Sierpinski triangle
Overview
Fractal
A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity...
and attractive fixed set named after the Polish
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
Wacław Sierpiński who described it in 1915. However, similar patterns appear already in the 13th-century Cosmati
Cosmati
The Cosmati were a Roman family, seven members of which, for four generations, were skilful architects, sculptors and workers in decorative geometric mosaic, mostly for church floors...
mosaic
Mosaic
Mosaic is the art of creating images with an assemblage of small pieces of colored glass, stone, or other materials. It may be a technique of decorative art, an aspect of interior decoration, or of cultural and spiritual significance as in a cathedral...
s in the cathedral of Anagni
Anagni
Anagni is an ancient town and comune in Latium, central Italy, in the hills east-southeast of Rome. It is a historical center in Ciociaria.-Geography:...
, Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
. and other places, such as in the nave of the roman Basilica of Santa Maria in Cosmedin
Santa Maria in Cosmedin
The Basilica of Saint Mary in Cosmedin is a minor basilica church in Rome, Italy. It is located in the rione of Ripa.- History :The church was built in the 8th century during the Byzantine Papacy over the remains of the Templum Herculis Pompeiani in the Forum Boarium and of the Statio annonae, one...
.
Originally constructed as a curve, this is one of the basic examples of self-similar
Self-similarity
In mathematics, a self-similar object is exactly or approximately similar to a part of itself . Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales...
sets, i.e.
