I found this site, and spent some 15 hours over three days learning how it works and obsessing over a griffin generator. The design philosophy was "make people really want to draw it!" for every single result.
It might seem simple, but under the hood, the color generator is a giant tangle, it's been finely tuned to have existing colors or variations of them occasionally show up as color details on other bodyparts, and never return silly things like "black with black spots". And the probabilities are carefully weighted, more exotic colors and patterns are harder to find, but all possible.
And beside the color, there's tons of other traits, some quite rare, like magical powers or horns!