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Pengguna:Dedhert.Jr/Uji halaman 01/17

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Revisi sejak 28 April 2022 14.49 oleh Dedhert.Jr (bicara | kontrib) (←Membuat halaman berisi 'jmpl|338x338px|Pola alami terbentuk saat angin menghembuskan pasir di bukit [[Gurun Namib. bukit berbentuk bulan sabit dan riak pada permukaannya terulang kembali apabila kondisinya cocok.]] jmpl|225x225px|Pola [[bunglon terselubung, ''Chamaeleo calyptratus'', sebagai kamuflase sekaligus sebagai isyarat suasana hati dan untu...')
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Pola alami terbentuk saat angin menghembuskan pasir di bukit Gurun Namib. bukit berbentuk bulan sabit dan riak pada permukaannya terulang kembali apabila kondisinya cocok.
Pola bunglon terselubung, Chamaeleo calyptratus, sebagai kamuflase sekaligus sebagai isyarat suasana hati dan untuk berkembang biak.

Pola di alam adalah keteraturan bentuk yang terlihat di dunia yang alami. Pola ini berulang dalam konteks yang berbeda dan kadang-kadang dapat dimodelkan secara matematis. Pola alami meliputi simetri, pohon, spiral, berkelok-kelok, gelombang, busa, teselasi,celah dan garis-garis.[1] Para filsuf Yunani awal seperti Plato, Pythagoras dan Empedokles telah mempelajari pola dan berusaha untuk menjelaskan ketertiban yang ada di alam ini. Pemahaman modern tentang pola yang terlihat berkembang secara bertahap dari waktu ke waktu.

Pada abad ke-19, fisikawan Belgia Joseph Plateau menguji film sabun yang menuntunnya merumuskan konsep permukaan minimal. Ahli biologi dan seniman Jerman Ernst Haeckel melukis ratusan organisme laut untuk menunjukkan soal simetri mereka. Ahli biologi Skotlandia D'Arcy Thompson memelopori studi pola pertumbuhan pada tumbuhan dan hewan yang menunjukkan bahwa persamaan sederhana dapat menjelaskan pertumbuhan spiral. Pada abad ke-20, ahli matematika Inggris Alan Turing meramalkan mekanisme morfogenesis yang menimbulkan pola bintik-bintik dan garis-garis. Ahli biologi Hongaria Aristid Lindenmayer dan ahli matematika Amerika-Prancis Benoît Mandelbrot menunjukkan bagaimana matematika fraktal dapat menciptakan pola pertumbuhan tanaman.

Matematika, fisika dan kimia dapat menjelaskan pola di alam pada level yang berbeda. Pola dalam makhluk hidup dijelaskan oleh proses biologi dari seleksi alam dan seleksi seksual. Studi formasi pola memanfaatkan model komputer untuk mensimulasikan berbagai pola.

Asal-muasal

 
Fibonacci number patterns occur widely in plant structures, including this cone of queen sago, Cycas circinalis

Early Greek philosophers attempted to explain order in nature, anticipating modern concepts. Pythagoras (c. 570–c. 495 BC) explained patterns in nature like the harmonies of music as arising from number, which he took to be the basic constituent of existence.[a] Empedocles (c. 494–c. 434 BC) to an extent anticipated Darwin's evolutionary explanation for the structures of organisms.[b] Plato (c. 427–c. 347 BC) argued for the existence of natural universals. He considered these to consist of ideal forms (εἶδος eidos: "form") of which physical objects are never more than imperfect copies. Thus, a flower may be roughly circular, but it is never a perfect circle.[2] Theophrastus (c. 372–c. 287 BC) noted that plants "that have flat leaves have them in a regular series"; Pliny the Elder (23–79 AD) noted their patterned circular arrangement.[3] Centuries later, Leonardo da Vinci (1452–1519) noted the spiral arrangement of leaf patterns, that tree trunks gain successive rings as they age, and proposed a rule purportedly satisfied by the cross-sectional areas of tree-branches.[4][3]

In 1202, Leonardo Fibonacci introduced the Fibonacci sequence to the western world with his book Liber Abaci.[5] Fibonacci presented a thought experiment on the growth of an idealized rabbit population.[6] Johannes Kepler (1571–1630) pointed out the presence of the Fibonacci sequence in nature, using it to explain the pentagonal form of some flowers.[3] In 1658, the English physician and philosopher Sir Thomas Browne discussed "how Nature Geometrizeth" in The Garden of Cyrus, citing Pythagorean numerology involving the number 5, and the Platonic form of the quincunx pattern. The discourse's central chapter features examples and observations of the quincunx in botany.[7] In 1754, Charles Bonnet observed that the spiral phyllotaxis of plants were frequently expressed in both clockwise and counter-clockwise golden ratio series.[3] Mathematical observations of phyllotaxis followed with Karl Friedrich Schimper and his friend Alexander Braun's 1830 and 1830 work, respectively; Auguste Bravais and his brother Louis connected phyllotaxis ratios to the Fibonacci sequence in 1837, also noting its appearance in pinecones and pineapples.[3] In his 1854 book, German psychologist Adolf Zeising explored the golden ratio expressed in the arrangement of plant parts, the skeletons of animals and the branching patterns of their veins and nerves, as well as in crystals.[8][9][10]

 
Beijing's National Aquatics Center for the 2008 Olympic games has a Weaire–Phelan structure.

