how i can create 2d pixels image

Question

Is it possible to create an image with a defined number of pixels? For example, create a circle through the equation x ^ 2 + y ^ 2 <= 200 ^ 2 in a 400x400 pp image and define different colors for points inside and outside of the circle.

Thanks

Answer 1

Using the equation explicitly,

img1 = Image[Table[
             If[x^2 + y^2 > 200^2, Yellow, Red],
             {x, -200, 200}, {y, -200, 200}], 
             ImageSize -> {400, 400}]

Or, using graphics primatives

img2 = Graphics[{
        Yellow, Rectangle[{-200, -200}, {200, 200}], 
        Red, Disk[{0, 0}, 200]}, 
        ImageSize -> {400, 400}]

Answer 2

i use the followings instructions:

emptyImage = Image[Table[0, {i, 1, 300}, {j, 1, 300}]]


NewImage = emptyImage;
For[i = 1, i < 300 + 1, i++,
For[j = 1, j < 300 + 1, j++,
If[(i - 150)^2 + (j - 150)^2 <= 300^2/4,
 NewImage = ReplacePixelValue[NewImage, {i, j} -> 1];
 ]
 ]]

It is a bit slow but it works perfectly.