Well, your map makes zero sense, so yes, you do not understand how this works. Displacements require gradients to stretch out stuff. All the effect does is apply a transform with a multiplier and that multiplier is the same for the same color. In order to stretch out a 5 pixel square you will have to have a 5 pixel gradient underneath it. that of course doesn't do you much good, since multiplying just 5 grey levels across the whole screen width will inevitably cause it to quantize and have banding, so your whole approach is unsuitable. So instead of trying to play it quick & dirty using effects I'm afraid you will really have to lay out at least some parts of it as proper "geometry" e.g. using shape layers and animate that.
Thanks for the quick reply. I started with gradients but when my actual project (this rainbow pict and displacement map are both tests) started distorting parts of the image that shouldn't have been moving, looking like a wormhole from Interstellar, I thought, "let me reduce this to basics to get at what's really going on here. Two colors. White full-on and grey no-effect." The end result for the project will actually require part of the image to be moved the full multiplier (white), part of the image to be moved a fraction of the multiplier (light grey) and part of the image not moving at all (50% grey). The fact that parts of the image mapped to 50% grey were ending up being translated - just like my example above - was really confusing.
- Any idea why parts of the image mapped to grey move at all?
- Any suggestions on how to achieve a result that doesn't move the parts of the image mapped to grey?
Maybe this old blog post of mine will help: Advanced Displacement Maps
In your example the parts under gray don't move, but the image under white does. You are expecting the pixels boundary between the gray and white to create a mask so you can move just the block in the white area. Displacement mapping would create some very unusual results if that happened. Using a gradient to create most of the visual effects you would use a displacement map for would turn into a complete mess. You can use red and the opposite of red (0º and 180º in hue) to move the pixels on the red side one way and the pixels on the opposite of red or minus red the other, but you can't cut out the boundary between them and create an alpha channel or transparency.