This article proposed a new geometric design methodology for the systematic expansion of fractal linear and planar array antennas. Using this proposed geometric design methodology any deterministic polygon shape can be constructed. In this article, two element fractal linear and triangular array antennas are examined using proposed methodology up to four iterations of two expansion factors. Due to the repetitive nature of the proposed geometric design methodology, both linear and planar fractal arrays shows multi-beam behavior with excellent array factor properties. The behavior of the proposed arrays shows better performance than linear and planar fractal array antennas generated by concentric circular ring sub array geometric generator. Triangular planar fractal array of expansion factor two at fourth iteration achieved a single valued beam width of 3.80 with -31.6 side lobe level. The suggested fractal arrays are analyzed and simulated by MATLAB-13 programming.