Help with an Art project: methodology of number sequence

[Bellerophon]

Hello,
I'm trying to define/explain/formulate a simple methodology(???) I applied to a Photography Project I'm working on.
It's a sequence of numbers (from 0 to 3) on a table (or grid).

A- The numbers (from left to right) indicate a 90 deg. rotation of a module: 0 = no rotation; 1 = rotated right once; 2=rotated right twice, etc.
B- The numbers (from right to left) indicate a -90 deg. rotation of a module: 0 = no rotation; 1 = rotated left once; 2 = rotated left twice, etc.

-------------------------------------------------

Photo #1


0 1 2 3 0 1 - 1 0 3 2 1 0
1 2 3 0 1 2 - 2 1 0 3 2 1
2 3 0 1 2 3 - 3 2 1 0 3 2
FLUID
3 0 1 2 3 0 - 0 3 2 1 0 3


Photo #2


1 2 3 0 1 2 - 2 1 0 3 2 1
2 3 0 1 2 3 - 3 2 1 0 3 2
3 0 1 2 3 0 - 0 3 2 1 0 3
FLUID
0 1 2 3 0 1 - 1 0 3 2 1 0


Photo #3


2 3 0 1 2 3 - 3 2 1 0 3 2
3 0 1 2 3 0 - 0 3 2 1 0 3
0 1 2 3 0 1 - 1 0 3 2 1 0
FLUID
1 2 3 0 1 2 - 2 1 0 3 2 1




Photo # 4


3 0 1 2 3 0 - 0 3 2 1 0 3
0 1 2 3 0 1 - 1 0 3 2 1 0
1 2 3 0 1 2 - 2 1 0 3 2 1
FLUID
2 3 0 1 2 3 - 3 2 1 0 3 2

etc.
-------------------------------------------------

How can I explain in layman terms what I'm applying to manipulate/transform the images?
Please note the symmetry as well as the continuity (permutation?) between each image. This project is just an exercise but I would really like to be able to explain it succinctly, with the proper terms.

Please see images attached.

P.S. I was trying to explain this to a friend of mine and she responded that this did not constitute a methodology but rather, the application of an algorithm (albeit simple).
I'm not quite sure that she's right. I really appreciate anyone taking the time to answer and help me understand and explain. Needless to say, math is not my forte

 

[Ishuda]

I'm not sure I see the difference between a methodology and the application of an algorithm.

Also, just what do you want? Something to explain the methodology/algorithm? Is the rotation from a base position or from the last position?. What is the rotation direction, +90$\displaystyle ^\circ$ is clockwise or counter-clockwise? For example. given that the + direction is clockwise from a base position, one might interpret the first left hand row [0 1 2 3 0 1] as something like "The view of a building facing north, the view facing west, the view facing south, the view facing east, the view facing north, the view facing west"

 

[Bellerophon]

Hello Ishuda,
Thank you for your response.

I'm not sure I see the difference between a methodology and the application of an algorithm.

You're right, I didn't think so either...

...For example. given that the + direction is clockwise from a base position, one might interpret the first left hand row [0 1 2 3 0 1] as something like "The view of a building facing north, the view facing west, the view facing south, the view facing east, the view facing north, the view facing west"

Rotation is always from a base position (0). The "view" is always two-dimensional, as you can see in the examples photos; so there is no three-dimensional rotation (i.e.: north, south, west, etc.) It's literally what you see in the examples photos.
Let me try to explain with a simpler table (please see attached). Forget the rotation, etc.

Just take into account the "natural" progression, both horizontally & vertically, from one column to the next.

Does this makes it clearer?

thank you

 

[Ishuda]

Hello Ishuda,
Thank you for your response.



You're right, I didn't think so either...



Rotation is always from a base position (0). The "view" is always two-dimensional, as you can see in the examples photos; so there is no three-dimensional rotation (i.e.: north, south, west, etc.) It's literally what you see in the examples photos.
Let me try to explain with a simpler table (please see attached). Forget the rotation, etc.

Just take into account the "natural" progression, both horizontally & vertically, from one column to the next.

Does this makes it clearer?

thank you

Not really. As far as the images, I'm seeing the same one in all photos so if they are supossed to be showing something different, I'm not seeing it.

The pattern for the progression of the numbers is easy. It is mod(4) arithmetic (remainder when divided by 4) starting with 0 in the upper left of the first (left) block of, in this case, 4 columns and 4 rows. The progression is to add one going down as well as going to the right. The next block starts in the upper left corner with one more that that of its right hand neighbor. The other table was similar in construction. Other, equivalent explanations are possible.

 

[Bellerophon]

Not really. As far as the images, I'm seeing the same one in all photos so if they are supossed to be showing something different, I'm not seeing it.

I assure you, the images are all different (only the first 4 of the group of 8 are included in the animation below):

http://zanspace.com/tectonic4.gif


In any case, you seem to have answered my question.

The pattern for the progression of the numbers is easy. It is mod(4) arithmetic (remainder when divided by 4) starting with 0 in the upper left of the first (left) block of, in this case, 4 columns and 4 rows.

Upon digging and reading a bit about it, it looks like i'm using a "complete residue system"... The least residue system modulo 4 {0, 1, 2, 3} , to be exact.
Thank you so much for this. I truly appreciate your help and you taking the time to reply.
Cheers

Other, equivalent explanations are possible.

I'm curious about what other explanation(s) might be possible
thank again.