How to paint a good RGB color map?

I'm trying to paint a full RGB color map that eventually will allow a user to select a color by tapping that visual map at any point. My current code is the following:

- (void)drawRect:(CGRect)rect
{
    CGContextRef c = UIGraphicsGetCurrentContext();

    for (float x=0; x<320; x++) {
        for (float y=0; y<416; y++) {

            float r = x / 320;
            float g = y / 416;
            float b = (y < 208) ? y / 208 : (416 - y) / 208;

            CGContextSetRGBFillColor(c, r, g, b, 1.0);
            CGContextFillRect(c, CGRectMake(x, y, 1, 1));

        }
    }
}

The result is not too bad but I'm not satisfied yet. The spectrum misses bright colors including white. The reason is clear: red, green and blue will never reach 1.0 at the same time.

Do you have any advise how to improve that map so it represents the full spectrum of the RGB color space?

Thanks for all your input!

UPDATE:

As suggested by Josh Caswell I've used the HSB color space and the following code:

- (void)drawRect:(CGRect)rect
{
    CGContextRef c = UIGraphicsGetCurrentContext();

    int size = 20;

    for (float x=0; x<320; x+=size) {

        float s = x < 160 ? 1       : (320 - x) / 160;
        float b = x < 160 ? x / 160 : 1;

        for (float y=0; y<416; y+=size) {

            float h = y / 416;

            [[UIColor colorWithHue:h saturation:s brightness:b alpha:1.0] setFill];
            CGContextFillRect(c, CGRectMake(x, y, size, size));
        }
    }
}

This results in the following output which is perfect for my needs.

Thanks for all input!