In this study, we investigated the sensitivity, specificity, and predictive values of morphometric parameters of thyroideal follicular neoplasms based on concepts of fractal geometry. Thirty-seven follicular adenomas and 36 well-differentiated follicular carcinomas were assessed morphometrically. The nuclear area, nuclear area fraction, nuclear regularity factor, nuclear elongation factor, and slope setting (representing the ratio between the nuclear perimeter and nuclear regularity factor) were subjected to fractal dimensions analysis. By univariate analysis, the nuclear area, nuclear area fraction, nuclear regularity factor and slope values discriminate between adenomas and carcinomas. By multivariate analysis, the nuclear area, nuclear area fraction and slope values possess significant discriminatory powers in distinguishing between adenomas and carcinomas. Incorporating the nuclear area, nuclear area fraction, and slope values leads to a discriminatory power with 92% specificity and 83% sensitivity. The reciprocal relationships between the nuclear area, nuclear perimeter, and nuclear regularity factor of the cells of thyroideal adenomas and carcinomas may be expressed by fractal dimensions. Analysis limited to one parameter provides incomplete data. Expressing variations of the nuclear perimeter as a function of the nuclear regularity factor, the slope values constitute an independent attribute that significantly differentiates thyroideal adenomas from carcinomas.