Line Drawing”

As I mentioned in my first blog, there are many definitions of “Continuous Line Drawing”, most of which refer to a line which does NOT re-connect.

One of these is that the pen never leaves the paper and you draw until the picture is finished, but that you start and end where you like.  Also “Blind Contour Drawing” puts emphasis on looking at the subject throughout whilst you draw a single line.  These types may also have many merged lines and it may be unclear whether there is only one line, eg. when shading is done by repeatedly going over an area with the line.

To me, a line is only Continuous if it ends at the start point.  Lines that do not re-connect I call “One Line” or “Single Line”.  I only use the word “Continuous” if the line completes a circuit continually.   I own a book entitled “Picasso’s One Liners” which has over 50 of his great drawings, which all start and end in different places and, correctly, there is no mention of “Continuous”.

Here is a demonstration drawing I did last year based on a Picasso “One Liner”.  To be “Continuous” the line would need to return from the foot to the start point in the hat.

My definition of “Continuous Line Drawing” is one drawn line which ends back at the start point and the continuous route can be clearly followed throughout.

My basic style has lots of cross overs of the line, but some artists produce continuous lines which never cross over – which is fine.

Here are the “rules” of my basic style, where the line crosses over itself many times.

• The finished continuous line has to cross over itself at least once, but must end where it starts.  It can be drawn in sections as long as the completed line is continuous (you don’t have to amaze everyone by doing it in one go without taking the pen off the paper !)
• Where the line crosses itself it must be clear that there is only one line (not several merged lines).
• A line can be drawn off the side of a sheet as long as it clearly re-enters the sheet at the corresponding point on the opposite side.  Similarly, if the line goes out at the top it must re-enter at the corresponding point at the bottom.  This enables the continuous route to be still clearly identified.  I call these “Spherical” drawings, in the way that an atlas map of the earth on a flat sheet denotes a globe.

So that is it !  I just wished to make it clear that most of the images which are referred to on the internet as “Continuous Line Drawings” are not really (to me).