The first time I heard about fractals was four years ago in my Calculus class. I remembered how fascinated I was by a pattern that is so common yet overlooked. Fractal patterns can be seen everywhere in nature--clouds, lightning, seashells, ferns, broccoli, river systems, blood vessels, and the list continues. This demonstrates how nature has specific designs with which it builds its beings and structures. And this amazes me because it shows that nature can be random and spontaneous (based on thermodynamics), but at the same time, highly systematic and organized. Fractals are simple in terms of their attributes but are varied and complex in the ideas and applications that accompany them. Salient attributes of fractals include: self-similarity, iteration and shape irregularity (Baish & Jain, 2000; Dokukin, Guz, Woodworth, & Sokolov, 2015; Losa, 2014). Self-similarity means that when one fragment of an object is examined on various scales, that fragment is similar to and "reproduce the whole object from which it is derived (Losa, 2014). Recently, fractals and the concepts related to them, which first arose in mathematics, are used to examine cell and tissue morphologies (Baish & Jain, 2000; Dokukin et al., 2015; Losa, 2014). Using fractals as an approach to studying structures in biological systems may provide new perspectives and insights on structures, and thus functions, of cells and tissues.
Fractal pattern seen in Romenesco broccoli. Image retrieved from McNally (2010).
Cancer is a complex disease that many researchers are trying to address and fractals have been observed in cancerous cells (Baish & Jain, 2000; Dokukin et al., 2015). Cancer is often characterized as a "chaotic, poorly regulated growth" and cancer cells have "irregular shapes" (Baish & Jain, 2000). Fractal geometry is a "vocabulary of irregular shapes" (Baish & Jain, 2000). Because structure is closely related to function, examining the fractality in cancer cells provides a new perspective on combating cancer. However, Dokukin et al. (2015) recently published their research of fractals on human cervical epithelial cells and found that, contrary to most studies of fractals and cancer, fractals was only observed at a limited time frame. True fractal patterns develop at the "precise point in which precancerous cells transform into cancer cells" (Dokukin et al., 2015). This suggests that fractals may play a role in the transformation of nonmalignant cells into malignant tumors, however, the authors have not confirmed this. There is a fairly new perspective and there is more progress to be made. And according to Losa (2014), the fractal approach is valuable in that it prevents oversimplification or approximation in analyzing structures and therefore, functional behaviors of cellular components and tissues.
1. Baish, J.W. & Jain, R.K. (2000). Fractals and Cancer. Perspectives in Cancer Research, 60, 3683-3688.
2. Dokukin, M.E., Guz, N.V., Woodworth, C.D., & Sokolov, I. (2015). Emergence of fractal geometry on the surface of human cervical epithelial cells during progression towards cancer. New Journal of Physics, 17, 1-12. doi:10.1088/1367-2630/17/3/033019
3. Losa, G.A. (2014). The fractal geometry of life. Rivista di biologia, 102, 29-59.
4. McNally, J. (2010, 09 10). Earth's most stunning nature fractal patterns. Wired, Retrieved from http://www.wired.com/2010/09/fractal-patterns-in-nature/