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| {{Infobox Artwork
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| | image_file=The_Swallowtail.jpg
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| | backcolor=#FBF5DF
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| | painting_alignment=right
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| | image_size=300px
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| | title=The Swallow's Tail — Series on Catastrophes
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| | artist=[[Salvador Dalí]]
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| | year=1983
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| | type=[[Oil painting|Oil on canvas]]
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| | height_metric=73
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| | width_metric=92.2
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| | height_imperial=28.7
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| | width_imperial=36.3
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| | metric_unit=cm
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| | imperial_unit=in
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| | city=[[Figueres]]
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| | museum=[[Dalí Theatre and Museum]]
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| }}
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| '''''The Swallow's Tail — Series on Catastrophes''''' ({{lang-fr|La queue d'aronde — Série des catastrophes}}) was [[Salvador Dalí]]'s last painting. It was completed in May 1983, as the final part of a series based on [[René Thom]]'s [[catastrophe theory]].
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| Thom suggested that in four-dimensional phenomena, there are seven possible equilibrium surfaces, and therefore seven possible discontinuities, or "elementary catastrophes": [[Catastrophe theory#Fold catastrophe|fold]], [[Catastrophe theory#Cusp catastrophe|cusp]], [[Catastrophe theory#Swallowtail catastrophe|swallowtail]], [[Catastrophe theory#Butterfly catastrophe|butterfly]], [[Catastrophe theory#Hyperbolic umbilic catastrophe|hyperbolic umbilic]], [[Catastrophe theory#Elliptic umbilic catastrophe|elliptic umbilic]], and [[Catastrophe theory#Parabolic umbilic catastrophe|parabolic umbilic]].<ref>Thom, René, ''Structural stability and morphogenesis. an outline of a general theory of models'', (D.H.Fowler, trans.) (Reading, Mass. London. Benjamin. 1975). Originally published in French as ''Stabilité structurelle et morphogénèse'', 1972.</ref> "The shape of Dalí’s Swallow’s Tail is taken directly from Thom’s four-dimensional graph of the same title, combined with a second catastrophe graph, the s-curve that Thom dubbed, "the cusp". Thom’s model is presented alongside the elegant curves of a [[cello]] and the instrument’s f-holes, which, especially as they lack the small pointed side-cuts of a traditional f-hole, equally connote the mathematical symbol for an integral in [[calculus]]: <math>\int_{}^{}</math> ."<ref>King, Elliott in Dawn Ades (ed.), ''Dalí'' (Milan: Bompiani Arte, 2004), 418-421.</ref>
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| In his 1979 speech, "Gala, Velázquez and the Golden Fleece", presented upon his 1979 induction into the prestigious Académie des Beaux-Arts of the Institut de France, [[Dalí]] described Thom’s theory of catastrophes as ‘the most beautiful aesthetic theory in the world’.<ref>Dalí, Salvador, ‘Gala, Velásquez and the Golden Fleece’ (9 May 1979). Reproduced in-part in Robert Descharnes, ''Dalí, the Work, the Man'' (New York: Harry N. Abrams, 1984) 420. Originally published in French as ''Dalí, l'oeuvre et l'homme'' (Lausanne: Edita, 1984).</ref> He also recollected his first and only meeting with René Thom, at which Thom purportedly told Dalí that he was studying tectonic plates; this provoked Dalí to question Thom about the railway station at [[Perpignan]], France, which the artist had declared in the 1960s as the centre of the universe. Thom reportedly replied, "I can assure you that Spain pivoted precisely — not in the area of — but exactly there where the Railway Station in [[Perpignan]] stands today". Dalí was immediately enraptured by Thom’s statement, influencing his painting ''Topological Abduction of Europe — Homage to René Thom'', the lower left corner of which features an equation closely linked to the ‘swallow’s tail’: <math>V = x^5 + ax^3 + bx^2 + cx,</math> an illustration of the graph, and the term ‘queue d'aronde’. The seismic fracture that transverses ''Topological Abduction of Europe'' reappears in ''The Swallow’s Tail'' at the precise point where the y-axis of the swallow’s tail graph intersects with the S-curve of the [[Cusp (singularity)|cusp]].<ref>King, E., 418-421.</ref>
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| ==References==
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| {{Reflist}}
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| {{Salvador Dalí}}
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| {{Use dmy dates|date=September 2010}}
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| {{DEFAULTSORT:Swallow's Tail, The}}
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| [[Category:Paintings by Salvador Dalí]]
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| [[Category:1983 paintings]]
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| [[Category:Mathematics and culture]]
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| [[Category:Singularity theory]]
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