Atomic force microscopy has been applied to study the surfaces of Y2Ba4Cu7O15 (247) and YBa2Cu4O8 (124) high-temperature superconductor single crystals at ambient temperature and pressure. In contrast to very thin (<10 mum) crystal platelets, which exhibit by scanning tunneling microscopy clean terraces with steps of the height of one or multiple unit cells, thicker crystals show surfaces partially covered by a contamination layer with a highly curved boundary line originating from BaCuO2/CuO flux used to grow 124 and 247 single crystals under high oxygen pressure. The evaluation of the length of such flux boundaries by the box counting method reveals that they are fractal with a fractal dimension of about 1.4. Close to crystal steps, higher fractal dimensions are observed provided the terrace width is sufficiently large. The fact that the residual flux is always found on the lower terrace level of a crystal step allows discussion of a possible mechanism of flux migration on the crystal surface.