Mandelbrot introduced fractals to describe his observation of shapes in nature, such as curves, surfaces, disconnected “dust,” and odd shapes. The word fractal originates from the Latin word “fractus,” which means broken. By using fractal mathematics, several studies have analyzed various fractal patterns in the human body. Fractal analysis is a mathematical method of describing complex shapes and structural patterns of the nature and is expressed numerically as fractal dimension [1, 2]. Trabeculae are thin columns with numerous large spaces that give a honeycomb or spongy appearance of cancellous bone, which is also called trabecular bone or spongy bone [3]. Previously, fractal analysis has been reported as a useful method to detect various diseases that affect the trabecular bone structure [4,5,6]. Especially in the field of dentistry, studies have indicated that fractal analysis by the box counting method can successfully evaluate trabecular changes in the mandible of patients with osteoporosis [7,8,9] and periodontal diseases [10] and in lactating women [11]. Furthermore, studies have been conducted to determine the changes in trabecular bone induced by surrounding bone tissues of implants [12,13,14,15].

Many studies have examined the effect of fractal analysis on image acquisition parameters [16, 17]. Although some studies have stated that fractal measurement of trabecular bone microstructures is affected by exposure time and noise, most studies support the belief that fractal measurement is relatively affected by imaging parameters but do not lead to a significant difference [18, 19]. One study that investigated the diagnostic imaging of the trabecular bone structure of oral implants by using cone beam computed tomography (CBCT) reported the highest accuracy of the measurement of fractal analysis. This study also highlighted the disadvantage of CBCT with regard to its accessibility and cost in dental clinical practice; however, it emphasized the practicality and accessibility of panoramic and periapical dental radiographs [20]. Fractal analysis can be performed on nonstandardized dental radiographs to assess pathological changes in bone or to assess the quality of peri-implant bone [17, 19, 21].