Is there a way to resize an image without creating new colors in the output image? I have been working with a file from the USGS that is a heightmap of the Moon. I resized it to 65536 x 32768 px for use as a displacement map in Blender, and turned it into tiles. Then I created tiles from the original image and noticed that they were about a fifth of the file size of the ones from the resized image, even though they have twice the pixels. Image Magick had remapped the image using many tones of gray that weren't present in the original. Presumably this is why the files are now so much bigger.
Original histogram:

Resized histogram:

Is there any way I can resize this image without the process creating new gray tones?
A nearest-neighbor resize will do what you ask but I am not certain it will give you much smaller tiles.

It is quite likely that the tiles made from the original image are smaller simply because they have less high frequency content and thus compress far better.

You can look at it the other way around: there are more terrain features in the tiles of the resized image so it takes more space to store them. That's a very gross simplification of the truth, of course. And it assumes a reasonably efficient compression algorithm.