2023, Number 6
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Rev Mex Urol 2023; 83 (6)
Fractal penis and golden penis. The hidden dimensions of penile tissue
Uribe AJF
Language: Spanish
References: 48
Page: 1-16
PDF size: 609.88 Kb.
ABSTRACT
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 ofMathematics. John Wiley & Sons; 2011.
Finch SR. Mathematical Constants. CambridgeUniversity Press; 2003.
Dixon RA. Mathographics. England: DoverPublications; 1991.
Uribe Arcila JF. El pene áureo. La razón áureay su relación con la anatomía interna del pene.Revista Urología Colombiana. 2008;17(1): 91–99.
Kurakin A. The self-organizing fractal theory asa universal discovery method: the phenomenonof 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 DiBiologia. 2009;102(1): 29–59.
Mandelbrot B. The Fractal Geometry of Nature.New York: WH Freeman; 1982.
Goldberger AL, Amaral LAN, HausdorffJM, Ivanov PC, Peng CK, Stanley HE. Fractaldynamics in physiology: alterations with diseaseand aging. Proceedings of the National Academyof 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. Academicpress; 2014.
Falconer K. Fractal geometry: mathematicalfoundations and applications. John Wiley & Sons;2004.
Peitgen HO, Saupe D. The science of fractalimages. Springer-Verlag; 1988.
Falconer KJ, Falconer KJ. Techniques in fractalgeometry. Wiley Chichester; 1997.
Gallo CBM, Costa WS, Furriel A, Bastos AL,Sampaio FJB. Development of the Penis duringthe Human Fetal Period (13 to 36 Weeks afterConception). 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 TensileStrength of Tunica Albuginea of the CorporaCavernosa. 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, Areaand Dimension: Measuring Complexity andScaling Properties. In: Peitgen HO, Jürgens H,Saupe D (eds.) Chaos and Fractals: New Frontiersof 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 inMedicine. WORLD SCIENTIFIC; 1990. https://doi.org/10.1142/1025.
Goldberger AL, West BJ. Fractals in physiologyand medicine. The Yale Journal of Biology andMedicine. 1987;60(5): 421–435.
Glenny RW, Robertson HT, Yamashiro S,Bassingthwaighte JB. Applications of fractalanalysis to physiology. Journal of AppliedPhysiology. 1991;70(6): 2351–2367. https://doi.org/10.1152/jappl.1991.70.6.2351.
Mandelbrot BB. Los objetos fractales: forma, azary dimensión.. 7a. ed. Barcelona: Tusquets; 2009.
Bossard JA, Lin L, Werner DH. Evolvingrandom fractal Cantor superlattices for theinfrared using a genetic algorithm. Journal of TheRoyal Society Interface. 2016;13(114): 20150975.https://doi.org/10.1098/rsif.2015.0975.
Grebogi C, Ott E, Yorke JA. Chaos, StrangeAttractors, and Fractal Basin Boundaries inNonlinear Dynamics. Science. 1987;238(4827):632–638. https://doi.org/10.1126/science.238.4827.632.
Garfinkel A, Spano ML, Ditto WL, WeissJN. Controlling Cardiac Chaos. Science.1992;257(5074): 1230–1235. https://doi.org/10.1126/science.1519060.
Goldberger AL. Non-linear dynamicsfor clinicians: chaos theory, fractals, andcomplexity at the bedside. The Lancet. 1996May;347(9011):1312–4. doi: https://doi.org/10.1016/s0140-6736(96)90948-4
Rodríguez J, Prieto S, Ortiz L, Correa C, ÁlvarezT L, Bernal P, et al. Variabilidad de la dimensiónfractal de la ramificación coronaria izquierda enausencia y presencia de enfermedad arterialoclusiva moderada y severa. Revista Colombianade Cardiología. 2007 Jul;14(3):173–80.
Canals M, Olivares R, Labra F, Caputo L, RiveraA, Novoa FF. Caracterizacion de la geometriafractal 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 ofpenile erection: tissue designs for increasingand maintaining stiffness. Integrative andComparative Biology. 2002;42(2): 216–221.https://doi.org/10.1093/icb/42.2.216.
Hsu GL, Brock G, Martínez-Piñeiro L, VonHeyden B, Lue TF, Tanagho EA. Anatomy andStrength of the Tunica Albuginea: Its Relevanceto Penile Prosthesis Extrusion. Journal ofUrology. 1994;151(5): 1205–1208. https://doi.org/10.1016/s0022-5347(17)35214-x.
Goldstein AMB, Padma-Nathan H. TheMicroarchitecture of the IntracavernosalSmooth Muscle and the Cavernosal FibrousSkeleton. 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 clinicalapplications. 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 andpathophysiology. In: Campbell`s Urology. 8th ed.Panamericana; p. 718–749.
Varela FG, Maturana HR, Uribe R. Autopoiesis:the organization of living systems, itscharacterization and a model. Currents inModern Biology. 1974;5(4): 187–196. https://doi.org/10.1016/0303-2647(74)90031-8.
Dorr L, Brody M. Hemodynamic mechanismsof erection in the canine penis. American Journalof 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 thepenis: 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 ofaging on penile ultrastructure. Asian Journal ofAndrology. 2001;3(4): 281–284.
Hsu GL, Wen HS, Hsieh CH, Liu LJ, ChenYC. Traumatic glans deformity: reconstructionof distal ligamentous structure. The Journalof Urology. 2001;166(4): 1390. https://doi.org/10.1016/s0022-5347(05)65781-3.
Christensen GC. Angioarchitecture of thecanine 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). MicrostructuralDisorders ofTunica albuginea in PatientsAffectedby Impotence. European Urology. 1994;26(3):233–239. https://doi.org/10.1159/000475386.
Conti G. L’érection du pénis humain etses bases morphologico-vasculaires. ActaAnatomica. 1952;14(3): 217–262. https://doi.org/10.1159/000140711.
Hsu G, Hsieh C, Wen H, Hsu W, Wu C, FongT, et al. Anatomy of the Human Penis: TheRelationship of the Architecture BetweenSkeletal and Smooth Muscles. Journal ofAndrology. 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, KuoT, et al. Distal Ligament in Human Glans: AComparative 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: TheRhythms of Life. Princeton University Press;1988.
Peng CK, Hausdorff JM, Goldberger AL.Nonlinear Dynamics, Self-Organization, andBiomedicine, edited by J. Walleczek. CambridgeUniversity Press, Cambridge; 1999.
Erdoru T, Sava M, Yılmaz N, Baykara M.Are normal hemodynamic responses invariablyassociated with normal penile rigidity andpotency? International Journal of ImpotenceResearch. 2001;13(1): 10–13. https://doi.org/10.1038/sj.ijir.3900634.
Goldbeter A. Biochemical Oscillations andCellular Rhythms: The Molecular Bases ofPeriodic and Chaotic Behaviour. Cambridge:Cambridge University Press; 1996. https://doi.org/10.1017/CBO9780511608193. [Accessed6th January 2024].
Abel D. The Capabilities of Chaos andComplexity. International Journal ofMolecular Sciences. 2009;10(1): 247–291.https://doi.org/10.3390/ijms10010247.