## 6 Future Directions  
In summary, fractal analysis provides a powerful tool for characterizing and understanding complex, irregular patterns and structures that may not fit well within traditional geometric frameworks. It has broad applications across various scientific disciplines and has contributed to a deeper understanding of the complexity inherent in natural and artificial systems. In oral oncology, fractal analysis is worthy of consideration because it can be an effective and noninvasive diagnostic and prognostic tool for various premalignant lesions and conditions. It is economical, less time-consuming, and an accurate tool for measuring the progression of premalignant lesions [22], mainly when applied to clinical pictures, thus opening new perspectives toward cost-effective, noninvasive monitoring of OPMDs and suspicious lesions to support the patients' management [35]. Indeed, the fractal analysis could be applied virtually to all clinical and histological procedures to obtain significant progress in managing oral cancer and its precursors, to offer the capability to distinguish among oral lesions that are similar in shape but different in prognosis. At this point, it is reasonable to hypothesize the future directions for fractal analysis in oral oncology and modern dentistry. First, fractal analysis could be investigated for benefits in association with other digitally assisted imaging systems, such as in vivo microscopy, thus improving the qualitative assessment of in vivo-detected histological and cytological differences among OPMDs and OSCCs with mathematical analysis. In this case, in vivo confocal microscopy itself already has proven to be dramatically helpful, for diagnosing the early signs of malignancies/pathology in living tissues before biopsy, offering digital pictures of living tissues at microscopic resolution that could be fit to be considered appropriate fractal objects in future works, and for measuring the fractals of nuclear shapes, cellular borders, and/or other parameters easily visible and defined through this in vivo technique [49; 50]. Second, apart from histological samples and clinical photographs, it could be interesting to test the fractal analysis applied to innovative imaging procedures, which could fit well with the application of fractal analysis of vascular patterns, already proven to be distinct through conventional capillaroscopy, which will benefit from a mathematical analysis for diagnostic and prognostic purposes. Third, fractal analysis could be used to estimate responsiveness to treatments. Although the present review focused on the diagnostic and prognostic value of fractal analysis in oral oncology, the literature reported some sporadic and preliminary works dealing with the monitoring of treatments as reported by the Polish group of [PERSON] et al. [51, 52], who applied fractal dimension and texture analysis of lesion autofluorescence in the evaluation of oral lichen plants treatment effectiveness and in estimating the effectiveness of oral leukoplakia treatment using the LiteTouch(tm) Er:YAG Dental laser, or by [PERSON] et al., who recently explored the pre- and post-treatment objective evaluation of remission in oral lichen plants using fractal analysis and compared it with the visual analog (VAS) scale [53]. Moreover, it could be interesting to understand if fractal analysis could also be valuable for characterizing, distinguishing, and evaluating HPV-related oral and oropharyngeal lesions due to the evidence that HPV DNA integrates with human keratinocytes' DNA, giving origin to HPV-associated cancers. Last, to revolutionize oral cancer diagnosis and make the most of the potential of fractal analysis in oral oncology, it could be integrated with machine learning and other artificial intelligence-enhanced tools, as demonstrated in the case of breast and colon cancers [54, 55]. Conceptualization, M.C. and R.S. ; methodology, M.C. and F.D.S. ; investigation, F.F. and A.A.; data curation, M.C. and M.P.D.P. ; writing--original draft preparation, M.C. and F.D.S.