Given two seperate computers, how could one ensure that colours are being projected roughly the same on each screen?
IE, one screen might have 50% brightness more than another, so colours appear duller on one screen. One artist on one computer might be seeing the pictures differently to another, it's important they are seeing the same levels.
Is there some sort of callibration technique via software you can do? Any techniques? Or is a hardware solution the only way?
To get the best possible match between your monitors, calibrate them to the same color temperature, brightness and gamma settings if possible. Use the monitor with the lowest brightness as your common denominator for all the other monitors.
The pixels are in some pattern of red, blue, or green depending on the bit depth, a.k.a. how many can fit on the screen. If one monitor has a higher bit depth than the other, it will affect the resolution, which in turn, affects how visual content, namely color, shows up on the screen.
This is entirely normal. Uncalibrated monitors really work like this, no two monitor being alike. In fact even if you calibrate them they will slowly drift appart over time. So calibration is something you need to do periodically, with a hardware calibrator (no software will not do).
If you are talking about lab-critical calibration (that is, the colours on one monitor need to exactly match the colours on another, and both need to match an external reference as closely as possible) then a hardware colorimeter (with its own appropriate software and test targets) is the only solution. Software solutions can only get you so far.
The technique you described is a common software-only solution, but it's only for setting the gamma curves on a single device. There is no control over the absolute brightness and contrast; you are merely ensuring that solid colours match their dithered equivalents. That's usually done after setting the brightness and contrast so that black is as black as it can be and white is as white as it can be, but you can still distinguish not-quite-black from black and not-quite-white from white. Each monitor, then, will be optimized for its own maximum colour gamut, but it will not necessarily match any other monitor in the shop (even monitors that are the same make and model will show some variation due to manufacturing tolerances and age/use). A hardware colorimeter will (usually) generate a custom colour profile for the device under test as it is at the time of testing, and there is generally and end-to-end solution built into the product (so your scanner, printer, and monitor are all as closely matched as they can be).
You will never get to an absolute end-to-end match in a complete system, but hardware will get you as close as you can get. Software alone can only get you to a local maximum for the device it's calibrating, independent of any other device.
What you need to investigate are color profiles.
Wikipedia has some good articles on this:
https://en.wikipedia.org/wiki/Color_management
https://en.wikipedia.org/wiki/ICC_profile
The basic thing you need is the color profile of the display on which the color was seen. Then, with the color profile of display #2, you can take the original color and convert it into a color that will look as close as possible (depends on what colors the display device can actually represent).
Color profiles are platform independent and many modern frameworks support them directly.
You may be interested in reading about how Apple has dealt with this issue:
Color Programming Topics
https://developer.apple.com/library/archive/documentation/Cocoa/Conceptual/DrawColor/DrawColor.html
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