The fractal dimension δg(1) of turbulent passive scalar signals is calculated from the fluid dynamical equation. δg(1) depends on the scale. For small Prandtl (or Schmidt) number Pr < 10-2 one gets two ranges, δg(1) = 1 for small-scale r and δg(1) = 5/3 for large r, both as expected. But for large Pr > 1 one gets a third, intermediate range in which the signal is extremely wrinkled and has δg(1) = 2. In that range the passive scalar structure function Dθ(r) has a plateau. We calculate the Pr-dependence of the crossovers. The plateau regime can be observed in a numerical solution of the fluid dynamical equation, employing a reduced wave vector set approximation introduced by us recently.