Koch-like riblets that iteratively protrude toward the outside (the fluid region) or cave in at the wall are examined. The near-wall microscopic fluid problem is addressed by solving for the Stokes flow with a boundary element method, yielding slip lengths for all the surface shapes considered. Such lengths are then used in Navier boundary conditions of the macroscopic, turbulent problem, which is solved by direct numerical simulations. The results of the direct simulations demonstrate that inward-contracting riblets enjoy an additional drag reduction when compared to the base, triangular configuration, whereas outward-protruding riblets experience a skin-friction increase. The results are in excellent agreement with a theoretical model.