I'm going to change a few things, but I think you can fill in the gaps.
As background, any matrix can be considered an image, but image data is typically expected to be presented on a certain scale. The expected scale of image data is determined by its numeric class. The nominal range of an integer-class image is the maximum dynamic range allowed by the datatype (e.g. 0-255 for uint8). For floating-point classes, images are expected to be unit-scale (black is 0, white is 1). Most times when you're creating variables programmatically, they're floating-point (class 'double')
So the question becomes "do I want to create an image, or do I want to take data on some arbitrary scale and temporarily represent it as an image for visualization purposes". Both are valid objectives.
Let's say we just wanted to create an image. Then if we're working in 'double', it should be expected that the matrix we create falls within the unit interval.
outsize = [256 512]; % [y x]
% create some vectors
x = linspace(0,1,outsize(2)); % a row
y = linspace(0,1,outsize(1)).'; % a column
% you could use meshgrid, but it's slower and unnecessary
% post-R2016b implicit expansion means we can just use the vectors
% [x y] = meshgrid(x,y);
% create a matrix of some sort
% this image is nominally unit-scale
% in this case, the actual range is [0.2 0.8]
Z = 0.2 + 0.3*(x+y);
% imshow() will render the image fine as-is
imshow(Z)
% imagesc() will render the image the same with some setup
imagesc(Z) % use 'scaled' cdata mapping
caxis([0 1]) % specify the scale
colormap(gray(256)) % specify a gray colormap
axis image % preserve aspect ratio
On the other hand, let's say we're creating some arbitrarily-scaled data. We just want to view the data as an image. There's now no expectation that the data is any particular range. That's fine. We can still view it.
outsize = [256 512]; % [y x]
% create some vectors
x = linspace(0,1,outsize(2)); % a row
y = linspace(0,1,outsize(1)).'; % a column
% you could use meshgrid, but it's slower and unnecessary
% post-R2016b implicit expansion means we can just use the vectors
% [x y] = meshgrid(x,y);
% create a matrix of some sort
% this data is on some arbitrary scale
% in this case, the actual range is [-300 -100]
Z = 100*(x+y) - 300;
% imshow() normally expects the image to fall within [0 1]
% since the data is far less than 0, it is rendered as black
imshow(Z)
% otherwise, you can specify the displayrange parameter
% if this parameter is empty, it uses the range of the data extrema
imshow(Z,[])
% imagesc() will render the image the same with some setup
% by default, imagesc() renders a 2D array WRT its extrema
imagesc(Z) % use 'scaled' cdata mapping
colormap(gray(256)) % specify a gray colormap
axis image % preserve aspect ratio
Note that in the latter example, the displayed image extends from black to white, whereas in the first example, it extends from dark gray to light gray. In the second example, we're displaying the data with respect to its extrema, not some fixed values defining where black and white are, so the rendered image always extends from black to white. If our goal were to render an image as an image, this loss of brightness/contrast information is generally undesirable. Bear in mind that you can always set the displayrange parameter (or caxis()) to any explicit range you want. If there are contextually-important expectations regarding the possible range of the data, you might choose to render it with respect to those instead of to the data extrema.
As to how to change part of the data/image to be constant valued, that's just simple array indexing.
% change part of the image
% remember we're working with the prior example data
Z(50:100,50:100) = -150;
imshow(Z,[])
