Overlapping circles grid

Of special interest is the hexafoil or six-petal rosette derived from the "seven overlapping circles" pattern, also known as "Sun of the Alps" from its frequent use in alpine folk art in the 17th and 18th century.

Overlapping circles with similar geometrical constructions have been used infrequently in various of the decorative arts since ancient times.

The pattern has found a wide range of usage in popular culture, in fashion, jewelry, tattoos and decorative products.

The oldest known occurrence of the "overlapping circles" pattern is dated to the 7th or 6th century BCE, found on the threshold of the palace of Assyrian king Aššur-bāni-apli in Dur Šarrukin (now in the Louvre).

[8] Patterns of seven overlapping circles are found on Roman mosaics, for example at Herod's palace in the 1st century BC.

[13][14] The pattern and modern name have propagated into wide range of usage in popular culture, in fashion, jewelry, tattoos, and decorative products.

Teaser posters illustrating the cover art to A Head Full of Dreams were widely displayed on the London Underground in the last week of October 2015.

[17] The "Sun of the Alps" (Italian Sole delle Alpi) symbol has been used as the emblem of Padanian nationalism in northern Italy since the 1990s.

In the examples below, the pattern does not have a hexagonal outline: Martha Bartfeld, author of geometric art tutorial books, described her independent discovery of the design in 1968.

Her original definition said, "This design consists of circles having a 1-[inch; 25 mm] radius, with each point of intersection serving as a new center.

These overlapping circles can also be seen as a projection of an n-unit cube of spheres in 3-dimensional space, viewed on the diagonal axis.

Another triangular lattice form is common, with circle separation as the square root of 3 times their radius.

It is called a Kawung motif in Indonesian batik, and is found on the walls of the 8th century Hindu temple Prambanan in Java.