On the Penrose hypothesis on fingerprint patterns

Penrose hypothesized that fingerprint patterns such as loops, whorls, etc. are formed by ridges corresponding to the lines of curvature of the skin of the embryo at the time when the ridges were being formed. Under this hypothesis, Smith (1979) has shown analytically how some patterns emerge. In this paper it is shown that (i) Smith's differential equation has an exact solution and (ii) the extension given here supplies the remaining important patterns.