In the 19th century, the Belgian physicist Joseph Plateau (1801–1883) formulated the mathematical problem of the existence of a minimal surface with a given boundary, which is now named after him. He studied soap films intensively, formulating Plateau's laws which describe the structures formed by films in foams.[11] Lord Kelvin identified the problem of the most efficient way to pack cells of equal volume as a foam in 1887; his solution uses just one solid, the bitruncated cubic honeycomb with very slightly curved faces to meet Plateau's laws. No better solution was found until 1993 when Denis Weaire and Robert Phelan proposed the Weaire–Phelan structure; the Beijing National Aquatics Center adapted the structure for their outer wall in the 2008 Summer Olympics.[12] Ernst Haeckel (1834–1919) painted beautiful illustrations of marine organisms, in particular Radiolaria, emphasising their symmetry to support his faux-Darwinian theories of evolution.[13] The American photographer Wilson Bentley took the first micrograph of a snowflake in 1885.[14]

 
D'Arcy Thompson pioneered the study of growth and form in his 1917 book.

In the 20th century, A. H. Church studied the patterns of phyllotaxis in his 1904 book.[15] In 1917, D'Arcy Wentworth Thompson published On Growth and Form; his description of phyllotaxis and the Fibonacci sequence, the mathematical relationships in the spiral growth patterns of plants showed that simple equations could describe the spiral growth patterns of animal horns and mollusc shells.[16] In 1952, Alan Turing (1912–1954), better known for his work on computing and codebreaking, wrote The Chemical Basis of Morphogenesis, an analysis of the mechanisms that would be needed to create patterns in living organisms, in the process called morphogenesis.[17] He predicted oscillating chemical reactions, in particular the Belousov–Zhabotinsky reaction. These activator-inhibitor mechanisms can, Turing suggested, generate patterns (dubbed "Turing patterns") of stripes and spots in animals, and contribute to the spiral patterns seen in plant phyllotaxis.[18] In 1968, the Hungarian theoretical biologist Aristid Lindenmayer (1925–1989) developed the L-system, a formal grammar which can be used to model plant growth patterns in the style of fractals.[19] L-systems have an alphabet of symbols that can be combined using production rules to build larger strings of symbols, and a mechanism for translating the generated strings into geometric structures. In 1975, after centuries of slow development of the mathematics of patterns by Gottfried Leibniz, Georg Cantor, Helge von Koch, Wacław Sierpiński and others, Benoît Mandelbrot wrote a famous paper, How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension, crystallising mathematical thought into the concept of the fractal.[20]

Jenis pola

Gelombang dan bukit pasir

Waves are disturbances that carry energy as they move. Mechanical waves propagate through a medium – air or water, making it oscillate as they pass by.[21] Wind waves are sea surface waves that create the characteristic chaotic pattern of any large body of water, though their statistical behaviour can be predicted with wind wave models.[22] As waves in water or wind pass over sand, they create patterns of ripples. When winds blow over large bodies of sand, they create dunes, sometimes in extensive dune fields as in the Taklamakan desert. Dunes may form a range of patterns including crescents, very long straight lines, stars, domes, parabolas, and longitudinal or seif ('sword') shapes.[23]

Barchans or crescent dunes are produced by wind acting on desert sand; the two horns of the crescent and the slip face point downwind. Sand blows over the upwind face, which stands at about 15 degrees from the horizontal, and falls onto the slip face, where it accumulates up to the angle of repose of the sand, which is about 35 degrees. When the slip face exceeds the angle of repose, the sand avalanches, which is a nonlinear behaviour: the addition of many small amounts of sand causes nothing much to happen, but then the addition of a further small amount suddenly causes a large amount to avalanche.[24] Apart from this nonlinearity, barchans behave rather like solitary waves.[25]

  •  
    Gelombang pecah di belakang kapal
  •  
    Bukit pasir di gurun Taklamakan, dari luar angkasa
  •  
    Barchan gundukan pasir berbentuk bulan sabit

Referensi

Catatan kaki

  1. ^ The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things. Aristotle, Metaphysics 1–5 , c. 350 BC
  2. ^ Aristotle reports Empedocles arguing that, "[w]herever, then, everything turned out as it would have if it were happening for a purpose, there the creatures survived, being accidentally compounded in a suitable way; but where this did not happen, the creatures perished." The Physics, B8, 198b29 in Kirk, et al., 304).

