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.
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.
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.
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.
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.