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Sympathetic magic, also known as imitative magic, is a type of magic based on imitation or correspondence.
Similarity and contagion 
It has been said that the theory of sympathetic magic was first developed by Sir James George Frazer in The Golden Bough (1889); Richard Andree, however, anticipates Frazer, writing of 'Sympathie-Zauber' in his 1878 Ethnographische Parallelen und Vergleiche. Frazer further subcategorised sympathetic magic into two varieties: that relying on similarity, and that relying on contact or 'contagion':
If we analyze the principles of thought on which magic is based, they will probably be found to resolve themselves into two: first, that like produces like, or that an effect resembles its cause; and, second, that things which have once been in contact with each other continue to act on each other at a distance after the physical contact has been severed. The former principle may be called the Law of Similarity, the latter the Law of Contact or Contagion. From the first of these principles, namely the Law of Similarity, the magician infers that he can produce any effect he desires merely by imitating it: from the second he infers that whatever he does to a material object will affect equally the person with whom the object was once in contact, whether it formed part of his body or not.
Imitation in sympathetic magic 
Correspondence in sympathetic magic 
Correspondence is based on the idea that one can influence something based on its relationship or resemblance to another thing. Many popular beliefs regarding properties of plants, fruits and vegetables have evolved in the folk-medicine of different societies owing to sympathetic magic. This include beliefs that certain herbs with yellow sap can cure jaundice, that walnuts could strengthen the brain because of the nuts' resemblance to brain, that red beet-juice is good for the blood, that phallic-shaped roots will cure male impotence, etc.
Many traditional societies believed that an effect on one object can cause an analogous effect on another object, without an apparent causal link between the two objects. For instance, many folktales feature a villain whose "life" exists in another object, and who can only be killed if that other object is destroyed. (Examples including Sauron's One Ring in The Lord of the Rings trilogy, and the Russian folktale of Koschei the Deathless. Compare Horcrux and lich.) Mircea Eliade wrote that in Uganda, a barren woman is thought to cause a barren garden, and her husband can seek a divorce on purely economic grounds.
Hypotheses about prehistoric sympathetic magic 
The term is most commonly used in archaeology in relation to Paleolithic cave paintings such as those in North Africa and at Lascaux in France. The theory is one of prehistoric human behavior, and is based on studies of more modern hunter-gatherer societies. The idea is that the paintings were made by Cro-Magnon shamans. The shamans would retreat into the darkness of the caves, enter into a trance state and then paint images of their visions, perhaps with some notion of drawing power out of the cave walls themselves. This goes some way towards explaining the remoteness of some of the paintings (which often occur in deep or small caves) and the variety of subject matter (from prey animals to predators and human hand-prints). In his book Primitive Mythology, Joseph Campbell stated that the paintings "...were associated with the magic of the hunt." For him, this sympathetic magic was akin to a participation mystique, where the paintings, drawn in a sanctuary of "timeless principle", were acted upon by rite.
In 1933, Leo Frobenius, discussing cave paintings in North Africa, pointed out that many of the paintings did not seem to be mere depictions of animals and people. To him, it seemed as if they were acting out a hunt before it began, perhaps as a consecration of the animal to be killed. In this way, the pictures served to secure a successful hunt. While others interpreted the cave images as depictions of hunting accidents or of ceremonies, Frobenius believed it was much more likely that "...what was undertaken [in the paintings] was a consecration of the animal effected not through any real confrontation of man and beast but by a depiction of a concept of the mind."
However, as with all prehistory, it is impossible to be certain due to the relative lack of material evidence and the many pitfalls associated with trying to understand the prehistoric mindset with a modern mind.
Popular culture 
Several studies have found that even today humans maintain a belief that "certain properties are contagious, either in a good or a bad way", in a manner similar to sympathetic magic, such that even a replica of a celebrity's guitar may become a fetish.
- "3: Sympathetic Magic", The Golden Bough, Bartleby, 1922 Unknown parameter
- Harrison, Regina (1989). Signs, songs, and memory in the Andes: translating Quechua language and culture. University of Texas Press. p. 178. ISBN 978-0-292-77627-2.
- Eliade, Mircea (1976). In Beane, Wendell C; Doty, William G. Myths, Rites, Symbols: A Mircea Eliade Reader. New York: Harper & Row. p. 385. ISBN 978-0-06-090510-1. OCLC 2136392.
- Tierney, John (March 8, 2011). "Urge to Own That Clapton Guitar Is Contagious, Scientists Find". The New York Times. Retrieved March 9, 2011.
- Campbell, Joseph (1991). Penguin Books. ISBN 978-0-14-019443-2. OCLC 470180186. Unknown parameter
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- Frobenius, Leo (1993) . Kulturgeschichte Afrikas. Prolegomena zu einer historischen Gestaltlehre [A Cultural History of Africa] (in German). Wuppertal: Hammer. pp. 131–32. ISBN 978-3-87294-525-9. OCLC 311991077. (reprint of the 1954 Phaidon-Verlag edition)