Is it possible to create a script that plots a specific no. of points on a plane, then creates a texture/shader by displaying those points as pixels?

Question

Let's say that I have a normal square plane.

Now, I want a script that plots points on the plane from -128 to 128 from one end to the other on both the x-axis and y-axis.

Then, I like to display those points as pixels and control their RGB values. I want to use them for, as an example, applying a gradient. If this is possible, then I can change the values of each pixel according to a given function.