A new kind of patterns in mathematics

Cellular automata constitute an alternative way of pattern generation. Cellular automata had been developed the first time by John von Neumann and Stanislav Ulam. Their idea at the end of the 1940’s was to create a virtual self-reproducing machine. Cellular automata (CA) consist of a grid of interrelated cells, which can result in very complex pattern formations. Bioinformaticians discovered that CA are good means for modelling and simulating biological pattern formations. The mathematician Stephen Wolfram remarked in his book "A New Kind of Science" that he did not find applications of CA in former cultural applications like developing ornaments (p42/p43). This fact is astonishing because CA based patterns do not need computers but also can generated on a chess board.

At least "a new kind of image"?
According to Stephen Wolfram there are no classical ornaments created by the simple rules of cellular automata.

patterns in biology

Cellular Automaton Modeling of Biological Pattern Formation (Andreas Deutsch/ Sabine Dormann)
Bacterial Linguistic Communication and Social Intelligence by Eshel Rephael Breslav Ben Jacob/ Tel Aviv
From Pattern Formation to Morphogenesis - Multicellular Coordination in Dictyostelium discoideum by Stan Marée/ Utrecht

bacterial motion pattern

strip weaving

Pure striped textiles have been very rare in history. Before striped clothes had been a sign for unnormal people like court jester or later prisoners. In Western Africa exists a tradition of weaving striped clothes with a different connotation (more...)

Africain Kente strip weaving

links for patterns in islamic arts & architecture

see also: oriental pixels
Peter Lu discovered a quasicrystalline geometry in Islamic architecture
Puzzle der Unendlichkeit -German article about infinite patterns refering to Lu's discovery
The topkapi scroll: geometry and ornament in Islamic architecture.

Decoration in Islamic architecture
Links to Middle Eastern ethnomathematics
Arab Gateway: art and architecture

Pdf-Essay: Computer Generated Islamic Star Patterns

Friday Mosque at Herat in Afghanistan

patterns in the arts

Ebtisam AbdulAziz, an artist from the Emirates, developed with "Ten Triangles" a subtle work that only can be decoded mathematically by the spectator.

Azra Akšamija's Kunstmoschee, Sezession Vienna

Ten Triangles, 2004

further links

pattern recognition information page

Essay: Discovering Patterns -The Interface Between Art and Science, Santa Fe Institute Bulletin Fall 1999 (1,6 Mb, pdf)

the topkapi scroll