Fractal penis and golden penis. The hidden dimensions of penile tissue
DOI:
https://doi.org/10.48193/81q9tw48Keywords:
Penis, fractal penis, Golden penis, divine proportion, penile anatomyAbstract
The penis is an organ with a unique and complex structure. It is formed by a fractal architecture, meaning its design is based on highly complex repetitive patterns. In addition, its dimensions follow what are known as "golden proportions", also known as "the divine proportion". These proportions are a mathematical relationship that is found in many natural structures and, in the case of the penis, provide stability and improve its performance. This design is not the result of chance, but rather the result of an underlying mathematical message. Fractal geometry, based on complex numbers, is a key tool in understanding the internal structure of the penis, which cannot be described using traditional Euclidean geometry. In addition to fractal geometry, the presence of golden proportions in the penis suggests that its design is influenced by mathematics. To fully understand this relationship, additional studies are required and the creation of innovative mathematical models that include tools such as artificial intelligence. In conclusion, the penis is an example of how mathematics and nature are closely related and how mathematical complexity can improve the functioning of natural structures.
References
Brown D. El código Da Vinci. Barcelona: Umbriel; 2003.
Boyer CB, Merzbach UC. A History of Mathematics. John Wiley & Sons; 2011.
Finch SR. Mathematical Constants. Cambridge University Press; 2003.
Dixon RA. Mathographics. England: Dover Publications; 1991.
Uribe Arcila JF. El pene áureo. La razón áurea y su relación con la anatomía interna del pene. Revista Urología Colombiana. 2008;17(1): 91–99.
Kurakin A. The self-organizing fractal theory as a universal discovery method: the phenomenon of life. Theoretical Biology and Medical Modelling. 2011;8(1): 4. https://doi.org/10.1186/1742-4682-8-4.
Losa GA. The fractal geometry of life. Rivista Di Biologia. 2009;102(1): 29–59.
Mandelbrot B. The Fractal Geometry of Nature. New York: WH Freeman; 1982.
Goldberger AL, Amaral LAN, Hausdorff JM, Ivanov PC, Peng CK, Stanley HE. Fractal dynamics in physiology: alterations with disease and aging. Proceedings of the National Academy of Sciences of the United States of America. 2002;99 Suppl 1(Suppl 1): 2466–2472. https://doi.org/10.1073/pnas.012579499
Barnsley MF. Fractals everywhere. Academic press; 2014.
Falconer K. Fractal geometry: mathematical foundations and applications. John Wiley & Sons; 2004.
Peitgen HO, Saupe D. The science of fractal images. Springer-Verlag; 1988.
Falconer KJ, Falconer KJ. Techniques in fractal geometry. Wiley Chichester; 1997.
Gallo CBM, Costa WS, Furriel A, Bastos AL, Sampaio FJB. Development of the Penis during the Human Fetal Period (13 to 36 Weeks after Conception). Journal of Urology. 2013;190(5): 1876–1883. https://doi.org/10.1016/j.juro.2013.05.050.
Bitsch M, Kromann-Andersen B, Schou J, Sjøntoft E. The Elasticity and the Tensile Strength of Tunica Albuginea of the Corpora Cavernosa. Journal of Urology. 1990;143(3): 642–645. https://doi.org/10.1016/s0022-5347(17)40047-4.
Peitgen HO, Jürgens H, Saupe D. Length, Area and Dimension: Measuring Complexity and Scaling Properties. In: Peitgen HO, Jürgens H, Saupe D (eds.) Chaos and Fractals: New Frontiers of Science. New York, NY: Springer; 1992. p. 183–228. https://doi.org/10.1007/978-1-4757-4740-9_5.
Peitgen HO, Richter PH. The Beauty of Fractals. Berlin, Heidelberg: Springer; 1986. https://doi.org/10.1007/978-3-642-61717-1
West BJ. Fractal Physiology and Chaos in Medicine. WORLD SCIENTIFIC; 1990. https://doi.org/10.1142/1025.
Goldberger AL, West BJ. Fractals in physiology and medicine. The Yale Journal of Biology and Medicine. 1987;60(5): 421–435.
Glenny RW, Robertson HT, Yamashiro S, Bassingthwaighte JB. Applications of fractal analysis to physiology. Journal of Applied Physiology. 1991;70(6): 2351–2367. https://doi.org/10.1152/jappl.1991.70.6.2351.
Mandelbrot BB. Los objetos fractales: forma, azar y dimensión.. 7a. ed. Barcelona: Tusquets; 2009.
Bossard JA, Lin L, Werner DH. Evolving random fractal Cantor superlattices for the infrared using a genetic algorithm. Journal of The Royal Society Interface. 2016;13(114): 20150975. https://doi.org/10.1098/rsif.2015.0975.
Grebogi C, Ott E, Yorke JA. Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics. Science. 1987;238(4827): 632–638. https://doi.org/10.1126/science.238.4827.632.
Garfinkel A, Spano ML, Ditto WL, Weiss JN. Controlling Cardiac Chaos. Science. 1992;257(5074): 1230–1235. https://doi.org/10.1126/science.1519060.
