I don't know about compression (though there's allegedly some research using fractals in video compression, but I have no idea if and how that works), but there is image pattern recognition method that is very similar. It's called Local Binary Patterns and it cuts image into square blocks and uses a clever way to turn that blocks into binary string, for example 3x3 pixels block into 8 bits. You run this process across a texture, and get a histogram of features the texture has, like corners, black spots, white spots, gradients and similar. LBP is also inherently invariant to lightning (it uses "lighter than/darker than" instead of absolute values) and there are modifications that make it rotation invariant too (rotating the strings to biggest sequence of ones, for example).

It's pretty smart, really.