Patterns are frequently used in art, since their structure is very appealing to the eye. They appear widely in nature, inspiring their use in cities and architecture, patterns in paper and others. Pattern art uses a combination of elements or shapes repeated in a recurring and regular arrangement, in an aesthetically pleasing way.
Patterns can be employed in art on many materials – these are some examples of pattern being used on tiling and wallpaper:
Some of the more famous patterns artists include William Morris (whose patterns are famously used as designs for materials such as wallpaper, tiles and textiles)…
… or larger-than-life patterns on walls, as per Damien Hurst…
…and of course pattern can be used on the more traditional medium of canvas, as per Gustav Klimt:
Patterns have been used in art in all parts of the world through different time periods, including Islamic, Egyptian, Moorish & African art, similarly used patterns as art on a variety of materials / objects:
Pattern in art can also involve a variety of techniques, most often using stencilling and linocuts, to make the repetition much easier:
Pattern in art also employs a variety of techniques that can “trick” the brain:
- Patterns can create optical illusions to make things seem 3D: Optical illusions such as the Fraser spiral strikingly demonstrate limitations in human visual perception – the black and white ropes that appear to form spirals are in fact concentric circles:
- Colour optical illusions: watch this brilliant TED talk with Beau Lotto explaining how context is everything for our eyes (so explaining “the dress” phenomenon!).
- I also love the Droste effect, where pictures appear as pictures within themselves, on and on forever (or as long as the resolution of the picture will allow at least!). The appearance is recursive: the smaller version contains an even smaller version of the picture, etc. Examples below include the cover of Pink Floyd’s 1969 album Ummagumma (top right):
- MC Escher is the master of mathematical optical illusions in art. He was a Dutch graphic artist who made mathematically inspired art. Early in his career, he drew inspiration from nature, making studies of insects, landscapes, and plants such as lichens, all of which he used as details in his artworks. He travelled in Italy and Spain, sketching buildings, townscapes, architecture and the tilings of the Alhambra and the Mezquita of Cordoba, and became steadily more interested in their mathematical structure. Although Escher did not have mathematical training—his understanding of mathematics was largely visual and intuitive—several of the worlds which he drew were built around “impossible” objects (e.g. the impossible stairs below, which ascend back on themselves) and other single-surface objects based on the mathematical Möbius strip:
- Maths can also be used directly to create artistic patterns: in the below the first is made from the formula (cos (t)+cos (5t)/2+sin (125t)/3, sin (t)+sin (5t)/2+cos (125t)/3), the second from cos (t)+cos (7t)/2+sin (343t)/3, sin (t)+sin (7t)/2+cos (343t)/3) and the third (cos (t)+ cos (29t)/2+ sin (61t)/3, sin (t)+ sin (29t)/2+ cos (61t)/3): (If you liked these, you could also try Frank A. Farris’ Creating Symmetry: The Artful Mathematics of Wallpaper Patterns, a maths book that also makes an outstanding coffee-table book)
- Data and numbers can literally be made into art too, e.g. the Forest of Numbers (FlowingData) and the Art of Pi:
Overall, I’d say maths & art can be hugely complementary 🙂
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