Research over the past years has focused on electromagnetic waves and meta-materials. These structures are designed to give electromagnetic properties that cannot be produced by traditional, well known natural structures. Meta-materials obtain their electromagnetic properties from their structures, not from their components. Meta-materials have new properties that define different mechanisms for electromagnetic wave propagation. These materials have been studied theoretically and have been used in many applications, especially microwaves and photonic fields. This research depends on these kinds of material, explains them, and analyzes the electromagnetic properties that yield from putting columns from these slabs with negative permittivity and permeability coefficient (MMs) in a fractal distribution of a natural medium. This research also compares the resulting properties with the electromagnetic properties that yield natural materials distributed the same way. We use the HFSS simulator which depends on the finite element method for calculating transmission and reflection coefficient for these structures.