Angelouscuitry opened this issue on Apr 05, 2007 ยท 30 posts
bagginsbill posted Thu, 05 April 2007 at 9:10 PM
Imaging this:
I put you in a room and tell you to stack some tiles up, covering the whole floor. Now I tell you to stack another layer, but leave one tile out of the middle. What does that one tile look like? It looks like a depression because all the other tiles are even and that one is low.
But in reality, it is not a depression because you put a tile in that spot, so it is higher than the floor. It's just that all around it the floor is covered with two tiles so the spot that only has one tile stands out as being "depressed", even though it has been raised.
Suppose I pick one more spot and tell you to place one more tile. So in that spot there are 3 tiles - the top is 3 tiles above the original floor. It looks raised, but only by 1 tile, even though it has been raised up 3 tiles.
Now I magically lower the entire floor, tiles and all by exactly 2 tile thicknesses.
The spot that had only one tile on it is now one tile thickness below the original floor level. The spot that had 3 tiles on it is now one tile thickness above the original floor level. And all the rest of the tiles, those stacked to a depth of 2, the tops of those are exactly where the floor used to be.
Does that make more sense?
So what I'm saying is, where you have gray, that actually means stack this up .5 times the displacement depth. Black, being a zero, means don't stack that up at all. And white, being a one, means stack that up to the full depth. When you subtracted .5 from that, you "lowered the floor" by .5 - thus anywhere there is gray is now at the original level. Anywhere there was black, well that didn't get raised, so the net is that it got lowered by .5 of the displacement depth. And the white area was raised a full displacement, but lowered by half.
So, adding or subtracting does indeed change the overall height of the pattern or surface, but it doesn't change the relationships of the elements of the pattern to each other.
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