Goldberger AL. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. The Lancet. 1996 May;347(9011):1312–4. doi: https://doi.org/10.1016/s0140-6736(96)90948-4
Rodríguez J, Prieto S, Ortiz L, Correa C, Álvarez T L, Bernal P, et al. Variabilidad de la dimensión fractal de la ramificación coronaria izquierda en ausencia y presencia de enfermedad arterial oclusiva moderada y severa. Revista Colombiana de Cardiología. 2007 Jul;14(3):173–80.
Canals M, Olivares R, Labra F, Caputo L, Rivera A, Novoa FF. Caracterizacion de la geometria fractal del arbol bronquial en mamiferos. Revista chilena de anatomía. 1998;16(2):237–44. doi: http://dx.doi.org/10.4067/S0716-98681998000200011
Kelly DA. The functional morphology of penile erection: tissue designs for increasing and maintaining stiffness. Integrative and Comparative Biology. 2002;42(2): 216–221. https://doi.org/10.1093/icb/42.2.216.
Hsu GL, Brock G, Martínez-Piñeiro L, Von Heyden B, Lue TF, Tanagho EA. Anatomy and Strength of the Tunica Albuginea: Its Relevance to Penile Prosthesis Extrusion. Journal of Urology. 1994;151(5): 1205–1208. https://doi.org/10.1016/s0022-5347(17)35214-x.
Goldstein AMB, Padma-Nathan H. The Microarchitecture of the Intracavernosal Smooth Muscle and the Cavernosal Fibrous Skeleton. Journal of Urology. 1990;144(5): 1144–1146. https://doi.org/10.1016/s0022-5347(17)39677-5.
Hsu GL. Hypothesis of human penile anatomy, erection hemodynamics and their clinical applications. Asian Journal of Andrology. 2006;8(2): 225–234. https://doi.org/10.1111/j.1745-7262.2006.00108.x.
Lue T F. Physiology of penile erection and pathophysiology. In: Campbell`s Urology. 8th ed. Panamericana; p. 718–749.
Varela FG, Maturana HR, Uribe R. Autopoiesis: the organization of living systems, its characterization and a model. Currents in Modern Biology. 1974;5(4): 187–196. https://doi.org/10.1016/0303-2647(74)90031-8.
Dorr L, Brody M. Hemodynamic mechanisms of erection in the canine penis. American Journal of Physiology-Legacy Content. 1967;213(6): 1526–1531. https://doi.org/10.1152/ajplegacy.1967.213.6.1526.
Hoznek A, Rahmouni A, Abbou C, Delmas V, Colombel M. The suspensory ligament of the penis: an anatomic and radiologic description. Surgical and Radiologic Anatomy. 1998;20(6): 413–417. https://doi.org/10.1007/bf01653133.
Shen ZJ, Jin XD, Chen ZD, Shi YH. Effect of aging on penile ultrastructure. Asian Journal of Andrology. 2001;3(4): 281–284.
Hsu GL, Wen HS, Hsieh CH, Liu LJ, Chen YC. Traumatic glans deformity: reconstruction of distal ligamentous structure. The Journal of Urology. 2001;166(4): 1390. https://doi.org/10.1016/s0022-5347(05)65781-3.
Christensen GC. Angioarchitecture of the canine penis and the process of erection. American Journal of Anatomy. 1954;95(2): 227–261. https://doi.org/10.1002/aja.1000950204.
Iacono F (A), Barra S (A), De Rosa G (B), Boscaino A (B), Lotti T (A). Microstructural Disorders ofTunica albuginea in PatientsAffected by Impotence. European Urology. 1994;26(3): 233–239. https://doi.org/10.1159/000475386.
Conti G. L’érection du pénis humain et ses bases morphologico-vasculaires. Acta Anatomica. 1952;14(3): 217–262. https://doi.org/10.1159/000140711.
Hsu G, Hsieh C, Wen H, Hsu W, Wu C, Fong T, et al. Anatomy of the Human Penis: The Relationship of the Architecture Between Skeletal and Smooth Muscles. Journal of Andrology. 2004;25(3): 426–431. https://doi.org/10.1002/j.1939-4640.2004.tb02810.x.
Hsu G, Lin C, Hsieh C, Hsieh J, Chen S, Kuo T, et al. Distal Ligament in Human Glans: A Comparative Study of Penile Architecture. Journal of Andrology. 2005;26(5): 624–628. https://doi.org/10.2164/jandrol.04145.
Bassingthwaighte JB, Liebovitch LS, West BJ. Fractal Physiology. Springer; 2013.
Glass L, Mackey MC. From Clocks to Chaos: The Rhythms of Life. Princeton University Press; 1988.
Peng CK, Hausdorff JM, Goldberger AL. Nonlinear Dynamics, Self-Organization, and Biomedicine, edited by J. Walleczek. Cambridge University Press, Cambridge; 1999.
Erdoğru T, Savaş M, Yılmaz N, Baykara M. Are normal hemodynamic responses invariably associated with normal penile rigidity and potency? International Journal of Impotence Research. 2001;13(1): 10–13. https://doi.org/10.1038/sj.ijir.3900634.
Goldbeter A. Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour. Cambridge: Cambridge University Press; 1996. https://doi.org/10.1017/CBO9780511608193. [Accessed 6th January 2024].
Abel D. The Capabilities of Chaos and Complexity. International Journal of Molecular Sciences. 2009;10(1): 247–291. https://doi.org/10.3390/ijms10010247.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Revista Mexicana de Urología
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.