Mixing processes are widely used in industries and are being studied by a number of scientists; even though, a fundamental insight of the subject is still lacking. In this paper, some basic thoughts are set on the analogy between fluid mixing phenomena and fractal geometry/properties/ processes. To this end, an unstable horseshoe pattern, which leads to a continuous extending boundary with maximum stretching and folding, is created and repeated. As a result, self-similarity property along with instability is imposed throughout the region, enhancing the fluid mixing. The procedures are verified computationally using the techniques of capacity and information dimensions, which are measured as time-dependent functions. The results can be used to explore how well a fractal representation can describe fluid mixing phenomena, how fractal-like processes can optimize it, when fractal properties grow rapidly in the fluid system, and ultimately how unsteady flows are impending chaotic behavior in dynamical mixing systems when local bifurcations occur.