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'in theory' the dimension of a contrast can be self-similar

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The measurement of the deformation of a contrast


Take a white page. Make black spots on it. You have then some contrast between black and white. The bigger the size of the spots, or the more the spots are numerous, the higher the contrast will be. At least at the beginning, as long as there is fewer spots than white surface.
You can measure the contrast, for instance by declaring that contrast has to be the proportion between the spotted surface and the still white surface.
At the beginning, the contrast is 0: the page is all white. Then it goes up, becomes 0.3 then 0.5 then 0.7 for example. When half the page is spotted, it is exactly equal to 1.
If you still spot the surface the contrast will decrease, for the surface will become more and more 'all black'. You can measure it in the same way, but calculating this time the proportion between the white surface and the black area. From 1, the contrast will then go back to 0 when the page will be all black.

We really did measure a 'value': 0, or 0.1, or 0.387, or 0,74, etc. So, it can be said that there is something of a dimension in the measured contrast. Still, we did not have to define one coordinate on the page. This is not a coordinate dimension.
If we state that contrast is the deformation of the whiteness or of the blackness of the page, then we define the calculated contrast, as a deformation dimension.
We point out immediately, a fundamental difference between deformation dimensions and coordinate dimensions:

     - a point can travel to infinity, and consequently its coordinates can go from - infinity  to + infinity;
     - on the contrary, a phenomenon cannot deform itself more than a maximum. When you continue the deformation past that maximum, you do not increase the value of the deformation but you put it back to 0: you do it smoothly if that's a phenomenon similar to the blackening of a sheet, you do it dramatically if the maximum corresponds to a breaking which stops the deformation.

That is to say a coordinate dimension travels as on a straight line which can go to infinity in the Euclidean space, and a deformation dimension turns like around a circle.

We can also grasp with this example, the complementarity of the two dimensional systems, that with coordinates and that of deformation. We can conceive for example, that the 0.3 contrast we gave to a space, does not limit itself to spots on a page, but could apply to a 2 D plane of infinite dimensions, or either has to deal with colored bubbles in an infinite 3 D space.
That is to say, that whatever the movement we shall do in that space, the contrast between the background of space and the spots we shall find in it, will be the same.
The contrast can deal with space with infinite coordinates, but itself can only have a value oscillating between 0 and 1.




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