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.

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.