Rendering a picture that is composed from points

I want to render a picture that is composed from points
I gave the following parameters
gluOrtho2D(0, window_width, 0, window_height)
glutInitWindowSize(window_width, window_height)
but unfortunately I get an unexpected gaps in the picture

I have looked for ways to write the points right into the framebuffer
But as far as I can see
Bitmaps support only one color – and I want to use RGB
And if I want to use glDrawPixels I have to read the pixels first form an existing buffer – which I don’t have and I don’t know how to create

Is there a way to write points right into the framebuffer?
Or any other way to solve this problem?

Raster I guess. But if you have points, and they usualy are RGB then you can create simple texture and then map in on quad.