Plot points in xy-plane with different colours

I have a function implemented in MATLAB which for each point in [-2;2] x [-2;2] (i. e. for -2 ≤ x,y ≤ 2) returns exactly one of three possible outputs. I want to plot the function such that every point in this square is coloured in one of three different colours (for example red, blue or green), based on what the output of the function was. Of course, colouring every point is not possible, which is why I am specifying a width of the grid of points beforehand. My code looks like this:

 for x = -2:width:2
    for y = 2:-width:-2
        %function f(x,y) with one of 3 different outputs here
        if (f(x,y) = output 1) %colour point (x,y) green
        if (f(x,y) = output 2) %colour point (x,y) red
        if (f(x,y) = output 3) %colour point (x,y) blue
    end
 end

How can I implement this colouring? In the end, I want a plot of the xy-plane in the given area (including axes) with points in different colours based on the above procedure.

Additional question: The function is actually a fixed-point iteration which is stopped as soon as the result is closer to either output 1, 2 or 3 than a tolerance specified in advance. Is it possible to alter the "brightness" of the point in my plot based on how many steps the iteration takes to fulfill the break criterion?

Answer 1

[Star Strider]

One option:

figure(1)
hold on
for x = -2:width:2
    for y = 2:-width:-2
        %function f(x,y) with one of 3 different outputs here
        if (f(x,y) = output 1) %colour point (x,y) green
            scatter(x,y,'pg', 'MarkerFaceColor','g')
        elseif (f(x,y) = output 2) %colour point (x,y) red
            scatter(x,y,'pr', 'MarkerFaceColor','r')
        else (f(x,y) = output 3) %colour point (x,y) blue
            scatter(x,y,'pb', 'MarkerFaceColor','b')
        end
    end
end
hold off

Some variation of it should give you the result you want. (I like to plot stars. Change the marker to your preference.)

NOTE — This is UNTESTED CODE. You will have to experiment with it.

[Ryan]

Thank you, this is exactly what I was looking for.

Do you have any idea on how to adjust the brightness of the color based on the number of iterations needed (see question)? For example, for only one required iteration the point should be colored green, for twenty iterations it should be coloured in a very light green.

[Star Strider]

My pleasure.

You can alter the colour saturation of the green stars (in my code) by changing the values of the components of the RGB triplets. You will need to experiment to get the result you want.

Example —

figure(1)
plot(1,1, 'p', 'MarkerSize',20, 'Color',[0 0.9 0], 'MarkerFaceColor',[0 0.9 0])
hold on
plot(2,2, 'p', 'MarkerSize',20, 'Color',[0 0.8 0], 'MarkerFaceColor',[0 0.8 0])
plot(1,2, 'p', 'MarkerSize',20, 'Color',[0 0.5 0], 'MarkerFaceColor',[0 0.5 0])
plot(2,1, 'p', 'MarkerSize',20, 'Color',[0 0.1 0], 'MarkerFaceColor',[0 0.1 0])
hold off
axis([0  3    0  3])