Kutipan

  1. ^ Stevens 1974, hlm. 3.
  2. ^ Balaguer, Mark (7 April 2009) [2004]. "Platonism in Metaphysics". Stanford Encyclopedia of Philosophy. Diakses tanggal 4 May 2012. 
  3. ^ a b c d e Livio, Mario (2003) [2002]. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number (edisi ke-First trade paperback). New York: Broadway Books. hlm. 110. ISBN 978-0-7679-0816-0. 
  4. ^ Da Vinci, Leonardo (1971). Taylor, Pamela, ed. The Notebooks of Leonardo da Vinci. New American Library. hlm. 121. 
  5. ^ Singh, Parmanand. Acharya Hemachandra and the (so called) Fibonacci Numbers. Math. Ed. Siwan, 20(1):28–30, 1986. ISSN 0047-6269
  6. ^ Knott, Ron. "Fibonacci's Rabbits". University of Surrey Faculty of Engineering and Physical Sciences. 
  7. ^ Browne, Thomas (1658). How Nature Geometrizeth. The Garden of Cyrus. 
  8. ^ Padovan, Richard (1999). Proportion: Science, Philosophy, Architecture. Taylor & Francis. hlm. 305–306. ISBN 978-0-419-22780-9. 
  9. ^ Padovan, Richard (2002). "Proportion: Science, Philosophy, Architecture". Nexus Network Journal. 4 (1): 113–122. doi:10.1007/s00004-001-0008-7  . 
  10. ^ Zeising, Adolf (1854). Neue Lehre van den Proportionen des meschlischen Körpers. preface. 
  11. ^ Stewart 2001, hlm. 108–109.
  12. ^ Ball 2009a, hlm. 73–76.
  13. ^ Ball 2009a, hlm. 41.
  14. ^ Hannavy, John (2007). Encyclopedia of Nineteenth-Century Photography. 1. CRC Press. hlm. 149. ISBN 978-0-415-97235-2. 
  15. ^ Livio, Mario (2003) [2002]. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway Books. hlm. 111. ISBN 978-0-7679-0816-0. 
  16. ^ About D'Arcy. D' Arcy 150. University of Dundee and the University of St Andrews. Retrieved 16 October 2012.
  17. ^ Turing, A. M. (1952). "The Chemical Basis of Morphogenesis". Philosophical Transactions of the Royal Society B. 237 (641): 37–72. Bibcode:1952RSPTB.237...37T. doi:10.1098/rstb.1952.0012  . 
  18. ^ Ball 2009a, hlm. 163, 247–250.
  19. ^ Rozenberg, Grzegorz; Salomaa, Arto. The Mathematical Theory of L Systems. Academic Press, New York, 1980. ISBN 0-12-597140-0
  20. ^ Kesalahan pengutipan: Tag <ref> tidak sah; tidak ditemukan teks untuk ref bernama Mandelbrot
  21. ^ French, A.P. (1971). Vibrations and Waves. Nelson Thornes. 
  22. ^ Tolman, H.L. (2008). "Practical wind wave modeling" (PDF). Dalam Mahmood, M.F. CBMS Conference Proceedings on Water Waves: Theory and Experiment. Howard University, USA, 13–18 May 2008. World Scientific Publ. 
  23. ^ "Types of Dunes". USGS. 29 October 1997. Diakses tanggal May 2, 2012. 
  24. ^ Strahler, A.; Archibold, O.W. (2008). Physical Geography: Science and Systems of the Human Environment (edisi ke-4th). John Wiley. hlm. 442. 
  25. ^ Schwämmle, V.; Herrman, H.J. (11 December 2003). "Solitary wave behaviour of sand dunes". Nature. 426 (6967): 619–620. Bibcode:2003Natur.426..619S. doi:10.1038/426619a. PMID 14668849. 

Bibliografi

Pioneering authors

 
Wikisource Latin memiliki teks asli yang berkaitan dengan artikel ini:

General books

Patterns from nature (as art)

  • Edmaier, Bernard. Patterns of the Earth. Phaidon Press, 2007.
  • Macnab, Maggie. Design by Nature: Using Universal Forms and Principles in Design. New Riders, 2012.
  • Nakamura, Shigeki. Pattern Sourcebook: 250 Patterns Inspired by Nature.. Books 1 and 2. Rockport, 2009.
  • O'Neill, Polly. Surfaces and Textures: A Visual Sourcebook. Black, 2008.
  • Porter, Eliot, and Gleick, James. Nature's Chaos. Viking Penguin, 1990.
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