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Introduction. The fractal geometry has shownto be adapted in the mathematical description ofirregular objects; this measurement has denominatedfractal dimension. The application of thefractal analysis to measure the contours of thenormal cells as well as those that present sometype of abnormality, has shown the possibility of mathematical characterization of itsirregularity. Objectives. To measure, from thefractal geometry cells of the squamous epitheliumof uterine neck classified like normal,atypical squamous cells of undetermined significance(ASC-US) and Low Grade IntraepitelialLesion (L-SIL), diagnosed by means of microscopicobservation, in search of mathematicalmeasurements that distinguish them. Methodology.This is an exploratory descriptive studyin which the fractal dimensions were calculated,with the simplified and the conventional boxcounting method, of the cellular and nuclearcontours of 13 normal and with abnormalitiescells of the scaly epithelium of uterine neck likeASC-US and L-SIL, from digital photographiesof 7 normal cells, 2 ASC-US and 4 L-SIL diagnosedwith cytomorphologic criteria by meansof microscopic conventional observation. Results.There developed a quantitative, objective and reproduciblemeasurement of the degree of irregularityin the cells of the scaly epithelium of uterineneck identified microscopically like normal, ASCUSy LEI BG. Conclusions an fractal organizationwas demonstrated in the cellular normal architecture,as well as in cells ASC-US and the injuriesintraepiteliales of low degree L-SIL. They did notfind differences between the cellular studied types.