Fingerprint formation is like the growth of capillaries and blood vessels in angiogenesis. The pattern is not strictly determined by the genetic code but by small variables in growth factor concentrations and hormones within the tissue. There are so many 
variables during fingerprint formation that it would be impossible for two to be alike. However it is not totally random, perhaps having more in common with a chaotic system than a random system.
It is believed that the development of a unique fingerprint ultimately results from a combination of gene-environment interactions. One of the environmental factors is the so-called intrauterine forces such as the flow of amniotic fluid around the fetus. Because identical twins are situated in different parts of the womb during development (although they are not static), each fetus encounters slightly different intrauterine forces from their sibling, and so a unique fingerprint is born.
Your genes specify only your biochemistry and through it, your general body plan. The pattern of your fingerprints forms rather in the way that wrinkles form over cooling custard. At most you may predict, say, the fineness of the wrinkles and their general pattern. Fingerprints are just one example. Many of your features could mark you out from any clone. Your genome only controls gross characteristics such as the rates at which the skin and its underlying attachments develop and grow. Even if there is no way for genes to specify everything exactly, there is no way the genome could carry enough information for the details. If our genomes had to specify everything, we would not be here. But, while the consequences of imperfect specification are usually trivial, they may have more serious effects. A minor distortion of a blood vessel could give poor blood flow or an aneurysm, and the branching and interconnection of brain cells affect mental aptitudes. That is why, though bright parents tend to have bright children, dimmer ones may have a child genius and vice versa.