Passive micromixers are the preferred systems for a variety of uses in biology, medicine, chemistry, chemical engineering and biotechnology, particularly when portability and simplicity to operate are necessary. Chaotic behavior of the flow field seems to be the only viable option for mixing at such small scales and in microchannels it can be efficiently achieved by patterning of one or more walls of the channel. In this work we present a new approach for patterning in such microfluidic devices which enhances mixing and can be easily implemented in manufacturing. The approach considers fractal patterning to improve chaotic behavior and is based on a protocol making use of the Weierstrass function. We perform numerical simulations for three different mixers designed using this protocol and analyzed their performances by comparison with a fourth channel having a periodic patterning of the wall. We use entropy to quantify mixing of two fluids in these systems. We also characterize the structures generated by mixing in these microchannels, by assessing the dynamics of the multifractal dimensions of the interface between the two fluids. We found correlations between mixing efficiency and the fractal structures generated in mixing.