This is a simple tool to help you estimating your system's gamma. The gamma is visualized over wide range of shades to allow you to better estimate a good average gamma value. If your monitor is properly calibrated, it will probably display in sRGB color space. That, in turn, means that no single exponent value is exactly correct, however 2.2 will come close.
Relax your eyes, and look slight past the screen. Within each rectangle, identify the center block of solid colour and compare it to the surrounding striping pattern. If the colours do not match, attempt to tweak it by changing the gamma value. The right value should be close to 2.2.
The pattern is built of horizontal stripes with CRTs in mind. That way, the monitor's ability to resolve a dither pattern should not come into play here, so this will actually probably work best with CRT monitors.
LCD displays must be at native resolution. (Almost all LCDs have scalers that totally fuck up the gamma of striped or dithered patterns.) If your LCD has picture smoothing options, they should be turned off completely. If your LCD has colour temperature options, chances are that the monitor accomplishes this partially through dithering. Look at 'Artifacts' section below.
For graphics cards, no picture sharpening effects should be enabled.
In general: Try to get as raw, bog-standard picture as possible without any fancy tweaks.
The left-half stripe pattern and the right-half stripe pattern within each rectangle should look the same. If you detect alterations in brightness or tone, it is most likely due to some component in your system dithering the display colours for screen. This type of striping patterns may not be appropriate measurement tools, depending on how large the difference seems.
If you have a LCD, try to move the browser window up or down on screen in 1-pixel steps. If you see the halves to swap colours, then this is a proof of some type of processing happening in your system, most likely at the LCD monitor. You're out of luck.
Note that adjusting the viewing angle can cause large apparent changes in brightness. This is unfortunate property of many LCD panels.