ABSTRACT Global positioning and geographic information systems are essential for studying foraging animal behavior. This study aims to implement a fractal self-similarity and chaos game computational efficient methodology to determine the behavior-associated fractal using GPS data of activity sequences in spatial ranges of livestock movement trajectories in interaction with habitat factors. Six cows were randomly selected with an average weight of 480 kg, maintained under the same conditions, and a GPS-equipped collar was installed, programmed at intervals of 1 min and an average of 9 h daylight. Roughly 192810 registries and an average of 32135 signals per cow from trajectory tracking in spatial activity sequencing were used as a variable of interest in the fractal characterization methodology. Spatial patterns were evaluated using the Morán’s spatial autocorrelation indices, cluster, and non-parametric statistics, evaluating deterministic spatial patterns of preferential activities associated to spatial ranges of less than 7.1 m (resting 42 %, grazing 38 %). GPS information was refined through spatial ranges and changes in activities under resting, eating, traveling, and complementary schemes associated to the fractal displacement behavior of grazing cattle. This information was processed and mapped using fractal self-similarity rules in the Sierpinski triangle to determine the typical fractal of spatial activities per animal in the habitat. The particular fractal record of each bovine as a function of trajectory sequences was mapped for binary image matrices, registering a good classification (83 %) of the animals by breed and climatological cycle, using information from the sequencing of spatial activities associated to the preferred behavior in the habitat.