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Suppose, in your program:
color A is a color we randomly select
Knowing color A, how can I pick a color B that will be in high contrast with color A?
The problem can be further reduced to: “imagine 2 squares filled with color next to one another. It should be unambiguously clear to a human eye that colors are not the same”
Example:
There is some information in the Web Content Accessibility Guidelines (WCAG) 2.0 (http://www.w3.org/TR/2008/REC-WCAG20-20081211)
Visual contrast: http://www.w3.org/TR/2008/REC-WCAG20-20081211/#visual-audio-contrast-contrast
Contrast ratio: http://www.w3.org/TR/2008/REC-WCAG20-20081211/#contrast-ratiodef
Relative luminance : http://www.w3.org/TR/2008/REC-WCAG20-20081211/#relativeluminancedef
There’s a good example in this site but he calculate where two colors are enough, not how to get them.
To choose a color with good contrast, I’d go with complementary colors: for example, choose the random color A, transform it to a HSV space, get the complementary hue.
Complementary hue: after you transform color from RGB to HSV, complementary hue will be 180 degrees appart (or 0.5, in a 0-1 normalized hue value). This site has something about it in PHP